WIND FEEDFORWARD CONTROL OF A USV. Huajin Qu. A Dissertation Submitted to the Faculty of. The College of Engineering and Computer Science

Transcription

1 WIND FEEDFORWARD CONTROL OF A USV by Huajin Qu A Dissertation Submitted to the Faculty of The College of Engineering and Computer Science In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Florida Atlantic University Boca Raton, Florida May 2016

2 Copyright 2016 by Huajin Qu ii

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4 ACKNOWLEDGMENTS I wish to express sincere thanks to my committee members for their guidance, expertise, and support throughout my dissertation work. Special thanks to my advisor Dr. Karl von Ellenrieder, for his invaluable advice and clear instructions. His capabilities as motivators and inventors cannot be over commended. I would like to express my gratitude to friends and colleagues at Seatech FAU, especially Ivan Bertaska that made the research presented in this document possible by the system platform and software framework. I have benefited greatly from continuous testing and research with Edoardo I. Sarda, based on which the dissertation conducted. And also thank you to all those who helped in the field tests: Ivan Bertaska, Edoardo Sarda, Jared Wampler, and Travis Moscicki. Without their help and support, it would impossible to conduct experiments. Finally, many any thanks to my whole family, my boyfriend, who are the most precious and I will always love you. iv

5 ABSTRACT Author: Title: Institution: Dissertation Advisor: Degree: Huajin Qu Wind Feedforward Control of a USV Florida Atlantic University Dr. Karl von Ellenrieder Doctor of Philosophy Year: 2016 In this research, a wind feedforward (FF) controller has been developed to augment closed loop feedback controllers for the position and heading station keeping control of Unmanned Surface Vehicles (USVs). The performance of the controllers was experimentally tested using a16 foot USV in an outdoor marine environment. The FF controller was combined with three nonlinear feedback controllers, a Proportional Derivative (PD) controller, a Backstepping (BS) controller, and a Sliding mode (SM) controller, to improve the station-keeping performance of the USV. To address the problem of wind model uncertainties, adaptive wind feedforward (AFF) control schemes are also applied to the FF controller, and implemented together with the BS and SM feedback controllers. The adaptive law is derived using Lyapunov Theory to ensure stability. On-water station keeping tests of each combination of FF and feedback controllers were conducted in the U.S. Intracoastal Waterway in Dania Beach, FL USA. Five runs of each test condition were performed; each run lasted at least 10 minutes. The experiments were conducted in Sea State 1 with an average wind speed of between 1 to 4 meters per second and significant wave heights of less than 0.2 meters. When the performance of the controllers is compared using the Integral of the Absolute Error (IAE) of position criterion, the experimental results indicate that the BS and SM feedback controllers significantly outperform the PD feedback controller (e.g. a 33% and a 44% decreases in the IAE, respectively). It is also found that FF is beneficial for all three feedback controllers and that AFF can further improve the station keeping performance. For example, a BS feedback control combined with AFF control reduces the IAE by 25% when compared with a BS feedback controller combined with a non- v

6 adaptive FF controller. Among the eight combinations of controllers tested, SM feedback control combined with AFF control gives the best station keeping performance with an average position and heading error of 0.32 meters and 4.76 degrees, respectively. vi

7 To my family.

8 WIND FEEDFORWARD CONTROL OF A USV LIST OF TABLES... x FIGURES...xi 1 INTRODUCTION Objectives Chapter Layout LITERATURE REVIEW Applications of USV Control Development Nonlinear Control Feedforward Control Wind Model and Parameter Estimation Adaptive Control Control Allocation and Stability Analysis Experimental Verification for Control Law The WAM-V USV Overview of the USV Propulsion System Guidance, Navigation, and Control system Anemometer METHODOLOGY Equations of Motion Coordinate Frames Nonlinear Dynamic Equations of Motion System Identification viii

9 4.2 Nonlinear Feedback Control Proportional Derivative (PD) Control Backstepping Control Sliding Mode Control Wind Feedforward Control Adaptive Control Design Adaptive Wind Feedforward with Backstepping Control Adaptive Wind Feedforward with Sliding Mode Control Control Allocation Extended Force Representation Lagrangian Multiplier Solution Simulation Tests EXPERIMENTAL RESULTS Drifting Tests Station Keeping Tests Feedback With/Without Wind Feedforward Control Robust Feedback with Adaptive Wind FF Station Keeping Experimental Results Summary CONCLUSIONS Research Significance Dissertation Achievements Future Work APPENDIXES Appendixes A. Model Reference Adaptive Control Appendixes B. Simulink Model... Error! Bookmark not defined. Appendixes C. SM & Adaptive Control Testing Results Appendixes D. Representative Software Appendixes E. Lyapunov Stability Theory viii

10 REFERENCES ix

11 TABLES Table 3.1 Principle characteristics of the WAM-V USV Table 3.2 Anemometer specifications Table 4.1 Notation used for marine vehicles Table 4.2 Relationship of motor command and thrust from bollard pull tests Table 4.3 Hydrodynamic coefficients for the WAM-V USV Table 5.1 Comparison of the six controllers tested for station keeping averaged across five runs Table 5.2 Station keeping control performances of BS&AFF and SM&AFF averaged across 5 runs Table 5.3 Comparison of the eight controllers with PD for station keeping averaged across 5 runs with unitized wind speed Table A.1 Summary of the basic theorem of Lyapunov x

12 FIGURES Figure 3.1 The WAM-V USV14 in the Intracoastal Waterway (ICW) Figure 3.2 WAM-V USV16 propulsion system Figure 3.3 Port and starboard thrust ranges directions. Both port and starboard can provide thrust at ±45 with respect to demihull centerlines Figure 4.1 Body-fixed ( and earth-fixed ( reference frames Figure 4.2 Top view of WAM-V USV16 with the 3 DOFs body-fixed coordinate system Figure 4.3 Frontal projected area Figure 4.4 Lateral projected area Figure 4.5 Representation of vehicle orientation and wind direction Figure 4.6 Quadratic fit of surge speed and drag in surge direction for USV16 model Figure 4.7 Surge speed of simulation and experimental results of 70% throttle command Figure 4.8 Surge speed of simulation and experimental results of 100% throttle command Figure 4.9 Surge speed of simulation and experimental results during circle tests Figure 4.10 Yaw speed of simulation and experimental results during circle tests Figure 4.11 Yaw rates of simulation and experimental results during zigzag tests with 100% throttle command Figure 4.12 Curve fit to get the slope of the acceleration curve with 70% throttle command Figure 4.13 PD station-keeping controller Figure 4.14 BS station-keeping controller Figure 4.15 Illustration of Saturation Function for a single saturation argument for SM Figure 4.16 SMstation-keeping controller Figure 4.17 Apparent wind speed collected from a stationary vehicle Figure 4.18 Apparent wind angle collected from a stationary vehicle Figure 4.19 Wind feedforward model xi

13 Figure 4.20 Block Diagram of WAM-V USV 16 Control System with Wind Feedforward Figure 4.21 Block Diagram of WAM-V USV 16 Control System with AFF Figure 4.22 Block diagram of control allocation in the USV control system Figure Control allocation using the extended thrust representation to convert from desired forces to an extended thrust representation [66] Figure Control allocation logic [66] Figure 4.25 Overall Control System of WAM-V USV Error! Bookmark not defined. Figure 4.26 Trajectory of Open Loop Control, Run Figure 4.27 Trajectory of Feedback Control, Run Figure 4.28 Zoomed Trajectory of Feedback Control, Run Figure 4.29 Trajectory of Feedback & Adaptive FF, Run Figure 4.30 Zoomed Trajectory of Feedback & Adaptive FF, Run Figure 4.31 Control Forces of Adaptive FF Run Figure 4.32 Trajectory of Open Loop Control, Run Figure 4.33 Trajectory of Feedback Control, Run Figure 4.34 Zoomed Trajectory of Feedback Control, Run Figure 4.35 Trajectory of Feedback & Adaptive FF, Run Figure 4.36 Zoomed Trajectory of Feedback & Adaptive FF, Run Figure 4.37 Control Forces of Adaptive FF Run Figure 4.38 Trajectory of Open Loop Control, Run Figure 4.39 Trajectory of Feedback Control, Run Figure 4.40 Zoomed Trajectory of Feedback Control, Run Figure 4.41 Trajectory of Feedback & Adaptive FF, Run Figure 4.42 Zoomed Trajectory of Feedback & Adaptive FF, Run Figure 4.43 Control Forces of Adaptive FF Run Figure 5.1 Testing Location Figure 5.2 USV trajectory and wind speed in drifting test, run Figure 5.3 Relationship between wind speed and vehicle drifting speed, run xii

14 Figure 5.4 Relationship of shifted time and correlation coefficient of wind speed and vehicle s drifting speed., Run Figure 5.5 USV trajectory and wind speed in drifting, run Figure 5.6 Relationship between wind speed and vehicle drifting speed, run Figure 5.7 Relationship of shifted time and correlation coefficient of wind speed and vehicle s drifting speed, run Figure 5.8 Relationship of shifted time and correlation coefficient of wind speed and vehicle s drifting speed, run Figure 5.9 Position and heading errors for PD with/without FF Figure 5.10 Apparent wind speed and heading for PD with/without FF Figure 5.11 Relationship between wind speed and vehicle s position error for PD station keeping Figure 5.12 Relationship of shifted time and correlation coefficient of wind speed and vehicle s position error for a representative PD station keeping test Figure 5.13 Relationship between wind speed and vehicle s position error for PD & FF Figure 5.14 Relationship of shifted time and correlation coefficient of wind speed and vehicle s position error for a representative PD &FF Figure 5.15 Position and heading errors for BS with/without FF Figure 5.16 Apparent wind speed and heading during BS with/without FF Figure 5.17 Position and heading errors for SM with/without FF Figure 5.18 Apparent wind speed and heading during SM with/without FF Figure 5.19 Heading errors of the PD, BS, and SM Figure 5.20 Heading errors of the PD, BS, and SM &FF Figure 5.21 Position errors of BS &AFF Figure 5.22 Heading errors of BS & AFF Figure 5.23 Apparent wind speed during station keeping tests of BS &AFF Figure 5.24 Apparent wind direction during station keeping tests of BS & AFF Figure 5.25 Position errors of SM & AFF xiii

15 Figure 5.26 Heading errors of SM &AFF Figure 5.27 Apparent wind speed during station keeping tests of SM &AFF Figure 5.28 Apparent wind direction during station keeping tests of SM & AFF Figure A. 1 Control Allocation Subsystem of WAM-V USV Error! Bookmark not defined. Figure A. 2 SMSubsystem of WAM-V USV Error! Bookmark not defined. Figure A. 3 Visualizer of WAM-V USV Figure A. 4 Position errors of SMSM&AFF, Run Figure A. 5 Heading errors of SM&AFF, Run Figure A. 6 Apparent wind speed during SM&AFF, Run Figure A. 7 Apparent wind angle during SM&AFF, Run Figure A.8 Position errors of SMstation-keeping controller with adaptive wind FF, Run Figure A. 9 Heading errors of SMstation-keeping controller with adaptive wind FF, Run Figure A. 10 Apparent wind speed during SM&AFF, Run Figure A. 11 Apparent wind angle during SM&AFF, Run Figure A.12 Position errors of SM&AFF, Run Figure A. 13 Heading errors of SM&AFF, Run Figure A. 14 Apparent wind speed during SM&AFF, Run Figure A. 15 Apparent wind angle SM&AFF, Run Figure A.16 Position errors of SM&FF Run Figure A. 17 Heading errors SM&FF, Run Figure A.18 Position errors of SM&FF, Run Figure A. 19 Heading errors of SM&FF, Run Figure A.20 Position errors of SM&FF, Run Figure A. 21 Heading errors of SM&FF, Run Figure A. 22 Stable in the sense of Lyapunov Figure A. 23 Stable in the sense of Lyapunov Figure A. 24 Stable in the sense of Lyapunov xiv

16 1 INTRODUCTION Compared with large commercial ships, unmanned Surface Vehicles (USVs) are light weighted and have relatively large windage areas so that they can be sensitive to wind disturbances, especially during station keeping tasks. Feedforward feature is advantageous because it can reduce the burden of feedback controllers, and receive prompt response in rapid changing environment. Compared with feedback control, feedforward control still has not been widely explored. For example, precise wind models for wind feedforward controllers on small size of surface vehicle are hard to find in existing literature. Therefore, an adaptive controller is advantageous because it reduces the dependence on poorly defined wind models available for USVs control design. Feedforward control can also provide a preemptive correction of wind disturbances that can be measured from anemometers. The purpose of this dissertation is to develop an adaptive wind feedforward controller to mitigate wind disturbances on a small size of USV during station keeping tasks. Since the wind coefficients are adopted from models for ships in much larger dimension, an adaptive scheme is designed to obtain a more precise wind model. The uncertainty parts of the dynamic model are responded by robust controllers, such as sliding mode controller. Nonlinear PD and backstepping controller are also developed and implemented on the USV for control performance comparison Simulation models are first built, and then on-water tests are carried out on all the controllers: PD, backstepping, sliding mode controller with/without adaptive wind feedforward control. The unmanned surface vehicles (USV), which are capable of carrying out missions on the surface of water without human assistance, have widespread application in commercial, scientific and military, such as and environmental monitoring, mine hunting, communication gate way for launch and recovery of underwater vehicles [1] [2]. Once equipped with advanced control systems, sensor systems, communication systems and weapon systems, they can perform a variety of missions that include sea patrol and environmental monitoring, pollutant tracking, surveillance, and oceanographic research. They are also very 1

