IN recent years, there have been increasing activities related

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1 2824 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 20, NO. 6, DECEMBER 2015 A Study on Position Mooring System Design for the Vessel Moored by Mooring Lines Sang-Won Ji, Myung-Soo Choi, and Young-Bok Kim, Senior Member, IEEE Abstract This paper presents the experimental results about position mooring (PM) system applied to the barge ship. The aim of the PM is to maintain the position and motion of the ship s surge and sway directions as desired. In this paper, a system consisting of a barge vessel and mooring lines is mathematically modeled. The position and orientation of the vessel is controlled by changing the tensions of the mooring lines with the subwinch. A comparison of the newly designed mathematical model with the existing PID control method and the results of experiments indicated that the proposed designing method is more efficient than the traditional method. Index Terms Barge ship, experimental result, PID, position mooring (PM) system, robust control, subwinch, station keeping. I. INTRODUCTION IN recent years, there have been increasing activities related to oil exploration and exploitation, as well as offshore applications such that production and pipe laying (see Fig. 1). To increase the safety and efficiency of these activities, the offshore vessel must satisfy the requirements for station keeping operation, where the position and orientation of vessel is kept in the acceptable area. The dynamic positioning (DP) or position mooring (PM) system is a station keeping approach that exclusively uses thrusters to control the position and heading angle of vessel, and it is highly efficient for deep water operation or station keeping of surface vessel [1] [11]. Fossen and Berge [1] derived a control law for the conventional ship, where a nonlinear vectorial backstepping control law for commercial ships is derived by using the concept of vectorial backstepping. Especially the compensation problem for actuator dynamics is emphasized because the bandwidth of the propellers, thrusters, and rudders is closed to the bandwidth of the ship. Sordalen [2] presented a thruster allocation scheme, since this scheme can significantly reduce the fuel consumption for the dynamic positioning of ships with azimuth type thrusters. Strand [3] proposed several topics within the field of Manuscript received April 18, 2014; accepted February 17, Date of publication April 10, 2015; date of current version October 21, Recommended by Technical Editor M. O. Efe. This work was supported in part by the Basic Science Research Program funded by the Ministry of Education Science and Technology (2012R1A1A ) and the project The Development of Mooring Positioning Control System for Offshore Accommodation Barge by the Ministry of Oceans and Fisheries. S.-W. Ji and Y. B. Kim are with the Department of Mechanical System Engineering, College of Engineering, Pukyong National University, Busan , Korea ( kpjiwoo@pknu.ac.kr; realpneumatic@gmail.com). M.-S. Choi is with the Department of Maritime Police Science, College of Fisheries and Ocean Sciences, Chonnam National University, Yeosu Korea ( engine@jnu.ac.kr). Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TMECH Fig. 1. Vessel with mooring lines. positioning control for surface vessel based on nonlinear control theory. Also, Bodson [4] evaluated some optimum control allocation methods to suppress the deference between real control force and control signal calculated from the control law. Fossen [5] gave some general solutions for vessel control problem where the position keeping for DP systems with active propulsion system and tracking problem are the main issue. Im et al. [6] presented a design method for nonlinear autopilot and discussed the stability analysis for the ship-to-ship missiles with strong couplings between roll, yaw, and pitch dynamics. Bui and Kim [7], [8] considered the control allocation problem to make a sophisticated solution. The obtained result is applied to the position keeping problem for surface vessel with tugboats as the actuators. In [9], the authors proposed a new control allocation method. Especially, the controller design and control allocation problem are integrated through a one-step process in which the treatment of system stability, control performance, and allocation problem is unified. The obtained result will be introduced in this paper also. Other researches related vessel motion control are proposed in [10] and [11]. However, in these articles, tracking and motion keeping methods with active propulsion systems are considered. In contrast to the DP system, the vessel s position is basically kept by the mooring lines in the PM system. The mooring system with cables compensates for the slowly varying disturbances. In the normal weather condition, the PM system is considered as a passive control system. However, tension of the mooring lines should be controlled to ensure the vessel motions and prevent the line breakage in the hard disturbance condition. The PM system is the most efficient for moored vessels in shallow water, which reduces the operational cost as well as the risk. Several control strategies for modeling of vessels and PM control have been proposed [12] [16]. The PM system was IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See standards/publications/rights/index.html for more information.

