International Journal of Civil Engineering and Technology (IJCIET) Volume 9, Issue 3, March 2018, pp. 896 905, Article ID: IJCIET_09_03_089 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=9&itype=3 ISSN Print: 0976-6308 and ISSN Online: 0976-6316 IAEME Publication Scopus Indexed TOWARD DEVELOPMENT OF CONTROL SYSTEMS FOR AIRSHIPS UNIFIED TO THEIR TECHNICAL CHARACTERISTICS AND ACTUATORS Fedorenko Roman, Gurenko Boris, Konovalov Georgy, Devitt Dmitry Southern Federal University, Bolshaya Sadovaya ul. 105 / 42, Rostov-on-Don, 344006, Russia ABSTRACT The goal of this work is to give a review of task and approaches of development of control systems for airships, unified to their technical characteristics and actuators in format and limits of an article. Starting with unified control system structure, universal mathematical model of airship is given, external forces discussed as far as unified actuators mathematical model is given. Review of airship actuators was done and control allocation methods are discussed. Finally, technical details of modular control and actuation system for small blimps of non-conventional form is presented. Keywords: airship, blimp, control, actuator, mathematical model, control allocation, unified control system. Cite this Article: Fedorenko Roman, Gurenko Boris, Konovalov Georgy, Devitt Dmitry, Toward Development of Control Systems for Airships Unified to Their Technical Characteristics and Actuators, International Journal of Civil Engineering and Technology, 9(3), 2018, pp. 896 905. http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=9&itype=3 1. INTRODUCTION Advantages of airships possibility of long flight and hovering in areas with weak infrastructure, are realized best in automatic unmanned mode. Consequently, the development of methods for the design of automatic control systems for airships is actively conducted all over the world. At the present time, the requirements for airship control systems are increasing with regard to the requirement of their wide configuration, which is related to the market demand in a unified control system applicable to airships of various designs. Separate control systems for each design of airships development appears to be economically inefficient, since airships are produced by various companies in small series. Thus, developing of methods for designing control systems for airships challenges are on the one hand using most advanced control approaches (nonlinear model based), and, on the other hand, unification to technical characteristics of airships and design of their actuators. http://www.iaeme.com/ijciet/index.asp 896 editor@iaeme.com
Fedorenko Roman, Gurenko Boris, Konovalov Georgy, Devitt Dmitry The airship control approaches available at the moment make it possible to obtain a control law to calculate the desired forces and moments [1-3]. But these forces and moments implementation through actuators task, as far as controllability and stability of the system assessment tasks are solved by the developer on the basis of expert knowledge in each particular case [4, 5]. Most of the control systems being developed at the moment include a preliminary separation of the control channels and are intended for certain specific instances of airships. The issues of their unification have not been resolved. In the real control system, the controls are constrained due to the design and energy limitations of the actuators. It is obvious that a closed system can become unstable, if such constraints are not taken into account, which is unacceptable in real systems. Thus, the solution of the problem of designing control systems for airships, unified to their technical characteristics and the design of actuators, should be solved with controls constraints accounting. In addition, the reliability requirements for aviation technology lead to the need to work in emergency mode in the event of failure of any actuator, which also requires the use of technologies for automatic reconfiguration of the control system 2. UNIFIED CONTROL SYSTEM FOR AIRSHIPS STRUCTURE Unified control system for airships structure is shown at fig. 1. It shows two main configuration blocks for unified airship control system: design of actuators (type, quantity, arrangement, etc.) and technical characteristics of the actuators (the dependence of the generated force or torque on the control, speed, constraints, etc.); technical characteristics of the airship (mass-inertial, aerodynamic and aerostatic, etc.). Navigation system Sensors State estimator Planner Basic control laws Control allocation Actuators Environment Mathematical model parameters Actuators configuration Figure 1 Structure of the unified control system of an airship Also, approach of allocation and basic control law decomposition is illustrated. http://www.iaeme.com/ijciet/index.asp 897 editor@iaeme.com