17 desirable in the tasks that either too dangerous or too expensive for human to operate. Maintaining a fixed position and heading are required most of the time. For example, one potential application of USVs is bridge inspection. The performance of the task will be heavily affected if the vehicle drifts away by the wind, wave or current disturbances. Therefore, station keeping is a key element for USVs to conduct their tasks. Despite the widespread potential application of USVs, their motion control remains a less developed field since their low load capacity, limited endurance, and seakeeping ability. Advanced nonlinear dynamic model and state of art control laws, like PID control, linear quadratic optimal control, neural network control, fuzzy logic control, sliding model control, state feedback linearization and integrator backstepping, have been applied to large commercial ships. However, there are a lot of different characteristics between large ships and small size surface vessels, such as the response to wave, current, wind. Therefore, we cannot directly apply large ship control methods for designing USVs controllers. A few scattered researches on USVs are mostly restricted to basic tasks (for example heading control with constant surge speed). Moreover, the vast majority of the work is only limited to computational simulations or laboratory tests and ignores exogenous disturbances, which have great influence on the motion of marine vehicles. This reason is partly because there are only a few USVs on the market, and most are limited to military and scientific purpose [1]. Therefore, the existing technologies are far from perfect for advanced maneuvering control of USVs. Feedback controllers, especially the integral part can attenuate slowly varying environmental changes, but not rapid ones [3]. Feedforward is advantageous because it can reduce the burden of feedback controllers, and receive a prompt response in a rapidly changing environment. In conjunction with nonlinear sliding mode feedback control, wind feedforward control enables a USV to achieve more accurate station keeping than is possible with feedback control alone. While feedback controllers are designed to enhance the robustness of system for unknown disturbances, feedforward controllers can serve to foresee disturbances before they acting on the system. The wind feedforward controller allows compensation for disturbances arising from wind gust or rapid changes in wind speed or direction, in a sense giving the system a faster response to those changes. In order to get the best performance of wind feedforward controller, a feedforward tuning method was desired. 2

18 The USV utilized for this research is a small size surface vehicle (a 4.9 meters long, 180 kilograms). Compared to large commercial ships with an overall length of m, in the 150, ,000 DWT range, and with approximate wind loads of several hundred tons, it is light weighted and has substantial windage area and relatively small profile under water, and is more sensitive to wind disturbance. For example, it has been observed that if it is not actively trying to keep position with external propulsion forces, the USV will drift by more than 5 m in a minute even under low-speed wind ( ). [4]. Thus, the principle challenge of this dissertation is to reject wind disturbances during station keeping tasks. Different options for station-keeping control of a small twin-hulled USV are presented. More precisely, three station-keeping controllers are designed and implemented on a USV: a Proportional Derivative (PD) nonlinear controller, a Backstepping Multiple Input Multiple Output (MIMO) PD nonlinear controller and a Sliding Mode MIMO nonlinear controller. A wind feedforward control feature was also designed and added to the system to assist each station-keeping feedback controller. Experimental on-water station-keeping test results are presented for all three controllers, implemented with and without the wind feedforward feature. The outcomes of this work are the development and experimental validation of an optimal station-keeping control system for a USV tasked with common objectives, such as ALR and object localization. 1.1 Objectives The dissertation attempts to improve existing control methods of USVs station keeping by applying feedforward control to mitigate wind disturbances. The main focus of this effort is to develop an adaptive wind feedforward controller for the maneuvering control of a USV with two azimuth propellers. Beginning with the mathematical description of the USV motion, the paper will go through system identification, Simulink model presentation, and adaptive controller design methodology and procedures as well as sea trials for controller parameters tuning and control performance evaluation. The adaptive controller shall provide robust and precise maneuvering control of a USV with significant model uncertainties and under dramatic external disturbances. This means the vessel could operate with desired speed and heading in the harsh environment and has disturbance resistant ability The 3

19 extension of the adaptive controller could be modified for a group of vessels of different types, with different load conditions, operating environmental and control object. 1.2 Chapter Layout The remaining of this dissertation is organized as follows: In Chapter 2, the existing control technologies for unmanned surface vehicles are explored. Some representative work on the linear and nonlinear feedback control, feedforward control, wind modeling, adaptive schemes development, stable analysis and experimental results for the marine vehicle control are explained. Related previous work from the development of this effort is presented. In Chapter 3, the particular vehicle utilized in this dissertation is described. This includes its design and instrumentation: overall features, customized propulsion system, the Guidance Navigation and Control (GNC) System structures as well as the ultrasonic anemometer that used for the precise measurement of relative wind speed and direction. Chapter 4 is the main body of the dissertation. The mathematical framework of the coordinate system and equations of motion is firstly described. The system identification procedures and results are shown. With the identified vehicle model, three feedback controllers, namely a PD controller, a backstepping controller, and a sliding mode controller are developed with the detailed theory explained. A short analysis of the control ability of different feedback controllers is also included. It is followed by the development of a wind feedforward controller and its adaptation law, which is the main focus of this paper. Simulation models are built as the foundation for controller design and implementation for the station keeping of the USV. In Chapter 5, the results of extended duration of the station keeping performances of different controller with/without adaptive wind feedforward control feature are explored. The relationship between wind spectrum, control efforts, and control performance (such as position error, heading error) are explored. In Chapter 6, conclusions are drawn from the implications of work results. Future work is proposed, which involves the improvement and extension of the effort presented in this paper. 4

20 2 LITERATURE REVIEW 2.1 Applications of USV Unmanned Surface Vehicles (USVs) are playing increasing roles in commercial, scientific and military applications [1], [2]. Once equipped with advanced control systems, sensor systems, communication systems and weapon systems, they can perform a variety of missions that include sea patrol, environmental monitoring, pollutant tracking, surveillance, underwater terrain mapping and oceanographic research [5], [6], [7], [8], [2], [9], [10], [11]. To be effective, a USV needs to be capable of autonomously performing a variety of distinct maneuvers, with trajectory tracking and station-keeping being essential in their roles. While the former is necessary to allow the vehicle to navigate within different locations, the latter allows the system to maintain a constant position and heading over a period of time. A potential application of USVs is the automatic launch and recovery (ALR) of smaller unmanned systems, such as autonomous underwater vehicles (AUVs) [2], [12], [13] and object localization using acoustic [14] or vision subsystems [15], [16], [17]. Underwater object localization via acoustics can require maintaining a fixed position and orientation for up to one minute, allowing the filters in the acoustic system to remove refraction noise, thereby improving measurement accuracy [14]. The performance of the acoustic sensors can be heavily affected if the vehicle drifts during the measurement. A similar case is that of optical localization using a camera. Here, image processing algorithms may require a few seconds; however, the performance is heavily affected if the vehicle s heading is not maintained constant since small motions of the camera may result in dramatic changes in lighting conditions and image perspective. 2.2 Control Development Automated motion control of marine vehicle has been an active research topic since the early 20th century. There are different types of control techniques in the modern control system, such as PID control, linear quadratic optimal control, and nonlinear control theory. When dealing with the motion control of unmanned surface vehicles in general, the uncertainties of vehicle models (for example, hydrodynamic) and 5

21 external disturbances (such as wind loads on vehicles) cannot be ignored. In this chapter, the common linear and nonlinear controls of USVs, the wind models for marine vehicles, and the adaptive strategies for system uncertainty are presented in detail. In this part of the section, approaches using linear and nonlinear feedback control are presented. The development of efficient feedback control of marine vessels has been the subject of great interest. Linear feedback control is widely applied due to its similarity and good performances. The classic PID or just PD controllers are the simplest controllers, while still showing a good solution for the control of marine vehicles. PD controllers in the context of marine vehicles are wide spread, and the existing methods are used in many industrial systems. The linear controller is simple to design and implement, and the design procedure is very straightforward and underlying theory is very potent. For example, H. G. Sage gave a thorough review of the control methods for robot manipulators [18]. A linear feedback controller Linear Quadratic Regular (LQR) is utilized in [19] for the station keeping of a USV. The LQR controller is similar to the PID controller, with the differences lying on the tuning of control parameters. During design, the gains of a PID controller are tuned, while the weight matrix of an LQR controller is adjusted. LQR method is widely studied due to its simplicity and applicability However, the neglecting of nonlinear terms makes it not the most robust controller. It is proposed by K. P. Lindegaard that acceleration feedback added to PID control can improve control performance, and a model ship is used to exam the control method [20]. The analysis of state feedback linearization can be seen in [21], [22] and [23]. The basic idea is to linearize a nonlinear system so that conventional control techniques for linear systems, such as poleplacement and linear quadratic optimal control theory can be applied to the system. This control method is easily applicable to the motion control of marine ships, since the model can be treated as a mass-damperspring system. A widely applied tool for the control of the nonlinear system is feedback linearization. A nonlinear feedback operation is performed to cancel out the nonlinearities of the vehicle dynamics so that the system becomes linear. Sometimes, linear controllers need to be developed for different operating conditions. For 6

22 example, when a USV operates at different speeds, a great quantity of different controllers linearized about different speeds is needed [24]. This approach is not practical, and the stability is also questionable. Most previous work on USV station-keeping control focuses on underactuated systems and on enabling the vehicle to maintain position only, as if it was anchored, and without focusing on the USV orientation. Here we describe the development of an ideal station-keeping controller for an overactuated USV, enabling it to simultaneously maintain heading and position. For example, in [4] the dynamic positioning of an underactuated ASV is studied. The focus of the study is merely position, and the heading is not required to be in one particular direction. 2.3 Nonlinear Control The major drawback of linear control is the lack of physical tractability after the linearization of nonlinear systems. Although the simplified models of linear control are generally adequate in practice, exact expressions of nonlinear nature of the system can permit more advanced controllers and better control performances. While linear control often requires many linearized controllers for high-order nonlinear systems, such as marine vehicles, to achieve good performances, the nonlinear controller could allow single nonlinear model without linearization. Linear control schemes, e.g. PD control, are more favorable when there is little information about the dynamics of the vehicle system. However, nonlinear control can yield better performance when the system is well modeled, at the cost of system complexity. More advanced nonlinear control methods, such as backstepping, sliding mode controls are exploited in this section. Nonlinear control theory for marine vehicles can yield a more intuitive design process than the linear theory, since linearization can destroy model properties and lose physical insight of the model [24]. Backstepping is a recursive design method that uses a control Lyapunov function to construct a feedback control law. Instead of canceling all nonlinearities of the system as in feedback linearization methods, backstepping allows a flexible design to exploit good damping terms and cancel out destabilizing terms. A good tutorial of backstepping can be found in [25]. The approach of control design on USV with Lyapunov s second method and backstepping is shown in [26]. Globally Uniform Asymptotic stability is demonstrated, and the effectiveness is validated by simulation on a model ship. The surge speed and yaw speed controllers decouple as two subsystems, due to the nature of underactuated system. 7

23 The practice of adaptive backstepping for a nonlinear system is described in [27]. The parameter adaptation, tuning functions, and backstepping application are included in the paper. For the uncertain constant parameter in backstepping control, it can be adapted based on [28]. Adaptive backstepping can result in a simple PID control law if the system can be simplified as a mass-damper-spring system. Adaptive controllers can be designed in the followings steps as proposed in [23]. Backstepping also was suggested in [29] as means to station-keep a fully-actuated vehicle, although environmental disturbances were not explicitly stated in the problem formulation. The Lyapunov-based control approach is frequently used in the marine vehicles control literature for the analysis of the stability of non-linear systems, with mainly two steps: first a control law is proposed, and second the stability results are proven. The algorithms based on Lyapunov stability proofs have the advantages of solving the control problems entirely in a non-linear setting. However, due to the nature of the approach, the controllers rare show the physical insight into the system. Sliding mode control is another well-known nonlinear control method for the robust control of marine vehicles with system uncertainty, and it is also utilized in this paper as one of the feedback controllers. The basic idea of sliding mode control is to define a surface function of the system s state and to ensure via a non-linear control law that if the system deviates from the defined surface, it is forced back to it. In this sense, the system slides along the surface. Therefore, the system s dynamic properties depend considerably on the choice of the surface. In sliding mode, the system possesses considerable robustness to external perturbations or incorrectly modeled dynamics. However, in the initial transition phase towards sliding mode, the system may prove to be rather sensitive to these types of disturbances. Sliding mode controllers for marine crafts are robust and can be designed with relatively little information. The notion of a sliding surface and the associated control theory has been studied in great detail in [30] [31]. Detailed design approaches are presented in [32]. In [33] and [23] sliding mode control is applied on marine vehicles. 2.4 Feedforward Control In this part, the design of wind model, wind model gain estimation, and the existing feedforward control methods will be explored. For the feedforward control, the adaptive feature will be discussed. 8

24 Since the current generation of USVs is lightweight and has relatively large windage areas, wind is a major source of disturbance during station-keeping operations [3]. While slowly varying environmental changes, such as tidal currents, can be attenuated by applying robust feedback control laws, rapid environmental changes, like the ones caused by the wind, can be better counteracted by applying feedforward control theory [34]. This research highlights that the uncertain effect of currents on a small twin-hulled USV, tasked to autonomously station-keep, leads to the inability of the system to reach and maintain the desired state. It is shown that robust non-linear control theory, such as backstepping and sliding mode control, can be applied and refined for the purpose of station-keeping heading and position control of a USV. It is also shown that, implementing wind feedforward control, in addition to state feedback control, allows for fast correction of the final control signal, therefore providing the appropriate control effort. In [35], three methods of feedforward controllers, namely Iterative Learning Control (ILC), Iterative Feedback Control (IFC), and Adaptive Feedforward Control (AFC) were presented. The ILC method updates control law based on the information abstained from previous experiments. The IFC is an iterative method that tunes the control parameters to minimize a cost function. In AFC control law, uncertain parameters are estimated in real time to form the control input. In the paper [36] adaptive feedforward control algorithms were given and experimental evaluation showed excellent error reduction. Two feedforward control methods, namely an infinite impulse response filter that was designed off-line, and a finite impulse response filter that was adapted on-line using the Filtered-x LMS Algorithm were discussed in [37]. In [38] an extreme learning control framework using feedforward network was proposed, and output weights of the feedforward was updated by adaptive projection-based laws derived from Lyapunov approach. As proposed by E. Adam and J. Marchetti, tuning of feedforward controller is not independent of feedback-loop spectral characteristics. Even though feedforward control cannot influence the stability of feedback system, the control system requires the feedforward controller to be a stable function. And in order to reject disturbances efficiently, feedforward and feedback controller should be simultaneously tuned. 9