2 JI et al.: STUDY ON POSITION MOORING SYSTEM DESIGN FOR THE VESSEL MOORED BY MOORING LINES 2825 modeled on the basis of mooring line tension characteristic by solving the catenary equation [12]. The LQG controller design of a thruster-assisted position mooring system has also been studied, and the line breakage compensation with feed-forward control was recommended. Aamo and Fossen [13], [14] developed a finite-element model (FEM) for mooring lines, which are suspended in water, proposing a passive controller to reduce the fuel consumption by adjusting mooring lines stiffness. Nguyen and Sorensen [15] presented the switching control strategy for thruster-assisted position mooring. Depending on the environmental and operational conditions, a supervisor control was adopted to facilitate the automatic switching for heading, damping, restoring the mean force controllers of the PM system. In this paper, we introduce a new vessel motion control strategy using the mooring lines. Exactly describing, a something noble approach how to design a motion control system for the barge ship moored by cables is introduced. It is well known that motion control problem for the barge ship is not easy, since it does not have any device to actively control its motion. In this paper, we investigate the method of controlling the dynamic motions of the barge ship by controlling the tension of cables attached to the barge ship s winch, without using a separate propelling system such as a side thrust. The tensions of mooring cables are measured through load cells. Four sail winches installed on the vessel are used to control the cable tension by pulling or releasing the lines. To secure good control performance, the controller is designed based on H control framework named robust control strategy. And the PID and robust control strategies are applied to evaluate the efficiency of the proposed control strategy. The evaluation process will be done by the experimental study. II. CONTROL STRATEGY AND MATHEMATICAL MODEL A. Control Strategy In the previous results, the mooring lines are only used for position keeping without motion control. It means that the results reported previously are DP and PM system assisted by active propulsion apparatus. It is clear that the main winch is not used for dynamic positioning keeping due to large size, long and slow operating response etc. In general, it is impossible or difficult to keep the vessel in the range of several meters in the presence of wave, current, and wind disturbance only using the main winch. If we consider these facts, it is necessary to apply another control strategy to this problem. Therefore, in this paper, the authors introduce a new positioning keeping strategy. The key idea is illustrated in Fig. 2. Considering the constrain that the main winch is not used for the control system, we introduce an actuator system (or subwinch), which can be installed between the main winch and the cable guiding roller as shown in Fig. 2. The newly introduced actuator is absolutely smaller and faster than the main winch system to obtain good control performance. The actuator can control the cable tension by pulling and Fig. 2. Vessel motion control strategy by using cable tension control with the actuators. releasing the cable without operating the main winch in the specified range. However, the tension control can be obtained by using many strategies also. However in this paper, we install the subwinch type actuator between the main winch and the guiding roller instead of cylinders appeared in Fig. 2. The system configuration for this research will be illustrated more precisely in the Section III. B. Vessel Dynamic The floating vessel is usually described by low-frequency (LF) and wave frequency (WF) model. The WF model accounts for the motions due to the first-order wave disturbance, whereas the LF model primarily considers the effect of second-order mean and slow varying wave, current, and wind load. However, in the PM system, the effect of WF motion is small enough to be ignored [5]. The 3 DOF LF motions in surge, the sway and yaw of the floating vessel are generally formulated as follows: η = R(ϕ)v, M v + C RB (v)v + C A (v r )v r + D(v r )+G(η) = {τ wave2 + τ wind + τ moor + τ thr (1) where η =[x, y, ϕ] T R 3 represents inertial position (x, y) and heading angle ϕ in the earth fixed coordinate frame and v = [u, v, r] T R 3 describes the surge, sway, and yaw rate of ship motion in the body fixed coordinate frame. The rotation matrix in heading direction R(ϕ) describes the kinematic equation of motion; that is