Output Toward Development of Control Systems for Airships Unified to Their Technical Characteristics and Actuators 3. MATHEMATICAL MODEL 3.1. Basic airship mathematical model Airship kinematics equation is composed of the body to earth frame rotations for linear velocities vector and angular rates : [ ] [ ] (1) where,, are body frame coordinates, Euler angles of roll, pitch and yaw, body to earth frame rotation matrix, 3x3, Euler angles rates body to earth frame rotation matrix, 3x3. x, y, z γ, θ, ψ Flight controller U Actuators γ, θ, ψ x, y, z x, y, z x, y, z γ, θ Gravity Kinematics γ, θ, ψ γ, θ, ψ γ, θ, ψ γ, θ Buoyancy Aerodynamics coefficients c x, c y, c z m x, m y, m z V w, ω w ρ Aerodynamics F, M U Dynamics Power calculation V, ω P P E α, β Angles of attack and sideslip V w, ω w ρ V w, ω w Environment model x, y, z γ, θ, ψ Figure 2 Structure of the mathematical model of the airship Airship dynamics equation is composed of the translational and rotational motion equations: [ ] [ ( ( )) ] (2) where is airship mass, inertia tensor, 3x3, resultant force in body frame, 3x1 vector, resultant force moments in body frame, 3x1 vector. Resultant force and it s moment consist of gravitational, buoyancy, aerodynamics and actuators control forces and moments. Forces and moments listed could be estimated http://www.iaeme.com/ijciet/index.asp 898 editor@iaeme.com
Fedorenko Roman, Gurenko Boris, Konovalov Georgy, Devitt Dmitry analytically and using observer. Parameters for such estimation are airship body parameters (mass distribution, buoyancy gas volume), aerodynamics coefficients and so on. Please, refer [6] for mathematical model details, annotation, coordinate frames conventions. Airship model structure is shown on diagram at fig. 2. This structure diagram shows the interconnection of model parts. Kinematics and Dynamics, supplemented by the integration block, constitute together a basic rigid body model. External forces calculation is performed by Gravity, Buoyancy, Actuators and Aerodynamics blocks. Sum of forces and moment calculated by these blocks forms resultant force and its moment. Aerodynamics coefficients are calculated as functions of angles of attack and sideslip by Aerodynamics coefficients block, using Angles of attack and sideslip and Environment model blocks data. 3.2. Actuators mathematical model Airship control system acts by means of control forces and moments,, formed by individual actuators forces and moments. where,, is number of actuators. Actuators scheme configuration is another parametrization of unified airships control system (in addition to airship body parameters). Airships control schemes (actuators configuration) review is done further, as well as control allocation task formalizations and approaches review. In the general, in order to obtain the complete system of equations of an airship as a control object, its equations of kinematics and dynamics (1), (2) are supplemented by equations of the dynamics of actuators, which have the following form: where the vector of actuators state (rotational speed of the propellers, the angles of rotations of the thrust vectors, etc.); T, K diagonal matrices of time constants and gains of actuators; U vector of actuators controls, generated by the control system. In the case where the actuator time constants are much less than the time constant of an airship, the matrix of time constants T in equation (3) is usually neglected. 4. BASIC CONTROL LAW The control systems of airships can be classified on linear and nonlinear; with the separation of the model of motion into longitudinal, transverse and multiply connected; with the function of motion planning and without it; non-adaptive and adaptive. There is a large set of publications on this subject, however, most of these regulators have the desired forces and moments at the output. In the future work the authors will use control algorithms design based on method of position-trajectory control of vehicles [1]. Control law has following form: http://www.iaeme.com/ijciet/index.asp 899 editor@iaeme.com