25 The thesis of H. Håvard focuses on dynamic positioning of USVs. It is suggested that a wind feedforward controller should be added on the control system to provide enhanced station keeping performances. The input of the feedforward controller is the reference points generated by a model. The effects of feedforward controller are examined by a simulation, where the feedback controller is switched off [19]. 2.5 Wind Model and Parameter Estimation The USV application of feedforward control theory, such as wind feedforward control, still has not been widely explored. Wind feedforward is advantageous when wind speed and direction is available from an anemometer. The integral part of a feedback controller can reduce the effect of slowly varying wind disturbances, but cannot provide fast control response, especially for the quick change of wind speed and direction. Wind feedforward control methods can also improve accuracy for rapid course changing maneuvers. In general, wind feedforward is helpful for reducing the loads on an integrator and obtaining better maneuvering performances and the startup of dynamic positioning task. The difficulty of building wind feedforward control is mainly because of the complexity of wind model. A few challenges are encountered when designing wind feedforward controllers. These include accurately measuring representative wind speed and direction and calculating the wind force coefficients. Anemometer errors can be minimized, but not eliminated, by appropriately calibrating the sensor [34]. It has been found that wind gust and turbulence can also cause large measurement errors [3]. A risk of applying wind feedforward control is that speed and direction of the wind can vary across different parts of a vessel. Thus, especially for larger vehicles, it may not be appropriate to analyze wind effects on the whole vessel with a single point measurement. One possible solution is to use several wind anemometers to measure the wind field [3]. For small USVs, the wind acting on the vehicle can be assumed to be uniform. The placement of the anemometer on the vehicle presents another challenge. Ideally, it should be mounted such that the measurements are least affected by wind interaction with the vehicle s structure. Wind guest still cannot be compensated by wind feedforward control since the actuators have a limited propulsion power to move the vehicle in such high frequency as wind gust. Lastly, wind models, capable of estimating wind forces and moments acting on small marine vessels, are very limited. 10

26 The vast majority of these models are based on large vessels and floating objects in the ocean, such as oil tanks, and commercial ships [3], [40], [41], [42], [43]. These models need to be validated and possibly modified for use on small vehicles. The wind model for a small size of USV shown in [4] is calculated by hand at discrete angles (0, 30, 45, and 60). In fact, even in more technologically mature areas such as AUV control, stabilization in the presence of environmental disturbances has only been partially addressed [44]. In [28] a nonlinear control approach is proposed for weather optimal position control. The weather-vanning object is achieved by estimating environmental disturbances. The vehicle utilized in that paper has multiple thrusters and is able to generate sway forces. Several solutions have been proposed for the station-keeping of surface vehicles. In [4], experiments were performed on a small underactuated USV with high windage, where a feedforward wind model was modified to accommodate a PD-based heading autopilot. A weighted scheme was implemented on the wind feedforward controller to improve the station keeping performance of the vehicle under slowly varying moderate wind conditions. The controller was tested in simulation, and the results show that the position error was around one vehicle length. In [45], the feasibility to reduce USV drifting rate, considering the wave drifting effect as the vehicle is under station-keeping mode, is discussed. Elkain and Kelbly [46] were able to add stationkeeping functionality to a wind propelled autonomous catamaran for the purpose of maintaining position at a given waypoint in the presence of unknown water currents. Switching between point and orientation stabilization and discontinuous control was employed to stabilize a marine vehicle at a fixed point in the presence of a current using dipolar vector fields as guidance in [47] and [48]. Similarly, a hybrid approach was taken in [49] where multi-output PID controllers with and without acceleration feedback were used to stabilize a vehicle in high sea states by the use of an observer to estimate the peak wave frequency. The system switched to controllers better suited to handle large disturbances as the peak wave frequency estimate decreased and, correspondingly, the sea state increased. Aguiar and Pascoal [44] devised a nonlinear adaptive controller capable of station-keeping an AUV with uncertain hydrodynamic parameters in the presence of an unknown current. 11

27 It pointed by R. Stephens that when wind feedforward is implemented, the wind data should be low-pass filtered to avoid rapid changes in heading command [9]. 2.6 Adaptive Control The nonlinear adaptive control schemes are usually directly derived from non-adaptive controller design strategies. In practical experiments, they can outperform non-adaptive controllers for its ability to adjust the uncertain terms. Three adaptive control schemes, namely gain scheduling PID control, model reference adaptive control, and adaptive control are compared in [50]. The controllers are tested on a USV for the smooth transition between displacement mode and planning mode operations. The adaptive control is used for the update of added mass terms in [51], to get a precise model for dynamic positioning or trajectory tracking. In [52], the adaptive combined with backstepping is explored for the decoupled yaw and sway direction on a Nomoto kind steering model. A switch control is found to handle parameter uncertainty in [53], where the vehicle utilized is underactuated. A. P. Aguiar extends this work by designing an adaptive backstepping controller for the estimation of hydrodynamic terms [44]. E. Borhaug and K. Pettersen present an adaptive control strategy to counteract environmental disturbances for waypoint tracking control of a six degrees of freedom autonomous vehicle [54]. The environmental disturbances are assumed to be unknown constant values. The controller is proved to be global asymptotic stable. The robustness and stability of adaptive controller have been analysed thoroughly by N. Saddegh and R. Horowitz [55]. The properties include global exponential stability and input/output stability for the non-adaptive control scheme and global asymptotic stability of the adaptive system. Unfortunately, the study only involved with simulations, no guidelines are provided for all the schemes have been tested in practical experiments. The theory of the stability and robustness is based on robot manipulators, but this can be easily adapted to USVs. 2.7 Control Allocation and Stability Analysis Azimuthing thruster configurations, such as those found on the USV16, create an overactuated system, since multiple solutions to the controller output can be found in terms of propeller thrust and azimuth angle. This is formulated as an optimization problem, and techniques such as linear programming [29], [56], quadratic programming [57], and evolutionary algorithms [58] can be used to find an optimal, or 12

28 near optimal, solution. Actuator dynamics create constraints on this system, leading to a constrained nonlinear optimization problem, which is nontrivial to solve. An alternative to this method is to use a Lagrangrian multiplier technique as described in [29]. The powerful tool for nonlinear system stability analysis is Lyapunov stability theory that is named after Russian mathematician and engineer Alexander Michailovich Lyapunov ( ), who laid out the foundation of the stability theory. His result was first published in 1892, Russia, and later translated into French in However, when the theory was really getting attention is in 1947, that it reprinted by Princeton University. Ever since then, the stability theory has been widely used for the system stability analysis and controller design. The Lyapunov theory is used for controller design and stability analysis in the Sections 4.2 and Experimental Verification for Control Law As can be seen in the previous discussion, there are a substantial number of studies on the motion control of marine vessels. However, only a few of them have been implemented on real USV platforms. Some of the control results are shown in simulation, such as [54] [55]. Even though in-water tests are critical for verifying the controllability of system, the validation of USV control laws is often limited to numerical simulation or small-scale experiments, rather than full-scale sea trials [59].. 13

29 3 The WAM-V USV 16 In this chapter, the detailed description of the USV utilized in this dissertation is described. This includes its design and instrumentation: overall features, customized propulsion system, the Guidance Navigation and Control (GNC) System structures as well as the ultrasonic anemometer that are used for the precise measurement of relative wind speed and direction. 3.1 Overview of the USV 16 The USV utilized throughout this paper is a Wave Adaptive Modular-Vessel (WAM-V) 16 feet USV (USV 16, see Figure 3.1). It is a twin hull, pontoon style vessel designed and built by Marine Advanced Research, Inc. of Berkeley, CA USA. The vessel structure consists of two inflatable pontoons, a payload tray connected to the pontoons by two supporting arches and a suspension system. It is designed to mitigate the heave, pitch, and roll response of the payload tray when the vehicle operates in waves. The vehicle s geometric specifics and physical characteristics are shown in Table 3.1. The location of the keel is taken as the bottom of the pontoons. w.r.t. is an acronym for the phrase with respect to. Figure 3.1 The WAM-V USV16 in the Intracoastal Waterway (ICW). 14

30 It was chosen as the standard surface vessel for the Maritime RobotX international competition on October 20-26, 2014 in Singapore. The competition included autonomously traveling through the desired course from the starting point to the ending point, detecting and avoiding obstacles and gates, identifying and locating underwater devices with an acoustic signal, observing an object buoy and report the sequence of buoy lights as well as craft docking and target identification. It was the competition that motived the effort on maneuvering control of the USV. Table 3.1 Principle characteristics of the WAM-V USV16. Parameter Value Length overall (L) 4.05 [m] Length on the waterline (LWL) 3.20 [m] Draft (aft and mid-length) 0.30 [m] Beam overall (BOA) 2.44 [m] Beam on the waterline (BWL) 2.39 [m] Depth (keel to pontoon skid top) 0.43 [m] Area of the waterplane (AWP) 1.6 [m 2 ] Centerline-to-centerline side hull separation ( ) 1.83 [m] Length to beam ratio (L/B) 2.0 Volumetric displacement ( ) 0.5 [m 3 ] Mass 180 [kg] Mass moment of inertia about z axis (estimated with 250 [kg*m 2 ] CAD) Longitudinal center of gravity (LCG) w.r.t. aft plane of 1.30 [m] engine The USV 16 control design is based on the previous study and achievements of the USV 12 and USV 14. The USV 12 and 14 vessels also belong to the WAM-V class of surface vehicles with the length of 12 feet and 14 feet respectively. Their propulsion systems have been designed by the students and technical of FAU staff. Electric motors are chosen to replace gasoline motors for the reliable response of the USV 12. Both the USV 12 and 14 motor pods have the problem of leakage, which can damage the engine and cause wind up the vessel. This issue should be avoided during the USV 16 propulsion system design. The USV 12 is waterjet propelled, and during the sea trials, it came up with many problems. The USV 16 will use skew propellers so that the focus is on controller design rather than troubleshooting of the propulsion units. Both the USV 12 and 14 are underactuated systems with fixed angle thrusters, and any change of direction relies on differential thrust between port and starboard. The two azimuthing propellers enable the USV 16 to operate in a fully-actuated configuration. Thus, the USV 16 has more potential for 15

31 precise maneuvering control at the price of more complex configuration. There is no sensor to measure the environmental disturbances for USV 12 and 14. However, an ultrasonic anemometer is used to measure the apparent wind speed and direction on the USV 16 so that wind loading can be estimated and mitigated by feedforward controller. The propulsion system, guidance, navigation, and control system, as well as anemometer to get wind information will be presented in detail in the following sections Propulsion System In order to get redundant sets of control actuators to perform station keeping tasks, the propulsion system is custom designed. This includes two electric thrusters that can provide a peak thrust of 480N in total, each powered by a 24V lead acid battery, and two 160 N, 15 cm stroke, linear actuators capable of rotating the thrusters through an azimuthal angle of with respect to the vehicle s longitudinal direction, so that the USV is fully-actuated. The propulsion system and thrust directionality can be seen in Figure 3.2. Figure 3.2 WAM-V USV16 propulsion system 16

32 Figure 3.3 Port and starboard thrust ranges directions. Both port and starboard can provide thrust at ±45 with respect to demihull centerlines. As shown in Figure 3.3, the azimuth angle is denoted by, where ranges from negative to positive as mentioned above. In the picture, subscripts s and p stand for starboard and port sides respectively. and are the thrusts on the port and starboard sides respectively, they can be pivoted in various directions based on the azimuth angle on each side ( and ), enabling the vehicle to output multiple combinations of surge and sway forces and yaw moment. The moment generated by the thrusters is calculated by multiplying and by their moment arms and. According to Fossen, T. I. [24], a system is considered overactuated when the number of actuators is greater than the number of degrees of freedom (DOF). Here, we have four actuators, namely two linear actuators and two thrusters, and three DOF ( ). The configuration of the propulsion system permits the USV16 to move in surge ( ), sway ( ) and yaw ( ) directions independently so that it is an overactuated system Guidance, Navigation, and Control system The guidance, navigation and control (GNC) system was developed for the testing of controllers of autonomous control for the WAM-V USV16. IMU/GPS, digital compass, single-board computer, and RF transceiver are hosted in a plastic, waterproof control box, as shown in Figure 3.1. The IMU is an 17

33 XSENS MTi-G sensor that measures the position and orientation of the USV during operations. The GPS is Wide Area Augmentation System (WAAS) enabled and can provide up to 1 meter accuracy in both latitude and longitude, depending on weather and satellite availability. The digital compass is used to monitor vehicle heading and has a resolution up to 0.1 degrees. The Lightweight Communication and Data Marshaling (LCM) system [60] is utilized as the underlying architecture for the GNC software. Sensor data was transmitted using drivers incorporating the LCM system to the control architecture and logged at 4Hz. A handheld remote control is used for operating the thrusters and the actuators in manual mode and also for initiating autonomous operations. The user can switch between remote manual control and autonomous navigation mode by the remote control that communicates with RF receiver installed in the control box. When the USV is conducting its missions, such as station keeping or trajectory tracking, it is in autonomous mode. When it switched to remote manual control mode, the USV can be manually guided to target positions. The remote controller can also be used for operating the linear actuators (Figure 3.2, Figure 3.3) to control the thrusting angles for both port and starboard sides. Real time state information collected by the sensor suite described above is relayed to a single board computer. Sensor data was transmitted using drivers incorporating the LCM system to the control architecture and logged at 4Hz. A handheld remote control is used for operating the thrusters and the actuators in manual mode and also for initiating autonomous operation. The detailed description of the GNC system can be found in the paper of the previous work on the USV 14, which shares the same control box [12]. All the sensors and equipment were calibrated before use. The accuracy and dynamic response of the IMU is hard to obtain, as it s a function of past motion history. It is calibrated with the software provided by the manufacturer Anemometer An ultrasonic anemometer is used to measure the wind information. The anemometer is an AIRMAR WeatherStation 100WX, and the dynamic range of the sensor is 0-40 m/s with a resolution of 0.1 m/s. Additional sensor specifications can be seen Table 3.2. The wind speed and direction data collected are relative wind speed and relative wind direction, which are filtered and passed to the feedforward controller. The anemometer is installed in an elevated position at the aft end of the payload tray to avoid the 18