3 2826 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 20, NO. 6, DECEMBER 2015 cos ϕ sin ϕ 0 R(ϕ) = sin ϕ cos ϕ 0. (2) The relative velocity vector considering the effect of current is defined as v r =[u u c,v v c,r] T. (3) And the current components are calculated by u c = V c cos(β c ϕ),v c = V c sin(β c ϕ) (4) where V c and β c are the velocity and direction of the surface current. And M R 3x3 is the LF system inertia matrix m X u 0 0 M = 0 m Y v Yṙ (5) 0 N v I z Nṙ where m is the vessel mass and I z is the inertia moment about the vessel fixed z-axis. For control application, the vessel motion is restricted to low frequency. The wave frequency is assumed to be independent from added inertia, which implies that Ṁ = 0. And C RB (v) R 3x3 and C A (v r ) R 3x3 are the skewsymmetric Coriolis and centripetal matrices of the rigid body and added mass. D(v r ) R 3 is the damping vector, which is a function of the relative velocity defined as follows: Xũ 0 0 D(v r )= 0 Yṽ Y r 0 Nṽ N r (6) where ũ = u u c, ṽ = v v c. The restoring vector G(η) R 3, caused by the buoyancy and gravitation just affected by heave, roll, and pitch motion is neglected in horizontal motion. In station keeping application, where the velocity of ship is assumed to be small, then C RB (v)v + C A (v r )v r can be ignored, and D(v r ) is assumed to be constant [12] [14]. τ wave2, τ wind, τ moor, and τ thr are second-order wave disturbance, wind, mooring, and thruster vectors, respectively. B. Multicable Mooring System The mooring line is attached at one end to the vessel via a winch system, and the other end is fixed to the sea floor by anchor. Commonly, the mooring line is subjected to three types of excitation: large amplitude LF motion, medium amplitude WF motion, and small amplitude with very high-frequency vortexinduced vibration [16]. In the PM system design, it is simplified by considering the influence due to LF motion. Thus, the model for the generalized mooring force is τ moor = R(ϕ)g mo (η) d mo (v) (7) where d mo is the additional damping, and g mo is the Earthfixed restoring force due to the mooring system. The Earth-fixed restoring force is a combination of tensions produced from the mooring lines. It can be given by the following expression: g mo = T (α)h (8) Fig. 3. Fig. 4. Mooring line configuration in vessel control system. Control system description based on the robust control framework. where T (α) R 3 N is the mooring line configuration matrix and N is the number of mooring lines. Then, this matrix can be defined as cos α 1... cos α N T (α)= sin α 1... sin α N x 1 sin α 1 y 1 cos α 1... x N sin α N y N cos α N (9) where x i,y i, and α i are moment arms and angle, between mooring line and x-axis of vessel as shown in Fig. 3. The horizontal force produced from each mooring line is the function of the horizontal distance between the top point and the anchor point of the line and the line length. Several marine software packages that solve the nonlinear horizontal force of mooring line are readily available. III. CONTROLLER DESIGN AND EXPERIMENT A. Controller Design and Experimental Setup This paper applies a robust control approach, which was initiated by us [9], to the position keeping experiment. In this paper, the control allocation strategy proposed in the previous work [9] is provided. As shown in Fig. 4, a control allocation problem is defined as a method of transferring the calculated control signal

4 JI et al.: STUDY ON POSITION MOORING SYSTEM DESIGN FOR THE VESSEL MOORED BY MOORING LINES 2827 from the controller to the plant with as little loss as possible. This is expressed as τ c τ a (f i,α i ) <γ(γ >0). (10) From the aforementioned equation, it is evident the objective of control allocation is to minimize the difference between controller output (τ c ) and actuator output (τ a ). Fig. 4 illustrates a general control allocation problem formulation with controller [9]. The general objective of control allocation is given by the condition that the error τ c τ a is made small, as described by (10). If the problem is described in the H control framework, this can be expressed in the following form for the generalized plant depicted in Fig. 3: T zw <γ(γ >0) (11) where T zw describes the transfer between w (exogenous inputs) and z (error and