Toward Development of Control Systems for Airships Unified to Their Technical Characteristics and Actuators (3) where is matrix of airship mass and inertia, vector of dynamic and external forces, vector of disturbing forces and moments, [ ] [ ],, where,,,, matrices of given path and speed of airship. 5. AIRSHIP ACTUATORS The arrangement of actuators implementing control forces and moments is important characteristic in construction of control systems for airships. The modern airship has a complex actuators scheme that involves the use of aerodynamic controls, the variation of the thrust vector of the engines, as well as the change in the centering of the aircraft mass and the pressure of the lift gas with ballonets. The basic layouts of the airship actuators include: one thruster with variable thrust vector scheme; classical pylon arrangement of actuators; scheme with thrusters with a bi-directional thrust vector; schemes with several pairs of actuators; schemes with additional actuators in the tail. a b c d Figure 3 Examples of airship actuators arrangement, a - the gondola of the airship Au-11 with one propeller and controlled thrust vector, b - the scheme of this design, c - the arrangement of the Aeros 40D airship propellers, d - a scheme with two propellers http://www.iaeme.com/ijciet/index.asp 900 editor@iaeme.com
Fedorenko Roman, Gurenko Boris, Konovalov Georgy, Devitt Dmitry a b c d e Figure 4 Examples of airship actuators arrangement, a - Skyship 600 airship propellers on the hinged connection, b - Stratospheric Lockheed-Martin HAA airship, c - four-propeller design, variants for spherical aerospace d - Aerotain and e - Spacial drone In a scheme with a single propulsor with a variable (in the vertical longitudinal plane) thrust vector, the propulsor is fixed in the lower part of the airship closer to the nose (see Fig. 3a). The deviation of the thrust vector allows to take off and accelerate to speeds sufficient for engaging the aerodynamic rudders. The classical arrangement of the actuating elements (Figure 3b) assumes the presence of two propellers that can be rotated independently of each other in a vertical plane and adjust the thrust (by changing the rotational speeds of propellers). When using a one thruster and a two-engine pylon schemes, it may also be advisable to use additional steering motors that are used in the mooring and sailing mode. Effective scheme of actuators arrangement is a scheme with two propellers located on a gimbal suspension (Fig. 4a). In this case, the control system designer has 6 control channels, but this scheme is complex and has practical disadvantages. Depending on the design of the airship and its purpose, more than two propulsors can be used (Fig. 4b, c). The arrangement of propellers according to Fig. 4b allows to control the pitch angle, creating a pitch moment, even at low air speeds. The peculiarity of such schemes includes some redundancy of the control channels. To increase the maneuverability of the airship, in some cases, in addition to the pylon scheme, tail actuators are used, creating additional forces and moments (longitudinal force and moments around the vertical axis and pitch angle). This scheme is used in Zeppelin NT and Airlander 10 airships (Figure 5a, b). a b c d e Figure 5 Examples of tail actuators of the airship, a-zeppelin NT, b - Airlander, the tail aerodynamic surfaces of the airship c - Aeros 40D, d - A-60, e - Zeppelin NT In addition to the main propulsors, large multifunctional airships are also equipped with aerodynamic surfaces. The most common are schemes with four aerodynamic surfaces in the form of "x" and "+" or with three surfaces arranged in the form of an inverted Y located in the tail (Figures 5c, d, e) are used. http://www.iaeme.com/ijciet/index.asp 901 editor@iaeme.com