34 effects of wind blockage and interference from other structures (Figure 3.1). Owing to the relatively small size of the USV, it is assumed that the wind speed and direction measured by a single point sensor is representative of the wind flowing past the entire vessel. Table 3.2 Anemometer specifications Parameter Wind Speed Range Wind Speed Resolution Wind speed accuracy (no precipitation) Wind direction range Wind direction resolution Wind direction accuracy Weight Communication interface Value 0 to 40 [m/s] 0.1 [m/s] 0.5[m/s] 0-360[deg] 0.1[deg] 2-8[deg] 300[grams] RS232 19

35 4 METHODOLOGY In this chapter, the detailed steps to develop an adaptive feedback and feedforward controller for the station keeping of the USV 16 are presented. First, a dynamic model of the WAM-V USV16 was developed, where the same notation as in the book written by T. I. Fossen [24] is adopted. Then system identification tests were conducted, following the same procedure as in presented by Marquardt, Alvarez and von Ellenrieder [61]. The system characterization experiments give a good estimation of the hydrodynamic terms in the mathematical model built. The results of previous studies on three feedback controllers, namely a PD controller, a backstepping controller, and a sliding mode controller show that a sliding mode controller can give the best control performance during station keeping tests. Therefore, a nonlinear sliding mode controller was used. Wind is a strong influence for the station keeping of the light weight USV, and in order to mitigate the disturbance, a wind feedforward controller was also designed. To further improve the control performance of the USV, an adaptive mechanism was also applied. The adapted terms are mainly hydrodynamic parameters and wind model coefficients. A Matlab Simulation was also developed to compare the results of station keeping with the following controllers: open loop nonlinear sliding mode feedback controller, sliding mode controller combined with wind feedforward controller, and model reference adaptive feedforward and feedback controller. 4.1 Equations of Motion The dynamic of marine vehicles is usually described by high-order, nonlinear and uncertain models [24]. The methods for producing good vehicle models are well documented and can be found in [24] [62] [40] [61]. In order to design the controller for station keeping, a suitable dynamic model is first built. The dynamic of marine vehicles can be divided into kinematics and kinetics. Kinematics only deals with geometrical parts of the motions, while kinetics treats the forces that causing the motion. The WAMV- USV 16 kinematics and dynamics in 3 DOF and environmental disturbances in term of wind are presented in this chapter. The paper follows that standard notation and adopts the vectorial setting that described in T. 20

36 I. Fossen [24] Coordinate Frames Before analyzing the equations of motion of the USV, it is convenient to define the reference frames and coordinates. It s common to define the body-fixed frame and earth-fixed frame when describing the motion of marine crafts. The body-fixed frame is fixed to the vehicle and is a moving coordinate system. The linear and angular velocities of marine craft, as well as the forces and moments acting on the vehicle are described in the body frame. The center of gravity (CG) is usually chosen as the origin of the body-fixed frame. The earth-fixed reference, with axis point towards North, East and downwards normal to the earth surface, is called the North-East-Down (NED) coordinate system. The position and orientation vector are described in this frame. These coordinate systems are illustrated in Figure 4.1., and are the applied surge, sway and have forces, respectively., and are the applied roll, pitch and yaw moments, respectively., and are the surge, sway and heave speeds (respectively) in body fixed coordinates. Lastly, and are the roll rate, pitch rate and yaw rate, respectively. In order to determine the position and orientation of marine vehicles in 6 degrees of freedom (DOF), six independent coordinates are needed (Table 4.1). For the station keeping purpose in this paper, the USV 16 operates at low speed (1-2 knots) and in mild sea states (SS 0/1). Thus, the vehicle s motion is assumed to be planar with linear motion in the and directions and rotation about the axis. Throughout this paper, a 3 degree of freedom (DOF), namely surge, sway, and yaw model, are used to represent the motion of USV 16 as illustrated in Figure

37 Figure 4.1 Body-fixed ( and earth-fixed ( reference frames. Figure 4.2 Top view of WAM-V USV16 with the 3 DOFs body-fixed coordinate system. 22

38 Table 4.1 Notation used for marine vehicles DOF Forces and moments Linear and angular vel. Positions and Euler angles 1 Motions in the x-direction (surge) X u x 2 Motions in the y-direction (sway) Y v y 3 Motions in the z-direction (heave) Z w z 4 Rotation about the x-axis (roll ) K p ϕ 5 Rotation about the y-axis (pitch) M q θ 6 Rotation about the z-axis (yaw) N r ψ Nonlinear Dynamic Equations of Motion If we only consider wind to be the only environmental disturbance, the nonlinear equations of motion in the body-fixed frame can be written in vectorial form: ( ( (4.1 ) [ ] (4.2 ) (4.3 ) where is the mass matrix, ( is the Coriolis matrix, ( is the drag matrix, is the vector of forces and moment generated by the propulsion system, and is the vector of forces and moment caused by the wind. and ( include both rigid body terms, and (, and added mass terms, and (. ( includes both the linear drag term ( and nonlinear drag term (. The vector describes the vehicle s North, East velocities and the angular velocity around the axis in an inertial reference frame, and the vector contains the vehicle surge velocity, sway velocity and yaw rate in the body-fixed frame. These two coordinate systems are illustrated in Figure 4.2. The subscript in the mass, drag, and Coriolis matrixes are nomenclature to represent a force or moment caused by motion in a specific degree of freedom. For instance, stands for the force in surge direction created by of forward speed. The terms with two subscripts denote a quadratic term such as, or nonlinear coupling terms, for example,. is an inertia tensor that is the sum of a rigid body mass matrix,, and an added mass matrix, : 23

39 [ ] (4.4 ) Where denotes the mass of the USV16, and are the coordinates of the vessel center of mass in the body-fixed frame, and denotes the moment of inertia about the -axis. All the terms representing the hydrodynamic coefficients in the mass matrix utilize SNAME (1950) nomenclature for representing a force or moment created by motion in a specific degree of freedom [43]. The subscript on each coefficient denotes the cause of the force/moment (e.g. produces a force in the direction from a change in the yaw rate ). ( is a Coriolis matrix, which includes the sum of a rigid body term, (, and added mass term, ( : ( [ ( ( ( ( ( ) ] (4.5 ) [ ( ) ] The model designates the body-fixed origin at the center of gravity and assumes port/starboard symmetry, making and. ( is the damping forces and moments vector, which consists of two parts, the linear forces and moments (, and the forces and moments ( due to nonlinear damping effects. Nonlinear damping involves velocity terms of high order, which are very small and can be neglected in station keeping situation. The summation of the linear and the nonlinear drag matrices: ( ( ( (4.6 ) where ( [ ] (4.7 ) and 24

40 ( [ ] (4.8 ) The drag in surge direction depends on the moving speed of the hull. The drags on port and starboard side of the USV are separated and defined as and, respectively. and are derived from the polynomial curve fit equation experimental data. More details can be found in the Section A coordinate transformation is carried out to obtain the velocities of each individual pontoon hull because they are offset from the CG. These transformed velocities are used in the drag model below as and : ( ) ( ) (4.9 ) ( ) ( ) (4.10 ) Incorporating the moment created by the two drag forces and, the term ( ) (4.11 ) is added to the yaw moment (not modeled in ( ). The rate of position-orientation is related to velocity vector by: ( (4.12 ) The vector describes the vehicle s North, East velocities and the angular velocity around the axis in an inertial reference frame, and the vector contains the vehicle surge velocity, sway velocity and yaw rate in the body. The transformation matrix that relates the body-fixed velocities to the earth-fixed velocities are: ( [ ] (4.13 ) The nonlinear system of the inertia matrix, Coriolis matrix, damping matrix and rotation matrix share the following properties, as presented in [63]: i. is positive definite 25

41 ii. ( ( is skew symmetrical ( iii. ( is strictly positive ( ( ( iv. ( is the rotation matrix in yaw ( ( is a vector of the forces and moment generated by the propulsion system: [ ] (4.14 ), and are the thrust in and directions, and resulting moment around the axis. The USV generates the propulsion forces and turning moment with two azimuth thrusters. The actuator commands are prop speed, and thruster turning angles, where the subscripts s and p stand for starboard and port sides respectively. We assume thrust has a linear relationship with RPM, so that, where is the peak thrust.,, and can be calculated in the following way: ( ( (4.15 ) (4.16 ) (4.17 ) (4.18 ) (4.19 ) where are vectors of port and starboard moment arms, and are parallel to direction, respectively. and is the distance between the center of gravity and the thruster, and is the overall beam (Figure 3.3). For station keeping operation, nonlinear drag terms can be neglected. A wind model was also designed for estimation of the wind loads in the surge, sway and yaw direction. Several models can be found in the literature of Gould [41], Isherwood [42], and Li, et al. [40] The one selected here is based on T. I. Fossen [62]. The detailed wind model development and wind feedforward design are shown in Section 4.3. The dynamic pressure is: 26

42 (4.20 ) where is the air density, and are apparent wind speed and angle of attack respectively that can be measured directly by the anemometer introduced in The wind forces and moments can be expressed as: [ ( ( ( ] (4.21 ) where AFw and A Lw are the frontal and lateral projected windage areas (Figure 4.3, Figure 4.4). They are calculated precisely by the computer with projected 3D model. The representation of vehicle orientation and wind direction is shown in Figure 4.5, where is vehicle heading is vehicle velocity, is true wind speed, is true wind direction is true wind angle of attack, is apparent wind speed, and is apparent wind angle of attack. Figure 4.3 Frontal projected area. Figure 4.4 Lateral projected area. 27

43 can be approximated by: Figure 4.5 Representation of vehicle orientation and wind direction. are empirical wind coefficients in the surge, sway and yaw directions, respectively, and ( ( ( ( ( ( (4.22 ) (4.23 ) (4.24 ) In T. I. Fossen [62], it is suggested that { } { } and { } are picked to be first in the model of wind feedforward controller. For better performance of the feedforward controller, a coefficient matrix is introduced so that the wind feedforward control law was taken to be: (4.25 ) 28

44 where is a diagonal matrix, and ( (4.26 ) And here for i =1, 2, 3. matrix is adapted based on the reference model of the vehicle. More details about the adaptive tuning method of it will be discussed in System Identification Parameters described in the dynamic model of the vehicle in Section need to be identified. The terms in the inertia matrix can be measured (such as the mass terms) or estimated by theoretical formulas. For the hydrodynamic terms, a series of open-loop maneuvering tests are conducted to for parameter identification. In some literature, the estimation is performed using Matlab tool boxes ( [4]. In other papers, a series of sea trials, including bollard pull tests, acceleration tests, circle tests, and zigzag tests, corresponding to standard maneuvers performed on surface vessels [64], were conducted for the system identification of the WAM-V USV16. A three DOF maneuvering model of the vehicle is then developed with the hydrodynamic coefficients identified to represent the WAM-V USV16. This model can be utilized for the design and development of various low-level controllers on the WAM-V USV16. A brief description of the procedure to characterize the vehicle and the development of the state space maneuvering model is given in this section. The system identification method is inspired by the similar work done in [65] [12], and the detailed procedures can also be found in these papers. During all runs, the azimuth angles of the thrusters, and were kept at 0 o. All system characterization sea trials were conducted at North Lake, Hollywood, FL. The location was chosen such that it would provide a benign environment with minimum wind, current and wave disturbances. Vehicle state, as well as wind speed and direction, were recorded throughout the experiments. The main characteristics of the USV, such as overall length, draft, mass, etc., can be measured and were given in Table I. The added mass terms can be derived by semi-empirical equations as described in T. I. Fossen [24]. The terms that need to be identified are the linear and nonlinear drag terms and. Acceleration tests were conducted to get linear and nonlinear drag terms in the surge direction and. Two types of circle tests were carried out for. And zig-zag 29

45 tests also performed for further validation of the identified model of USV. The specific procedure for the tests described in this section is presented in [65]. A bollard pull test was first performed to estimate the relationship between motor commands and thrust on the vehicle. For this test, the vehicle was tied to a load scale, connected to a fixed pole. The same thrust command was given to each motor, to apply the propulsion force uniformly in the surge direction. The reading of the load scale was taken after the vehicle had put enough tension on the line to keep it steadily taut. This reading then corresponded to the total thrust the propulsion system was outputting. Five readings were recorded from the load scale, for each motor command, before being averaged. The averaged values of thrust for each motor command are shown in Table 4.2. Table 4.2 Relationship of motor command and thrust from bollard pull tests. Motor Command [%] Thrust [N] Acceleration Tests Acceleration tests were then conducted to estimate the linear and nonlinear drag terms in the surge direction. For this, the USV was started from rest, with surge, sway speed and yaw rate as close to zero as possible, and accelerated with a throttle range of % on both motors for 60 seconds. When the vehicle achieved steady-state speed, the drag forces in the surge direction were equal to propulsion forces. Linear and nonlinear drag coefficients in the surge direction, and, were determined by quadratic curve fitting of surge speeds and drag forces, as shown in Fig Note that this assumes that there is not speed dependence for on the thrust developed by the propellers. This assumption does not affect the outcome of the station keeping experiments, as the forward speed of the vehicle will typically remain small during station keeping. The same assumption was previously used to develop a closed loop surge speed controller for a similar vehicle at speed and was found to work well in practice [65]. Decouple surge movement from sway and yaw, the equation of motion is: ( (4.27 ) When the vehicle achieved its steady speed, the drag forces in surge direction are equal to the thrusts of the USV. (4.28 ) 30