measured variables). The control scheme is illustrated in Fig. 4, and the control objective is to obtain a controller satisfying the norm condition (11). Then, a controller satisfying the condition shown in (11) can be easily calculated using MATLAB tool. Finally, we can obtain a robust controller candidate as follows: { ẋk = A k x k + B k y s (12) τ c = C k x k + D k y s. And, all the transfer functions shown in Fig. 4 are described as G T (s): actuators (mooring winch with cable), G V (s): controlled vessel, and K(s): controller. Using the obtained controller that satisfies the constraints (11), the experiment is carried out and the results are shown. The experimental setup is illustrated in Fig. 5, and the schematic diagram for experimental is shown in Fig. 6. As illustrated in these figures, the control system (NI CompactRio) is placed on the vessel. However, the vessel motions are captured by the CCD camera, which is attached on the celling. The image data (vessel motions) taken by the camera is transferred to the host onshore computer, and the vessel motions (surge, sway motions, and yaw angle) are calculated by using the vector code correlation technique in real time [17]. Then, the calculated positions and yaw angle are sent to the control system (NI CompactRio) placed on the vessel. Also, the information including vessel motions and all the sensing signals are transferred to the monitoring system (Host Computer) by the wireless network. The process and technique for experiment are illustrated in Figs. 5 and 6 as described earlier. The vessel comprises the barge ship and the mooring lines. Especially, the parameters of the barge ship model used in experiment are given in Table I. And four mooring lines are properly interconnected between the vessel through subwinches and the wall of the basin. Especially, where the subwinches role as the actuators illustrated in Fig. 2. Also, the load cells to measure the cable tension are installed between the cable and the vessel, as shown in Fig. 6. Fig. 5. Photo of the experimental setup. Fig. 6. Schematic diagram of experimental setup. (a) Excitation input (above) and speed (below): surge motion. (b) Excitation input (above) and speed (below): sway motion.

5 2828 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 20, NO. 6, DECEMBER 2015 TABLE I GENERAL DATA OF THE BARGE SHIP MODEL Parameter Value Unit mass 18.5 kg length 1.3 m width 0.4 m draft 0.1 m The numerical values obtained with the identification process are given as M = (13) D = diag{[1.6, 8.0, 1.2]}. (14) Where the mooring lines configuration on the vessel are described as (x 1,y 1 )=( 0.65, 0.2), (x 2,y 2 )=(0.65, 0.2), (x 3,y 3 )=(0.65, 0.2), (x 4,y 4 )=( 0.65, 0.2). (15) To show the comparison result with the PID control scheme, the following PI controller is introduced [5]: t τ controlpi = R T (ϕ)(k p (η d η)+k i (η d η)dt). 0 (16) where η: actual motion vector and η d : desired motion vector for surge, sway position, and yaw angle, respectively. The integral term is used to eliminate the steady-state error between the desired position and actual position of the vessel. Then, PI control gains K p and K i are chosen as follows by simulation and experiment: K p = (17) Fig. 7. Comparison results for excitation input : experiment result (solid line) and simulation result (dashed line). (a) Vessel speed of surge direction (X) and (b) Vessel speed of sway direction (Y) for excitation input. The submerged mass (balancing weight in Fig. 6) is suspended between the two end points of cable to illustrate the passive control property of the PM system, which provides the restoring, damping, and mean control forces to compensate the load variation caused by wind, wave, and current. Here, the weight of each mass is 0.2 kg. B. Experimental Results In this study, two control methods, PID and robust control, are applied to evaluate the proposed control strategy. The inertia and damping matrices of the barge ship, M and D shown in the (1) are obtained from the experiment and simulation. Fig. 7 shows the quality of the model fitting on an experiment for the excitation input of the longitudinal forces, which make surge and sway motion, respectively K i = (18) The structure of robust control scheme is shown in Fig. 5. The novel idea in this control approach is that the treatment of system stability, control performance, and control allocation is unified in the form of H control framework [7]. By using the (13) (15), the controller satisfying norm condition (11) is easily obtained. Then, the elements of the controller (12) are expressed as follows: [ ] Ak1 A A k = k2 (19) A k3 A k A k1 = A k2 = ,