Toward Development of Control Systems for Airships Unified to Their Technical Characteristics and Actuators Note that the above schemes of the arrangement of actuators are used for airships of the classical cigar-shaped form, while for airships of non-standard forms there are even more variants of the number and location of the actuators [7] (Fig. 4d, e) 6. CONTROL ALLOCATION Thus, the task of distributing the control forces and the moments produced by the control system or the pilot on actuators is important, which in general requires special approaches. Let s write down the forces and moments created by some actuator with thrust located at the position determined by the radius vector in the body coordinate system and fixed with the orientation determined by the rotation matrix with respect to the associated coordinate system. We also assume for this model that the actuator has a variable thrust vector. Let, the i-th actuator thrust vector could rotate by an angle of a pitch from a horizontal axis (in a OXY plane of the coordinate system connected with it). Then i-th actuator s thrust vector in body frame is calculated by: [ ] [ ] [ ] (4) Actuator s torque (in body frame) is calculated as follows: [ ] [ ] (5) For further use, we also introduce controls constraints for the i-th actuator: (6). (7) The total force and moment created by all actuators are determined by the expressions: [ ] [ ] [ ], (8) [ ] [ ] [ ] [ ]. (9) We denote the combined vector of forces and moments of the actuators by : [ ]. (10) Let us also designate the vector of desired (obtained from the automatic control system or operator) forces and moments through. http://www.iaeme.com/ijciet/index.asp 902 editor@iaeme.com
Fedorenko Roman, Gurenko Boris, Konovalov Georgy, Devitt Dmitry Control law or operator τ ref Control allocation α T Airship Figure 6 The task of control allocation We form the problem of control allocation as a minimization problem according to [8]: { ( ) ( ) ( ( ) ( )) } (11) subject to, (12), (13), (14). (15) The total power consumption is represented by the first term in the criterion, combining the power consumptions of the individual actuators. The second term penalizes the error between the commanded and achieved generalized force. This slack variable formulation is necessary in order to guarantee that the optimization problem always has a feasible solution. The diagonal weights in the matrix are chosen so large that the constraint is satisfied with whenever possible. The maximum and minimum thrusts produced by the actuators and angles of their rotation are specified through the constraints (13), (14), where means that the inequality is taken element-wise over the vectors left and right. Moreover, the rate-of-change in actuators rotation angles is constrained and minimized such that a large change is only allowed if this is necessary, represented by the third term ( ) ( ) in the criterion and the constraints (15). The matrix is used to tune this objective, and the vector contains the azimuths at the previous sample. Singularity is avoided through the fourth term in the criterion, where is required to avoid numerical problems and is a weighting parameter, ( ) is control matrix formed from equation (8), (9). Essentially, a large will lead to high maneuverability as the cost of increased steady-state power consumption. Conversely, a small will give low power consumption under steady-state conditions at the cost of reduced maneuverability with highly dynamic commands [8]. Dynamic reconfigurability and fault handling can be achieved by dynamically changing the constraint limits or weighting matrices. Works [9] shows possible approaches for solving this nonlinear non-convex optimization problem, including its linearization and using QP and MPC approaches, as far as explicit solution using Lagrange Multipliers for simplified task without actuators limitation applied for boat actuators model. Similar approaches could be applied for airship unified model (8), (9) and is focus for authors further publications. http://www.iaeme.com/ijciet/index.asp 903 editor@iaeme.com
Toward Development of Control Systems for Airships Unified to Their Technical Characteristics and Actuators Work [2] show a pseudo-inverse matrix approach for explicit control allocation problem for airships with no actuators limitation applied and note, that actuator limits introduction requires further development. 