46 With a wide range of speed data collected by the experiment tests, and can be determined by quadratic curve fitting of surge speeds and drag forces, (Figure 4.6). Circle Tests Figure 4.6 Quadratic fit of surge speed and drag in surge direction for USV16 model. Circle tests were conducted to get the drag term of. Similar to acceleration tests, circle tests were carried out via human remote operation as well as pre-programmed commands in the control box. During the circle test, the vehicle was first accelerated with 100% throttle on both sides for 20 seconds to establish a steady state, then port and starboard were set to -100% and 100% throttle respectively for 30 seconds. Following this procedure, the vehicle was spun in a circle around its center of gravity with minimal surge and sway velocity; the drag moment coefficient from yaw rate could be isolated. The vehicle needs to track a circular pattern for at least 1080 degrees (three full circles), and the test is repeated at different motor throttles for both port and starboard turns to obtain sufficient testing data for the calculation of. ( ) (4.29 ) When,. Similar to the acceleration tests, repeated trials with a throttle of ±70, % command were also carried out. 31

47 The circle test was performed in a different manner by setting port and starboard to 0% and 100% throttle, instead of to -100% and 100%. Following this procedure, the vehicle was able to steer around a turning radius; the drag coefficient in the sway directions from sway velocity therefore be estimated. In the equation, the only unknown term is, so we can get the drag term in the sway direction. Zig-zag Tests In contrast to traditional zig-zag tests, in which rudder commands are issued for a certain heading range, the tests are conducted via differential throttle command between port and starboard sides on the differential-thrust USV. The zig-zag tests were utilized to evaluate the model. During the tests, the vehicle was first accelerated with 100% throttle on both sides for 20 seconds, then port and starboard were set to 100% and 0% throttle alternately four times on each side. The zig-zag test was utilized solely to evaluate the model by comparing field data with simulations. Table 4.3 Hydrodynamic coefficients for the WAM-V USV16. Coefficient Name Non-Dimensional Factor Dimensional Term ( 0.5 ( 0.5 ( (See Fig. 4.6) -0.5 [ ( ) ] ( ) (See Fig. 4.6) ( -0.4 ( ) The equations to estimate all the hydrodynamic terms needed for the dynamic model of the vehicle were chosen, as in [65]. These coefficients were then non-dimensionalized and linearized about a nominal surge speed of (the typical transit speed of the USV). The equations and linearized numerical 32

48 values of the hydrodynamic coefficients used in the model are listed in Table 4.3. All hydrodynamics terms not listed in this table are assumed to be zero. Comparison of simulation and experimental results for the acceleration test, circle test, and zig-zag test is shown in Figure 4.7 to Fig In Figure 4.7 and Figure 4.8, it can be seen in the graph that the vehicle s full acceleration period is around 55 seconds. It also can be noted that the theoretical vehicle deceleration for both 70% and 100% throttle commands was more rapid than the experimental deceleration under the same circumstances. A possible explanation is that the water accelerated by the USV was still moving forward when conducting the experiments so that the vehicle began to decelerate, leading to a slower decay rate. In addition, unmodeled wind and current may have played a major role is affecting the decelerations of the USV during sea trials. Figure 4.7 Surge speed of simulation and experimental results of 70% throttle command 33

49 Figure 4.8 Surge speed of simulation and experimental results of 100% throttle command Figure 4.9 Surge speed of simulation and experimental results during circle tests. 34

50 Figure 4.10 Yaw speed of simulation and experimental results during circle tests. Figure 4.11 Yaw rates of simulation and experimental results during zigzag tests with 100% throttle command. The acceleration tests can also be used to find vehicle s dynamic response to actuators. Figure shows the curve fit result of the acceleration test with 70% throttle command. The slope is , and the stedy state surge speed is 1.13 m/s. Thus, the dynamic response of the USV to actuator can be estimated, and the value is 1.13/0.1335=8.46 s. The response time of different runs is calculated following this procedure, and the values vary between 3 to 10 s. 35

51 Figure 4.12 Curve fit to get the slope of the acceleration curve with 70% throttle command. 4.2 Nonlinear Feedback Control In this chapter the fundamental theory and design procedure for three types of feedback control, namely PD, BS, and SM will be presented. The nonlinear PD controller is used as the basic comparison for the nonlinear feedback controller and the adaptive feedforward controller presented in the following sections. The development of three feedback controllers is based on [66] Proportional Derivative (PD) Control After identifying the mathematical model and implementing the model into the Simulation, an initial nonlinear Proportional Derivative (PD) controller that based on [24] and [49] is developed to provide a basis for comparison for the nonlinear controllers presented in the following sections. Let be the desired pose of the vehicle in the earth-fixed frame,. An error vector is defined as the difference between the desired pose and the vehicle pose: (4.30 ) Consider the PID control law in the body-fixed frame: ( [ ( ( ] ( (4.31 ) For simplicity, it assumes that (PD control), and the control law becomes: 36

52 ( [ ( ( ] (4.32 ) The stability analysis is based on the assumption that and are positive definite diagonal matrices. The gains for these matrices were first tuned in simulation and then manually refined during field experiments. The block diagram of the PD stationkeeping controller described is provided in Figure Figure 4.13 PD station-keeping controller Although the PD controller is able to control the position of the USV moderately well around the target location, the heading oscillates constantly throughout the station keeping tests. The results support the assumption that linear controller cannot resist external disturbances. Nonlinear controllers, such as robust controller will likely adjust more quickly to the environmental changes, and to be more tolerant to model imprecision. Moreover, adding adaptive feature will adjust the uncertain parameter, such as the coefficients in the wind model, so as to improve overall control performances Backstepping Control Backstepping control theory was applied to station-keeping using the approach presented in [67] and [63]. Here only the final results with some necessary corrections are presented. Since the performance of the PD controller differed from that found during simulation, an MIMO backstepping controller was designed to overcome unmodeled dynamics and environmental disturbances. These two issues were considered to be the cause of high deviations between the simulated and experimental results. A virtual reference trajectory is first in the body-fixed frame and earth-fixed frame is defined as: (4.33 ) ( (4.34 ) Where is the derivative of the desired state of the vehicle, and, as we defined before. Here we assume that the reference trajectory is given by and are smooth and bounded. For the case of station-keeping of marine vehicles, the desired state 37

53 contains the desired position in the North-East-Down coordinate frame ( and ) and desired heading, while its derivative is since as the system approaches steady-state. represents the Lyapunov exponent gain matrix. Here is designed based on various candidates frequencies. Since multiple candidates exist, the selection is made by choosing the value that produces the slowest decay rate of the errors. Three different candidates were selected for : (4.35 ) (4.36 ) (4.37 ) where is the lowest resonant frequency expected, is the sampling frequency and sec is the largest unmodeled time delay. Since gives the minimum bandwidth, takes the following numerical form: [ ] [ ] (4.38 ) A measure of tracking also needs to be defined based on the Lyapunov exponents. This tracking surface is defined as: (4.39 ) The vector representation of equations of motion in earth-fixed frame is obtained by kinematic transformations: ( ( (4.40 ) ( ( ( [ ( ( ] (4.41 ) This yield the earth-fixed vector representation: ( ( ( (4.42 ) where ( ( ( (4.43 ) ( ( [ ( ( ( ] ( (4.44 ) ( ( ( ( (4.45 ) 38

54 ( (4.46 ) ( ( ( ( ( ( (4.47 ) where (. The backstepping design approach can be divided into the following steps: Step 1: The first backstepping variable is chosen as the error dynamics: (4.48 ) ( ( (4.49 ) Let be the virtual control vector, and define ( (4.50 ) where is the stabilizing functions to be designed, s is the second backstepping variable. Therefore, ( (4.51 ) The stabilizing function can now be chosen as: So that the position error dynamics can be written as: (4.52 ) ( (4.53 ) Choosing a positive definite CLF: (4.54 ) The derivative of with respect to time along the ( (4.55 ) (4.56 ) Step 2: The second CLF is chosen as: ( (4.57 ) 39

55 ( ( (4.58 ) [ ( ( ] ( ( ( ( (4.59 ) Using the skew-symmetry property [ ( ( ] (4.60 ) yields: ( ( ( ( ( (4.61 ) Hence the control law can be chosen as ( ( ( ( (4.62 ) where, and this results in: [ ( ] (4.63 ) Since is negative definite while is positive definite, the equilibrium point ( ( is GES. The error feedback control law for station-keeping then has the following form: (, are defined to simplify the implementation of nonlinear station-keeping controllers on the USV16. The simplification is based on three main assumptions: i. Negligible nonlinear drag : during station-keeping the vehicle speed. Therefore, much faster than. ii. Negligible off-diagonal terms for and : the effect of off-diagonal terms on the vehicle s dynamics during station-keeping is minimal compared to that of the diagonal terms. iii. The terms containing and in the centripetal matrix ( are negligible: a combination of approximate fore-aft symmetry and light draft suggest that the sway force arising from yaw rotation and the yaw moment induced by acceleration in the sway direction are much smaller than the inertial and added mass terms. After applying these simplifying assumptions, ( and ( reduce to: 40

56 [ ] (4.64 ) ( [ ( ( ( ( ] (4.65 ) [ ] (4.66 ) The control gains are assigned in two diagonal matrices ( and ) to eliminate errors in position, velocity, and orientation and yaw rate. The gains were initially chosen by modeling the controller in simulation, then manually tuned during in-water tests. The final result for control law is: [( ( ( ] ( ( ( ( ( (4.67 ) The block for the backstepping station-keeping controller described is provided in Figure Figure 4.14 Backstepping station-keeping controller Sliding Mode Control In this chapter, we will present the basic features of sliding mode control as well as the design implications. Compared to traditional linear control, sliding mode control can be designed more effectively since linearization is not required and it is robust to disturbances and model uncertainty. The designer can also flexibly tradeoff between model complexity and control performance. This feature of sliding mode control allows great simplification of the vehicle model, while still keeping system stability. A sliding mode controller that utilized in the previous study on the station keeping of the USV was adopted [68] [69] Models of vessels can be uncertain due to the error in the model structure or model parameter, or because some non-negligible terms have been dropped completely [33]. In general, robust control strategies 41

57 can be implemented to improve the response of a system when its dynamic model or the nature of the environmental disturbances that act upon it are uncertain. It is a nonlinear robust controller that accounts for model uncertainty, such as hydrodynamic terms of the USV model. Sliding mode can also simplify the design approach by reducing modeling effort. A robust sliding mode station-keeping controller was designed and implemented on the USV16 to mitigate slowly varying environmental disturbances, such as tidal currents, that the system cannot directly measure through its sensors. Applying sliding mode control, the gains and in the PD and backstepping control law are made hypothetically infinite and discontinuous, forcing the trajectories of the system to slide within a bounded sliding surface. As a result, the system diminishes its sensitivity towards parameters variations, including external disturbance and unmodeled dynamics. The advantage of this procedure is that the control signal is not required to be highly precise, since the sliding motion is invariant to small disturbances entering the system through the control channel. Sliding mode control theory was therefore considered highly suitable for the purpose of controlling a USV, tasked to maintain position and heading over an extended period of time, operating in an environment disturbed by slowly varying water currents. A linear function that specify a stable first order relationship between vehicle position and velocity error, as proposed by [33] is first defined as: (4.68 ) where is a constant matrix that set the break frequency of the desired first order error response. This linear error dynamics can be seen as a line that passes through the desired state, which is the point (. If the vehicle slides along the line, the desired dynamics are perfectly achieved. The line is called sliding surface, and the condition when vessel s real state slides along the surface line is called sliding condition. Sliding condition constrains vehicle state to point towards sliding surface. An integral term is added to account for slowly varying sources of errors. This shall enable the system to be more stable over extended periods of time, at the cost of requiring a longer period of time to reach steady-state. Therefore, the stable function can be expressed as: And a sliding surface can be defined accordingly: 42 (4.69 )

58 (4.70 ) Here,, are the same terms already defined in Section The robustness of the controller is therefore prioritized over its performance. The same integral term is also introduced, for the purpose of minimizing unmodeled environmental disturbances, in a newly defined reference trajectory: (4.71 ) Where is the derivative of the desired state as defined in the Section The control law then ensures that if the system deviates from the sliding surface, it is forced back to it. Once on the surface, the under-modeled system reduces to an exponentially stable, second-order system.. As a result, the system will possess considerable robustness against slowly varying external perturbations, like currents, and incorrectly modeled dynamics. It is suggested that the sliding controller design procedure is composed of two steps: first a model based control law that keeps the USVs state on a sliding surface if the model is perfect; the second element is a nonlinear feedback term that guarantees the achievement of sliding condition despite model imprecision and external disturbances. The sliding mode control law is similar to backstepping control law and is defined as follows: [( ( ( ] ( ( ( ( ( ( (4.72 ) The control law is composed of the terms [( ( ( ] ( ( ( ( that merely compensates for the known part of the dynamics, and the discontinuous part ( ( that guarantee a sliding condition, despite the disturbances and uncertainties. Although the desired target state for the uncertain nonlinear system can be achieved by the proposed control law, the control action is discontinuous, and the chattering could occur. The magnitude of the chattering depends on the uncertainties. In order to solve the undesirable chattering problem, the discontinue part of the control law is replaced by a continuous action, which can be expressed as: [( ( ( ] ( ( ( ( ( ( (4.73 ) 43

59 This method relaxes the constraint from perfectly sliding along the surface to allow a bandwidth limit, which means the dynamic state is allowed to depart a small distance from the desired surface. The tuning of the low pass filter enables a tradeoff between control precession and robustness. It can be noted that the only difference between the in backstepping and sliding mode is the last term. For the case of sliding mode control, the last term in the control law includes the bound on the uncertainties and the boundary layer thickness around the sliding surface, in place of the gains and in the backstepping control law. can be considered a positive definite diagonal gain matrix and is a vector defining the boundary layer within which the system will slide along the surface. The bound on the uncertainties in the last term of sliding mode controller acts similarly to controller gains and in for backstepping. The difference is that, once the system enters the boundary layer, the discontinuous control signal forces the system to slide along a cross-section of the state space, bounded by. In other words, as the system s errors are within specific boundaries dictated by, the control signal will vary based on, so that. A proper representation of such phenomena requires a three-dimensional plot to show the sliding surface bounded by and. For simplicity, an illustration of a linear signal for each element in and is given in a two-dimensional plot and can be seen Figure Figure 4.15 Illustration of Saturation Function for a single saturation argument for sliding mode controller. Both, the bound on the uncertainties matrix and the boundary layer thickness, were initially selected based on the results obtained while testing the PD and the backstepping controllers previously described, then tuned during in-water testing. More precisely, the values of all the terms in were chosen to be the average steady-state error resulting from on-water testing of the backstepping station-keeping controller described in the Section 4.2.2, while was treated as a gain matrix, and therefore, it was 44

60 iteratively tuned during experimental trials of the sliding mode controller described. It is important to note that that chattering and saturation of the control signal can compromise the functionality of the sliding mode controller, when used for the purpose of station-keeping heading and position of a USV. This was evident during sea trials. Fine tuning the values of and was therefore crucial to enable the vehicle to perform its desired maneuver. The control block for the sliding mode station-keeping controller described is provided in Figure Figure 4.16 Sliding Mode station-keeping controller. For the stability analysis, the sliding mode control law for the station keeping of the USV is an asymptotically stabilizing controller. The detailed proof can be found in the appendix 4.3 Wind Feedforward Control Based on the wind model of vehicle s motion and wind forces and moments discussed in section 4.1, the wind load can be calculated: [ ] [ ( ( ( ] (4.74 ) where apparent angle of attack. AFw and A Lw are the frontal and lateral projected windage area (Figure 4.3Fig. 4.4), is is the dynamic pressure as shown in section 4.1, where is the density of the air, and is the apparent wind speed. Both apparent wind speed and direction were measured with the ultrasonic anemometer described in Section Representative wind data, including apparent wind speed and direction are shown in Figure 4.17 and Figure The data was low pass filtered before being fed into the control system. The smoothed apparent wind speed and direction were also shown in Figure 4.17 and Figure The blue line represents raw wind speed and the red line is low 45

61 pass filtered wind speed. The wind speed oscillates, but the lengths of the cycles could not be read out easily. To find the period of wind speed, he autocorrelation of wind speed was first computed at zero lag, and then extended to positive and negative lags to ten minutes. For the wind with an average speed of 2.67 m/s that shown in Figure 4.17, the period was 32.4 seconds. The length scale of the large eddies was ( (. Therefore, for small size of USVs, one point measurment of wind information was sufficient enough to representative of the whole vehicle. Figure 4.17 Apparent wind speed collected from a stationary vehicle. 46

62 Figure 4.18 Apparent wind angle collected from a stationary vehicle. Apparent wind speed and angle of attack could also be estimated given the true wind speed and direction. This is often done when a weather station on land is used as primary sensor to estimate the wind disturbance [70], [71]. Since weather stations are rigidly fixed at a specific location on land, they are able to continuously measure true wind speed and direction. This approach requires, however, the major assumption that the characteristics of the wind at the weather station can be considered representative of the wind acting on the vehicle. This is only acceptable if the USV is performing within a short distance from the weather station on land. can then be decomposed in true wind velocity in each direction: ( ( (4.75 ) (4.76 ) Here, is the true wind speed in the direction, is the true wind speed in the direction. The true wind direction can also be calculated: (4.77 ) Here is the true wind angle of attack and is the vehicle s heading. Knowing the vehicle s surge ( ) and sway ( ) velocities from, the relative wind speed in the body-fixed coordinate frame in each 47

63 direction, and, can be calculated: (4.78 ) (4.79 ) Finally, the apparent wind speed and angle of attack in the body-fixed coordinate frame are obtained as follows: (4.80 ) ( (4.81 ) Thus, the wind forces and moment acting on the vehicle can be derived as long as either true or apparent wind speed and direction are given. For station-keeping maneuvers, the vehicle velocity as the system reaches steady-state, therefore it is assumed that, leading to and at all times. Based on the dynamic model of the USV16 and the wind model explained above, a wind feedforward controller was designed to mitigate the wind disturbance. In similar studies, it has been noted that the wind feedforward controller should be used with caution because it has the potential to make the system unstable or reduce the performance of the main feedback controller [3]. When the feedforward controller is implemented, the scheme is shown in Figure 4.12, Figure 4.13 and Figure 4.15 is modified to accommodate an additional control input that acts to oppose the wind forces and moment acting on the vehicle. is calculated based on the wind model in [24] The updated block diagram, which includes the wind feedforward controller, can be seen in Figure In addition to the state feedback, the control system utilizes two additional inputs: the apparent wind speed and direction. The wind data output by the anemometer are low pass filtered, using a moving average filter with a span of 20 samples, before being input into the feedforward controller. and are used in to calculate the wind disturbance, which is then subtracted from the output of the feedback controller, leading to: (4.82 ) Here is the output of the station-keeping controller, based solely on the vehicle state, and is a more accurate estimate of the output required that takes into account the effect of wind on the system. 48

64 is calculated utilizing both the anemometer output and the system state, while is based solely on the system state. Three adaptive controllers are derived by adding adaptive wind feedforward control to the nonlinear feedback controllers described in Section 4.2. Specifically, a wind feedforward PD stationkeeping controller similar to the one described in Section 4.2.1, a wind feedforward backstepping stationkeeping controller similar to the one described in Section and a wind feedforward sliding mode station-keeping controller similar to the one described in Section The control block for the wind model necessary for the wind feedforward controllers described is provided in Figure 4.19, and the block diagram of the control system with feedforward controller is shown in Figure Figure 4.19 Wind feedforward model. Figure 4.20 Block Diagram of WAM-V USV 16 Control System with Wind Feedforward 4.4 Adaptive Control Design Nonlinear adaptive controllers are usually directly derived from non-adaptive controller design strategies. In this section, adaptive schemes are derived based on the non-adaptive backstepping controller in and the sliding mode controller in In practical experiments, they can outperform non- 49

65 adaptive controllers by automatically adjusting unknown constants. In our case, the adaptive terms are the wind coefficients that can be assumed to be constant during our experiments. The basic steps of adaptive control involve first choosing a control law, which contains the parameters that need to be adapted, or choosing an adaptation law to adjust the uncertain parameters, and then analyzing the convergence of the resulting control system. Another alternative approach of designing an adaptive feedforward control is Model Reference Adaptive Control method, which can be seen in Appendix A. The method is based on Lyapunov s Second Law, and the stability of the controller is guaranteed. The design procedure of this new feedforward adaptive controller is inspired by the work of [12]. Figure 4.21 Block Diagram of WAM-V USV 16 Control System with Adaptive Wind Feedforward Adaptive Wind Feedforward with Backstepping Control First the position error, virtual reference trajectory, and tracking surface are respectively defined in the following equations, which are consistent with previous definition. (4.83 ) (4.84 ) (4.85 ) The meanings of the symbols shown here can be found in Section The Earth-fixed vector representation of the vehicle s dynamic motion is: ( ( (, (4.86 ) where, 50

66 ( ( (, (4.87 ) ( ( [ ( ( ( ] ( (4.88 ) ( ( ( ( (4.89 ) ( (4.90 ) ( (4.91 ) Using the definition of, we get. So that: ( ( ( ( ( ( (4.92 ) We first choose the positive definite LCF and differentiate along the dynamics. (4.93 ) derivative : For Since, we take as our second LCF (. Applying the control law we can get the following Lyapunov function ( ( (4.94 ) [ ( ( ] ( ( ( ( (4.95 ) Using the skew-symmetry property [ ( ( ] (4.96 ) yields: ( ( ( ( ( (4.97 ) Both ( and. Hence the control law can be chosen as ( ( ( ( (4.98 ) 51

67 where, is the estimated wind forces and moments. The difference between this control law and the one proposed in the backstepping controller is that we assume the wind loads are uncertain, so is used instead of. By defining, = (4.99 ) ( ( ) (4.100 ) where is a vector that determined by relative wind speed and relative wind angle From the equations (4.16) -(4.2) in section4.1.2, we can see that the true wind coefficient is [ ], and is the estimated diagonal wind coefficients matrix that will be adapted. We also define the wind loads estimation error as: This yields the final expression of : (4.101 ) [ ( ] ( (4.102 ) ( ( ( ( (4.103 ) Finally we choose as the third LCF. Differentiating along the solutions of the extended system gives: [ ( ] ( (4.104 ) In [66] it shows that the dynamic of wind forces varies over the time period of 80 seconds. The vehicle s response to wind disturbances is about 2-6 seconds, as will be shown in Section 5.1. In of Section 4.1.3, it shows that the vehicle s response to actuator forces falls between 3 to 10 s. Therefore, we can assume that since the dynamic of wind forces is much slower than the vehicle s dynamics. Since ( = ( [ ( ] ( ( (4.105 ) Choosing the adaptive update law for as: 52

68 ( (4.106 ) And this renders the Lyapunov function derivative globally negative semi-definite: [ ( ] (4.107 ) GES. Since is negative definite while is positive definite, the equilibrium point ( ( is Adaptive Wind Feedforward with Sliding Mode Control A sliding surface can be defined as: (4.108 ) Here,, are the same terms already defined in Section The robustness of the controller is therefore prioritized over its performance. The same integral term is also introduced, for the purpose of minimizing unmodeled environmental disturbance, in a newly defined reference trajectory: (4.109 ) [( ( ( ] ( ( ( ( ( ( (4.110 ) And (. 4.5 Control Allocation Control allocation module gives output from feedback and feedforward controllers, usually the forces and moment in surge, sway and yaw direction for a 3 DOFs system in an optimal manner. For an over-actuated differential thrust vehicles, the outcome of control allocation is the propellers RPM and azimuth angles (which is related to length of the linear actuator that described in Section ). The control allocation used on the USV control design will be briefly described in this Section. Control allocation is not the focus for this dissertation, and the work is mainly done in [66]. 53

69 Figure 4.22 Block diagram of control allocation in the USV control system The calculation from control forces to the actuators in terms of,,, and is a model based optimization problem [24]. The simplest condition is unbounded output. However, in the real situation the amplitude and rate of actuators are limited, and the control allocation becomes an constrained optimization problem. The thruster of the USV utilized in this dissertation also can rotate at the same time so that additional nonlinearities are produced, making the problem more complicated. The control allocation is not the focus of this dissertation, but the brief summary of our approach that based on previous study is presented below Extended Force Representation For the outputs of the controller,, let be the actuator forces in the surge and sway directions at each of the actuators, [ ] (4.111 ) A transformation matrix from the controller output force (or ) to the actuator frame force vector can be defined as: (4.112 ) where is generically defined in [72] as: [ ] (4.113 ) The constants and represent the longitudinal and lateral distances to the th actuator measured with respect to the vehicle center of gravity. The propulsion system mounted on the USV16 54

70 (Figure 3.3) consisted of two linear actuators and two thrusters, therefore. Thus, the generic equations are rewritten to define and for the system used: [ ] (4.114 ) [ ] (4.115 ) The subscripts and stand for the starboard and port sides, respectively. The solution to the allocation problem now rests in finding an inverse to the rectangular transformation matrix Lagrangian Multiplier Solution A cost function is set up to minimize the force output from each actuator subject to a positive definite weight matrix, { } The optimization problem is subject to the constraint (4.116 ), i.e., the error between the desired control forces and the attainable control forces is minimized. The weight matrix is set to skew the control forces towards the most efficient actuators. This is especially important for systems with rudders or control fins, as these actuators provide greater control authority with less power consumption. A Lagrangrian is then set up as in [71], ( ( (4.117 ) Differentiating ( with respect to, one can show that the solution for reduces to, where the inverse of the weighted transformation matrix is, ( If a vehicle has port/starboard symmetry with identical actuators, the weight matrix (4.118 ) can be taken as the identity matrix,, and the inverse of the transformation matrix becomes the Moore-Penrose pseudoinverse of the transformation matrix, ( Once the component force vector is found, a four-quadrant arctan function can be applied to find the desired azimuth angles ( and (, and to calculate the magnitude 55

71 of the thrust at each propeller and. The block for the control allocation described is provided in Figure Figure Control allocation using the extended thrust representation to convert from desired forces an extended thrust representation [66] to Owing to physical limitations on the travel of the linear actuators, the azimuth range of each propeller is from -45 o to +45 o. However, a 180 o offset from a value in this range is also attainable by reversing the propeller. A logic scheme is implemented on top of the control allocation that sets the thrust to zero if the allocation scheme requests an unachievable angle, and reverses it if an angle from -135 o to 135 o is required. This scheme is illustrated in Figure reverses thrust when and when. Thrust is set to zero, when and when. Careful tuning of controller parameters is necessary to ensure that these constraints are not violated. The approach produces a computationally efficient answer to the overallocation optimization problem, which is possible to implement on the USV s embedded processor. 56

72 Figure Control allocation logic [66] Due to the fact that the time responses of the thrusters and linear actuators aren t precisely modeled within the allocation scheme, the resultant forces and angles commanded are low-pass filtered with a user-set cutoff frequency to maintain a feasible response from the propulsion system. The low-pass filters used here are simple first order, infinite impulse response filters with a single time constant that is used to set the cut-off frequency. The time constant is set to conservatively match the actuator dynamics. Two separate low-pass filters were used to filter the control allocation output for the azimuth as well as thrust for each motor. The time constant for the thrust filter was found to be about an order of magnitude greater than that of the azimuth filter. 4.6 Simulation Tests This section presents the simulation model of the different feedback controllers, namely PD (PD controller), BS (backstepping controller), SM (sliding controller), the AFF (adaptive wind feedforward controller) and their combination. The simulation is performed in order to provide a functional development environment for future in-water tests. 57