7. SMALL BLIMPS UNIFIED MODULAR CONTROL SYSTEM EXAMPLE Unified control system development approach presented is proposed for application on advertisement and entertainment blimps. Main trend with such blimps is unconventional forms of envelopment, requires non-standard control approaches. The modular distributed structure of airship actuators makes it possible to create and control envelopes of arbitrary shape and of various sizes by the requirements of the customer. Due to the arbitrary form of the airship envelope, installation of various lighting, audio and video equipment, this form of providing information differs from existing analogues of advertising sources.. a b c d Figure 7 Control system modules The following basic modules of the control system are proposed: the base module with the on-board computer and navigation system, the actuator module, the sensor module, the video camera module, the control panel (Fig. 7). Airships of various shapes and sizes can be equipped with an arbitrary required number of actuator modules, as shown in Fig. 8. Figure 8 Examples of different control system modules configuration for airships of nonconventional shape 8. CONCLUSIONS This work gives a review of task and approaches of development of control systems for airships, unified to their technical characteristics and actuators in format and limits of an article. Starting with unified control system structure, universal mathematical model of airship is given, external forces discussed as far as unified actuators mathematical model is given. Review of airship actuators was done and control allocation methods are discussed. Finally, technical details of modular control and actuation system for small blimps of nonconventional form is presented. http://www.iaeme.com/ijciet/index.asp 904 editor@iaeme.com
Fedorenko Roman, Gurenko Boris, Konovalov Georgy, Devitt Dmitry Note that when airship is not able to generate some force or moment in due to its actuators configuration, basic control law should also be configured to take this into account. Such configuration example using mass-inertia matrix modification is shown in [2] and could be generalized in further work. The further work of the authors is devoted to detailing the described elements of the unified control system of airships. ACKNOWLEDGMENTS This work was supported by grants of the President of the Russian Federation for the state support of young Russian scientists MK-142.2017.8 "Development of methods for airships control systems design unified to their technical characteristics and actuators", MK- 3089.2017.8 "Methods for developing of an intelligent group control system of autonomous marine robotics". The authors are grateful to the Council on Grants of the President of the Russian Federation for this support. REFERENCES [1] Pshikhopov, V., Medvedev, M., Kostjukov, V., Fedorenko, R. et al. (2011). Airship Autopilot Design. SAE Technical Paper. doi: 10.4271/2011-01-2736. [2] Pshikhopov, V.Kh., Medvedev, M.Yu., Gaiduk, A.R., Fedorenko, R.V., Krukhmalev, V.A. and Gurenko, B.V. (2014). Position-Trajectory Control System for Unmanned Robotic Airship. IFAC Proceedings Volumes, vol. 47, iss. 3, pp. 8953-8958. doi: 10.3182/20140824-6-ZA-1003.00393. [3] Chen, L., Zhou, H., Wen, Y. and Duan, D. (2015). Control of the horizontal position of a stratospheric airship during ascent and descent. The Aeronautical Journal, 119(1214), 523-541. doi:10.1017/s0001924000010599 [4] Fedorenko, R., Krukhmalev, V. (2016). Indoor Autonomous Airship Control and Navigation System. MATEC Web of Conferences 42 01006. doi: 10.1051/matecconf/20164201006 [5] Chen, L., Zhou, H. and Duan, D. (2013). Control system design of a multivectored thrust stratospheric airship. Journal of Aerospace Engineering, vol. 228, iss. 11, pp. 2045-2054. [6] Pshikhopov, V. et al. (2013). Mathematical model of robot on base of airship. 52nd IEEE Conference on Decision and Control, pp. 959-964. doi: 10.1109/CDC.2013.6760006 [7] Burri, M. et al. (2013). Design and control of a spherical omnidirectional blimp. IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 1873-1879. doi: 10.1109/IROS.2013.6696604 [8] Johansen, T.A., Fossen, T.I. and Berge, S.P. (2004). Constrained nonlinear control allocation with singularity avoidance using sequential quadratic programming. IEEE Transactions on Control Systems Technology, vol. 12, no. 1, pp. 211-216. doi: 10.1109/TCST.2003.821952 [9] Fossen, T.I, Johansen, T.A. and Perez, T. (2009). A Survey of Control Allocation Methods for Underwater Vehicles. Alexander V. Inzartsev (Ed.), InTech, DOI: 10.5772/6699. Retrieved from URL: https://www.intechopen.com/books/underwater_vehicles/ a_survey_of_control_allocation_methods_for_underwater_vehicles [10] Zheng, Z., Liu, L. and Zhu, M. Integrated guidance and control path following and dynamic control allocation for a stratospheric airship with redundant control systems. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 230, iss. 10, pp. 1813-1826. http://www.iaeme.com/ijciet/index.asp 905 editor@iaeme.com