73 The Matlab Simulink simulation has the following features: Simulation of an arbitrary number of controllers and test their controller performances repeated without putting considerable efforts. Environmental disturbances, such as wind can be added to the vehicle dynamic model. The error of wind speed and direction measured can be set randomly by the user. The feature of limited output of control forces can easily achieved by saturation function. Other features, such as the delay of USV motion to external disturbances can be easily acquired using the Simulink tool boxes. The simulator can read and export USV states, which can be used for comparison of real world dynamics and simulation results easily. This feature is illustrated in the Section for the proof of accuracy of system identification results. The overall layout of Simulink model is shown in Error! Reference source not found.. The simulator can be mainly divided into feedback controller, adaptive feedforward controller, control allocation, WAMV-USV plant model subsystems. The detailed subsystem models are presented in Appendix B. As we can see from Error! Reference source not found. that there are three switches in the model. Switch 1 enables switch between feedback control alone\feedback with adaptive feedforward control. Switch 2 enables and disables direct control. And the last one simulates USV control with wind disturbance and none disturbance situations. Before simulation of station keeping tests, the open loop free drifting tests were first simulated. The wind speed and data collected in previous experiments were used as wind disturbances, and there is no control input. In Error! Reference source not found. switch 1, 2, 3 switch to no feedforward, direct control, with wind disturbance respectively. 58

74 59

75 The comparison of the trajectory of open loop with wind disturbance, closed loop with BS controller as well as closed loop with BS & AFF in the simulation can be found in the following plots: Figure 4.25 Trajectory of Open Loop Control, Run 1 Figure 4.26 Trajectory of Feedback Control, Run 1 60

76 Figure 4.27 Zoomed Trajectory of Feedback Control, Run 1 Figure 4.28 Trajectory of Feedback & Adaptive Feedforward Control, Run 1 61

77 Figure 4.29 Zoomed Trajectory of Feedback & Adaptive Feedforward Control, Run 1 Figure 4.30 Control Forces of Adaptive Feedforward Control Run 1 62

78 Figure 4.31 Trajectory of Open Loop Control, Run 2 Figure 4.32 Trajectory of Feedback Control, Run 2 63

79 Figure 4.33 Zoomed Trajectory of Feedback Control, Run 2 Figure 4.34 Trajectory of Feedback & Adaptive Feedforward Control, Run 2 64

80 Figure 4.35 Zoomed Trajectory of Feedback & Adaptive Feedforward Control, Run 2 Figure 4.36 Control Forces of Adaptive Feedforward Control Run 2 65

81 Figure 4.37 Trajectory of Open Loop Control, Run 3 Figure 4.38 Trajectory of Feedback Control, Run 3 66

82 Figure 4.39 Zoomed Trajectory of Feedback Control, Run 3 Figure 4.40 Trajectory of Feedback & Adaptive Feedforward Control, Run 3 67

83 Figure 4.41 Zoomed Trajectory of Feedback & Adaptive Feedforward Control, Run 3 Figure 4.42 Control Forces of Adaptive Feedforward Control Run 3 The simulation results clearly show that without any control action the USV will drift easily even in mild wind exposure (around 40 m in one minute). After applying feedback controller, the vehicle can stay closely to the original station keeping point, with position error about 1 m. When the feedforward controller is implemented, the station keeping ability is further improved to within 0.5 m position error. However, other environmental disturbance such as current and model uncertainty are not included in the 68

84 simulation, so the results could be more optimistic than reality. 69

85 5 EXPERIMENTAL RESULTS In this chapter, on-water tests, including open loop drifting tests, closed loop feedback controllers, feedback with non-adaptive controllers, and feedback with adaptive wind feedforward controllers are presented. All the tests are conducted in the U.S. Intracoastal Waterway in Dania Beach, FL in Sea State 1 (SS1): average wind speed between 1 to 4 m/s, and wave height less than 0.2 meters. To minimize the effect of waves on the vehicle, no tests are performed on the open water. During tests, wind is the dominant environmental disturbance compared with wave and current. A small map illustrating the testing location and dominant current and wind directions is shown in Figure 5.1. Figure 5.1 Testing Location. 5.1 Drifting Tests In order to find the effects of wind on the USV, series of drifting tests were first conducted. The USV 16 was manually positioned with a desired heading and location. Then the vehicle was allowed to freely drift (with no propulsion or actuation) under environmental influences. State data (USV position, velocity) and wind information (wind speed, direction) were logged. A series of runs with the USV drifting 70

86 in different initial directions (so that the angle of attack to the wind changed if we assume the wind velocity roughly kept the same) were conducted. Figure 5.2 illustrates vehicle s trajectory during a representative drifting test. The blue line is USV s trajectory, and red arrows represent relative wind speed (length of the arrow) and wind direction (arrow direction). The scale is shown at the lower right corner. Note that the staircase pattern is a result of quantization of the GPS positioning data, i.e. the recorded changes in position are near the resolution of the GPS sensor. The vehicle was facing north at the starting point. The mean wind speed was 2.89 m/s, and the USV drifted 23 m in 56 s. Figure 5.2 USV trajectory and wind speed in drifting test, run 1. As it can be seen from the upper plot of Figure 5.3, the drifting speed follows the same trends as the wind speed, but with a time delay. To explore the correlation between drifting speed and wind speed, the correlation coefficient between drifting and wind speed is analyzed. In test 1, the peak value of the correlation coefficient is 0.54, and it occurs when the drift speed is shifted ahead by 5.18 s. In Figure 5.4, the drift speed and the wind speed closely match when the drift speed is shifted 5.18 s earlier in time. In order to reveal the relationship of wind and drifting speed, the plots of both values were normalized by scaling between 0 and 1 using the simple rule described by (5.1), where is the maximum value of variable, and is the minimum one. 71

87 Normalized ( (5.1 ) Another episode of drifting test results is also shown in Figure 5.5, Figure 5.6, and Figure 5.7. The delay of vehicle s response to wind disturbance is also shown in other drifting tests. The peak values of correlation coefficient range from , and time delay varies from 2 s-6 s in three experiments that were performed. Figure 5.3 Relationship between wind speed and vehicle drifting speed, run 1. 72

88 Figure 5.4 Relationship of shifted time and correlation coefficient of wind speed and vehicle s drifting speed., Run 1. The peak correlation coefficient value is 0.54, and it occurs at. Figure 5.5 USV trajectory and wind speed in drifting, run 2. 73

89 Figure 5.6 Relationship between wind speed and vehicle drifting speed, run 2. Figure 5.7 Relationship of shifted time and correlation coefficient of wind speed and vehicle s drifting speed, run 2. The peak correlation coefficient value is 0.40, and it occurs at s. 74

90 Figure 5.8 Relationship of shifted time and correlation coefficient of wind speed and vehicle s drifting speed, run 3. The peak correlation coefficient value is 0.62, and it occurs at =5.07 s. As we can see from the drifting tests, the USV drifts easily even with mild wind disturbances. The vehicle s movement is closely related to the wind, but with a time delay in the order of several seconds. This conclusion proves that with proper feedforward control, we can mitigate, or even offset the wind disturbance before it affects the vehicle. 5.2 Station Keeping Tests Station keeping tests were carried out at the same location as drifting tests described in Section 5.1. The wave disturbance is negligible, and the current caused by tidal flow is roughly in the same direction as the wind. The effect of the wave and tidal current disturbance on the vehicle are not estimated or measured as part of this research. The apparent wind speed and apparent wind direction are recorded directly from the vehicle during the experiments to quantify the sensed disturbance. The purpose of the station keeping tests is to explore the performances of the proposed adaptive wind feedforward controller combined with three different feedback controllers, namely PD, BS, and SM as discussed in Section 4.2.1, 4.2.2, and respectively. 75

91 5.2.1 Feedback With/Without Wind Feedforward Control In the first part of the station keeping tests, the control performances of six groups of control system: PD, BS, SM, PD&FF, BS&FF, and SM&FF are tested to explore the effect of wind feedforward control on station keeping control performance. In this part, the FF used is the non-adaptive feedforward version designed in Section 4.3, and the wind model is similar to the one presented in [24]. Five runs of station keeping tests were conducted for each group. Each run lasted at least 10 minutes and with the same initial conditions (position and heading). The relationship between wind spectrum, control efforts, and control performance are explored. The location and vehicle initial orientation is shown in Figure 5.1, and the duration is around 700 s. The wind turbulence is characterized by turbulence density, which is defined as the ratio of the root-mean-square of the fluctuating component of wind velocity and its time-averaged mean value [73], [74]. (5.2 ) where is the mean wind velocity, and is the fluctuating component of the longitudinal wind velocity. The performance of each feedback control was tested with and without the wind feedforward feature. All experiments were initialized by bringing the vehicle to its desired state manually using a remote controller outfitted on the GNC hardware. The system was then commanded to engage in autonomous mode and maintain its state for at least 600 seconds. This procedure allowed the controller to act on the vehicle at steady-state conditions with zero initial error. Previous sea trials showed that, if the stationkeeping command was given with an initial error in heading and position, all controllers were able to drive the system to steady-state rapidly. Heading and position were recorded throughout each run. To evaluate the performance of each controller, the errors in both heading and position were plotted. To evaluate the effectiveness of the wind feedforward feature, the state error was plotted for the same station-keeping controller with and without wind FF. PD with/without wind FF As previously mentioned, the PD controller was implemented to provide a baseline for the performance of the nonlinear robust controllers. Position and heading error for the PD station-keeping 76

92 controller, with and without wind FF are shown in Figure 5.9. The resolution of the GPS sensor is about 1 m, the position measurements exhibit step-like appearance. The apparent wind speed and direction are shown in Figure It can be seen that, while the USV position error is maintained below 1 meter most of the time, the heading error steadily fluctuates between -20 o and +20 o. The position error is the square root of errors in surge and sway direction, and heading error is the deviation from the desired heading at the beginning of the test in the earth-fixed frame. The blue solid line represents state feedback, which means with single PD controller, while the red dash line denoted control with both feedback and feedforward features. It is important to note that the PD station-keeping controller always demonstrates a similarly limited functionality. The PD controller s capability to station-keep the vehicle is only achieved by setting a very high heading gain. This results in a highly oscillating heading error, caused by the large control effort. The steady oscillation of the vehicle s heading enables it to hold the position, maintaining the position error always at or below 3 m. Usage of standard gain tuning techniques were not sufficient to reduce the heading error; minimal improvements in the heading performance causes a drastic increase of position error, resulting in an inability of the vehicle to hold position. Adding the wind feedforward portion to the PD station-keeping controller reduces position error, at the cost of intensifying oscillations of the vehicle s heading. From Figure 5.10, we can see that the apparent wind speed and heading keep roughly consistent during the station keeping tests for PD controllers. 77

93 Figure 5.9 Position and heading errors for PD with/without FF. 78

94 Figure 5.10 Apparent wind speed and heading for PD with/without FF. Figure 5.11 and Figure 5.12 show the relationship of position error and wind speed. Similar to the drift tests, the position error also had a time delay respect to wind speed (upper plot in Figure 5.11 ). Figure 5.12 gave the relationship of shifted time and correlation coefficient of wind speed and vehicle s position error for the PD station keeping test. The peak value is 0.61, and occurs when the shifted time is 9.9 s. Thus in the lower plot of Figure 5.11, the position error is in line with wind speed after it is shifted 9.9 s ahead. This indicates a strong influence of wind disturbance on the vehicle s station keeping drift speed. It can be seen that the FF improves the station keeping performance. Figure 5.13 and Figure 5.14 show the performance of the position error-wind speed relationship of PD &FF. Compared to the results shown in Figure 5.11 and Figure 5.12, the peak correlation coefficient drops from 0.61 to 0.36, indicating that the wind effects on the USV s station keeping performance decrease since the FF counteracts the wind disturbance before it affects vehicle position. 79

95 Figure 5.11 Relationship between wind speed and vehicle s position error for PD station keeping. Figure 5.12 Relationship of shifted time and correlation coefficient of wind speed and vehicle s position error for a representative PD station keeping test. The peak correlation coefficient value is 0.61, and it occurs at =9.89 s. 80

96 Figure 5.13 Relationship between wind speed and vehicle s position error for PD & FF. Figure 5.14 Relationship of shifted time and correlation coefficient of wind speed and vehicle s position error for a representative PD &FF. BS with/without wind FF The first robust controller implemented is the BS described in Section The results for the BS station-keeping controller, with and without FF portion are shown in Figure 5.15, and the wind condition is 81

97 shown in Figure Figure 5.15 Position and heading errors for BS with/without FF. Applying BS robust techniques for the purpose of station-keeping enables the USV to maintain position and heading over an extended period of time. As a result, the heading error is minimized while still maintaining a small (~1m) position error. Different from the PD controller, the capability of vehicle to hold position is no longer dependent on the need to maintain high and steady oscillations of the heading parameter. The rate at which the heading error varies is also heavily reduced, when utilizing the BS. The addition of wind FF doesn t cause any relevant variation in the heading error of the BS station-keeping controller, but reduce the position error slightly. Again, the wind disturbances on the two sets of station keeping tests are approximately the same (the average wind speeds are both around 2 m/s, and for the apparent wind directions). 82

98 Figure 5.16 Apparent wind speed and heading during BS with/without FF. SM with/without wind FF Another nonlinear robust controller implemented on the USV16 for the purpose of station-keeping is the SM described in Section As discussed before, the difference between BS and SM is the last term in the control force. SM (4.72) includes the bound on the uncertainties and the boundary layer thickness around the sliding surface, in place of the gains and in the BS law (4.62). It is expected that SM can show best control performances with external disturbances (such as unmeasured current) and model uncertainty (for instance, hydrodynamic terms of USV model). The results for the SMstation-keeping controller, with and without the FF portion are shown in Figure 5.17 and Figure

99 Figure 5.17 Position and heading errors for SM with/without FF. The siding mode controller outperforms both the PD and the BS in heading performance, without a significant increase in position error. Figure 5.17 shows the improvement since the error was contained and slowly varied within the boundary layer thickness throughout the experiments. Due to the good control performance of SM, there is only a little room for further improvement by applying wind FF. Appropriate tuning of the SM parameters is essential to maximize the performance of the SM. This involves precise tuning of the boundary layer thickness presented in The reason is that excessively reducing its values causes constant saturation of the control output resulting in large errors, and excessively increasing its value causes uncontrolled chattering that deviates the system from its desired state. The bound around the uncertainties, also had to be tuned accordingly, based on the controller performance. Extensive testing was carried out to manually refine these parameters, until the final values were identified [66]. 84

100 Figure 5.18 Apparent wind speed and heading during SM with/without FF. Figure 5.19 and Figure 5.20 show the heading errors of the PD, BS, and SMs with\without applying wind feedforward feature respectively. The data is the average of 5 runs for all six episodes. Although the wind speeds vary slightly during the tests, the averaged wind speed and direction can be assumed the same for all six runs. From Figure 5.19 we can see the PD controller gives the largest mean heading error, while the SM outperforms both the PD and the BSs. Figure 5.20 shows the performance of the controllers with wind feedforward added. Compared to the heading errors plotted in Figure 5.19, the overall heading error has been significantly reduced. The SM still gives the best performance. 85

101 Figure 5.19 Heading errors of the PD, BS, and SM. Figure 5.20 Heading errors of the PD, BS, and SM &FF. Table 5.1 shows the control effectiveness of six control groups is compared using multiple metrics, including mean wind speed, mean wind angle, mean position error, mean heading error, Integral Absolute Error of position, and Integral Absolute Error of heading. is a commonly used measure for comparisons between different control schemes, and. All the numbers are the mean values for 5 runs of each group. 86

102 Table 5.1 Comparison of the six controllers tested for station keeping averaged across five runs. Control Mode: PD BS SM PD&FF BS&FF SM&FF (m/s) ( ) (m) ( ) (m) (m) The robust nonlinear BS stepping and SMs are considered to perform well with small heading error, position error, and standard derivations of heading and position Robust Feedback with Adaptive Wind Feedforward Control The wind feedforward controller designed in Section 4.3 uses a simple non-adaptive model, with wind coefficients estimated according to the book from T. I. Fossen [24]. In this section, the adaptive schemes derived based on the non-adaptive BS in and SM in are tested in practical experiments. Theoretically, they can outperform non-adaptive when the wind coefficients are not well known. To evaluate the adaptive wind FF, on-water tests are carried out at the same location with the same initial condition as Since the wind and current were stronger on the testing day for adaptive controllers, we re-run the BS and SM with non-adaptive FFs as comparison groups. Similar to the tests in Section 5.2.1, multiple metrics including mean wind speed, mean heading error, mean position error, standard derivation of heading error, and standard derivation of position error are used to compare control performances of different groups. Backstepping with adaptive wind feedforward control The representative station keeping results of the position errors, heading errors, relative wind speed and data of both BS&FF and BS&AFF are shown in Figure 5.21, Figure 5.22, and Figure 5.23, and Figure

103 Figure 5.21 Position errors of BS &AFF. Figure 5.22 Heading errors of BS & AFF. 88

104 Figure 5.23 Apparent wind speed during station keeping tests of BS &AFF. Figure 5.24 Apparent wind direction during station keeping tests of BS & AFF. Sliding mode with adaptive wind feedforward control SM showed a better control performance compared with PD and BS. Since SM is the only feedback control approach that includes an integral term, the comparison of SM with/without adaptive FF 89

105 will be emphasized. Similar to the BS with adaptive wind FF, the SM with adaptive wind FF is also examined by on-water tests. Five runs have been carried out for each controller. The results of one representative run are shown in Figure 5.25, Figure 5.26, Figure 5.27, and Table 5.2, and more results can be seen in Appendix C. In the table, BS&AFF and SM&AFF stand for BS feedback with AFF and SM feedback with AFF respectively. Figure 5.25 Position errors of SM & AFF. 90

106 Figure 5.26 Heading errors of SM &AFF. Figure 5.27 Apparent wind speed during station keeping tests of SM &AFF. 91

107 Figure 5.28 Apparent wind direction during station keeping tests of SM & AFF. Table 5.2 Station keeping control performances of BS&AFF and SM&AFF averaged across 5 runs. Control Mode: BS&AFF SM&AFF (m/s) ( ) (m) ( ) (m) (m) Station Keeping Experimental Results Summary In this section, station keeping of eight controllers, PD, BS, SM, PD&FF, BS&FF, SM&FF, BS&AFF, and SM&AFF are tested on a full scale USV model. Each group of controller includes at least 5 runs of station keeping tests, and the averaged results are shown in Table 5.1, Table 5.2 and Table 5.3. PD control mainly serves as the compression group for other controllers. Table 5.3 indicates the control performances of other controllers compared with PD controller when wind speeds are unitized. For 92

108 example, the (m) of SM&AFF is reduced by 86% compared with PD if the wind speeds are the same during PD and SM&AFF station keeping tests, which is highlighted in Table 5.3. Table 5.3 Comparison of the eight controllers with PD for station keeping averaged across 5 runs with unitized wind speed. Control PD BS SM PD&FF BS&FF SM&FF BS&AFF SM&AFF Mode: (%) 0% -17% -22% 6% -51% -42% -55% -65% (%) 0% -4% -27% -23% -56% -54% -56% -58% (%) 0% -33% -44% -23% -46% -74% -71% -73% (%) 0% -44% -49% -34% -67% -76% -79% -86% From the comparison of PD, BS, SM we can see that the robust controller BS and SM outperform PD control with to a large extent (e.g. 33% and 44% decreases of, 44% and 49% reduces of ), and SM achieves slightly better results than BS. This conclusion for three feedback controllers evaluation is also supported by the comparisons of PD&FF, BS&FF, and SM&FF. The effects wind FF on station keeping performances can be seen by comparing controllers PD vs PD&FF, BS vs BS&FF, SM vs SM&FF. It clearly shows that wind feedforward feature is beneficial for all of three controllers in all aspects. Finally, BS&FF vs BS&AFF, and SM&FF vs SM&AFF evaluate the effectiveness of adaptive mechanism. As we can see that BS&AFF reduces the and by 25% and 12% respectively compared with BS&FF, and 12% and 10% reduction of and from SM&FF to SM&AFF. In a nutshell, the SM&AFF gives the best station keeping control performance among all the eight groups of controllers with averaged position and heading error of 0.32 m and 4.76 degree. n see that SM&AFF is the best controller of all the eight groups of controllers. It can reduced the IAE_ψ by 128% compared to PD control. n see that SM&AFF is the best controller of all the eight groups of controllers. It can reduced the by 128% compared to PD control. 93

109 6 CONCLUSIONS An adaptive wind feedforward and three feedback controllers (PD, BS, and sliding mode) have been designed and tested, both in simulation and experiments, on a 16 foot USV. The wind FF with a novel adaptive approach developed in this research greatly improved the vehicle s station keeping performance in calm water with moderate wind disturbance. 6.1 Research Significance The result is of great significance because as surface vehicles are commonly light weight and have relatively large windage areas, they are fairly susceptible to wind disturbances. It was found in this research that wind FF has the capability to significantly mitigate, or eliminate wind disturbances. The mathematical model of wind forces is required in the FF. However, wind models for marine vehicles, especially small size USVs are poorly defined. An adaptive controller is advantageous because it reduces dependence on poorly defined wind models. The wind FF is also combined with classic feedback control to optimize the control system, and a great station keeping performance (position error within the GPS resolution 1 m, and less than 5.6% heading error) of the USV is achieved. Station keeping is critical for various tasks of USVs, and enhanced station keeping performance will expand their applications. Furthermore, the proposed adaptive wind FF was designed without any assumption regarding the vehicle type and wind condition, thus it can be implemented on different type of marine vessels and environments. 6.2 Dissertation Achievements The design of feedforward & feedback control on a USV requires a comprehensive study of the modeling, simulation, controller design, and field tests of the USV. The dissertation presented the following achievements: A 3 DOF mathematical model of the vehicle is first developed. The terms in the inertia matrix are either measured or estimated by theoretical formulas. System identification tests, including acceleration 94

110 tests, circle tests, and zig-zag tests, are conducted to identify hydrodynamic terms. The simulation results show that the simulation model is representative of the WAM-V USV16. This model can be utilized for the design and development of station keeping controllers. A FF was designed to augment three existing feedback control, namely PD control, BS, and SM. The effectiveness of the FF depends on many factors: the reliability of measured relative wind speed and direction, the accuracy of wind coefficients in the wind model, and so forth. The anemometer chosen for this work is an ultra-sonic, high resolution, wide range sensor. It is installed at the highest point on the aft of the USV, so that the interference of anemometer with other super structures on the vehicle is minimized. The wind coefficients are first estimated from the literature, and then an adaptive mechanism of the gain matrix on the FF was developed to improve control performance. Two adaptive laws are developed: adaptive FF based on BS, and adaptive FF based on SM. The adaptive algorithms are based on Lyapunov theory, and the stability is guaranteed. Both feedback and FF were built based on the vehicle s model developed through system identification tests. A Matlab simulator was designed to support the development of the station keeping controllers. The overall system of the simulator is shown in Section 4.6, and the detailed subsystems are attached in Appendix B. The simulator is augmented with an AFF feature. With the switches in the simulation model, we can test three different scenes: open loop simulation test with no control input and wind disturbance, nonlinear feedback control, and feedback & AFF. The results clearly show that without any control action the USV will drift easily even in mild wind exposure (around 40 m in one minute). After applying feedback controller, the vehicle can stay closely to the original station keeping point, with position error about 1 m. When the FF is implemented, the station keeping ability is further improved to within 0.5 m position error. However, other environmental disturbance such as current and model uncertainty are not included in the simulation, so the results could be more optimistic than reality. On-water experiments are also carried out to test control performances of different controllers. In free drift tests, the vehicle s drifting velocity and wind speed showed a strong correlation, especially if the drift speed is shifted 2-10 s earlier in time. The control performance of PD, BS, and SM can be compared in Table 5.1. The mean wind speed was slowest during PD controller test, but it gave larger mean 95

111 position error, mean square deviation of both heading and speed error. This means that the nonlinear BS and SMs can resist wind disturbances better than the linear PD controller. The overall control performances improved with wind feedforward feature, which suggests that the wind is offset by the FF before acting on the vehicle. The comparison of each controller without & with wind FF added shows that wind feedforward feature is beneficial for all three feedback controllers. Another set of on-water tests is the station keeping of two robust feedback controllers (BS and SM) combined with AFF. In order to understand the effects of the adaptive mechanism, the episodes of station keeping with BS or SM feedback controller alone are also conducted. The multiple measures including mean wind speed, mean wind angle, mean position error, mean heading error, Integral Absolute Error of position, and Integral Absolute Error of heading.are utilized to compare station keeping performances with non-adaptive\adaptive wind FF, and the results are shown in in Table 5.1, Table 5.2, and Table 5.3. The station keeping performances are slightly improved with the adaptive feature. However, due to the limitation of the resolution of GPS and other sensors, the accuracy of position measurement of the USV is only about 0.5 m, and the vehicle cannot obtain smaller position error than that. 6.3 Future Work The research presented in this dissertation can be expanded in many aspects. Some of the future research is suggested: Wind intensity is an important factor that influences the experimental results. It is assumed that the wind equally disturbed station keeping performances of all controllers. Averaged results from 5 groups of tests can further reduce environmental differences. The wind speed during the tests was relative low (1-3 m/s). Higher wind speed (up to 11 m/s) also frequently occurs, and in that situation, wind feedforward may perform better. It would be helpful to understand more about the limitation and effectiveness of the adaptive wind FF if we can test it in stronger wind conditions. These developments are based on a USV, but are also generic to a lot of other types of vehicles in the future work. Furthermore, as this dissertation focuses on the station keeping of USVs, the controller designed could also be modified to utilize in other tasks, such as trajectory tracking control. The proposed 96

112 adaptive wind FF is only applied to station keeping of a USV. The performances of other motion control, for example trajectory tracking, may also improve by adding the AFF feature. A natural continuation on this dissertation is to install a current sensor to acquire current information and feed it into FF. This would be especially helpful when the current and wind loads are dominant, while wave disturbance is minimum. 97

113 APPENDIXES 98

114 Appendixes A. Model Reference Adaptive Control Starting by the nonlinear equations of motion of body-fixed frame: ( ( (6.1 ) The control law can be chosen as: ( ( (6.2 ) The terms with superscript are the ones unknown and need be adapted. Thus, the control law can be rewritten as: ( ( (6.3 ) Using (4.49), (4.45) becomes: ( ( ( ) ( ) (6.4 ) Suggest a linear reference model: (6.5 ) The error model is defined as: Therefore we obtain: Substitute (4.54) into (4.45), we can get: (6.6 ) (6.7 ) (6.8 ) ( ( ( ( ) ( ) (6.9 ) ( ( ( ( ) ( ) (6.10 ) ( ( ( ( ) ( ( ) (6.11 ) Choosing a positive definite control Lyapunov functions (CLF): { ( ( ( ( )) ( ( ) } (6.12 ) 99

115 The symbol is trace, and is a 3-by-3 positive adaptation gain matrix. The trace of an n-by-n square matrix, which is 3-by-3 in our case, is defined to be the sum of the elements of the main diagonal. ( So that (4.58) can be expanded to: { ( ( )) ( ( ) } (6.13 ) The derivative of V with respect to (w. r.t) time gives: { [( ( )) ( ) ( )( } (6.14 ) To eliminate the uncertainty terms, the update laws are chosen as: (6.15 ) (6.16 ) (6.17 ) Which results in: ( (6.18 ) The inertia term and the coefficient of reference model so that It can be concluded that the origina of the error system is uniformly globally asymptotically stable (UGAS) by using the theorem from [62]. 100

116 101

117 102

118 Figure A. 1 Visualizer of WAM-V USV