6 JI et al.: STUDY ON POSITION MOORING SYSTEM DESIGN FOR THE VESSEL MOORED BY MOORING LINES A k3 = A k4 = B k =, C k =, D k = Fig. 8. Ship motions in wave disturbance without control. Figs show the disturbance responses. Where the pulling force with 1 N has been applied to the vessel from #1 mooring cable for a short time at 50 s. In same time, the wave disturbance begins attacking the vessel continuously. The wave conditions are: height: 3 5 cm, frequency range: 1 2 Hz, and wave attack angle to the vessel: 45 deg. made by the wave generator. With the condition aforementioned, Fig. 8 shows the vessel motion (surge, sway, and yaw angle, respectively) of the uncontrolled case. Even though the vessel is slightly restricted by the cables, we can see that the influence of the wave attack remains for long time (about ten times longer than the controlled cases). On the other hand, Figs. 9 and 10 show the controlled cases. In Fig. 9, PI control law given in (17) and (18) is applied, and in Fig. 10, the proposed robust control scheme of the (19) works. The two controlled results do not show significant differences. Fig. 9. Station keeping experiment in wave disturbance by using PI control. However, the comparison results between the commanded tension made by the controller and the actual tension of each mooring line is shown in Figs. 11 and 12 for a PI and the proposed robust control case, respectively. By controlling the winch by pulling and releasing each line, the tension of the mooring line can follow commanded tension based on the control allocation framework. This result explains that PI control is weak in coping with disturbance. Especially, let us look at the cable tension in the

7 2830 IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 20, NO. 6, DECEMBER 2015 Fig. 10. control. Station keeping experiment in wave disturbance by using robust Fig. 12. Comparison between commanded forces produced from robust controller and actual tension lines. Fig. 11. Comparison between commanded forces produced from PI controller and actual tension lines. IV. CONCLUSION In this paper, we studied how to design a mooring control system for the barge ship. A barge ship basically consists of the vessel part and a mooring winch and cables, and since it does not have any device to actively control its motion, a separate propelling system such as a side thrust has been generally introduced when it is desired to control the dynamic motion of the barge ship. In this paper, we investigated the method of controlling the dynamic motions of the barge ship by controlling the tension of cables attached to the barge ship s winch, without using a separate propelling system such as a side thrust. For this purpose, we proposed a tension control strategy using an actuator (or subwinch). And a mathematical model of the barge ship through experiments and simulations was developed. Based on this mathematical model, we designed a control system based on robust control framework. A comparison of the newly designed mathematical model with the existing PID control method and the experimental results indicated that the proposed designing method is more efficient than the traditional method. transient state region, and compare it with the proposed control case. In this state, the cable tension force variation of PI (in Fig. 11) is rough and violent. On the other hand, there is smooth and natural tension force variation in the proposed control system as shown in Fig. 12. In fact, because the harsh tension variation is the main cause of breakdowns of the mooring cable, it should be avoided in the real application. Finally, it is clear that the proposed control scheme works well and applicable in the real field. REFERENCES [1] T. I. Fossen and S. P. Berge, Nonlinear vectorial backstepping design for global exponential tracking of marine vessels in the presence of actuator dynamics, in Proc. 36th Conf. Decision Control, 1997, pp [2] O. J. Sordalen, Optimal thrust allocation for marine vessels, Control Eng. Practice, vol. 5, no. 9, pp , [3] J. P. Strand, Nonlinear position control system design for marine vessels, Ph.D. thesis, Dept. Eng. Cybernetics, Norwegian Univ. Sci. Technol., Trondheim, Norway, [4] M. Bodson, Evaluation of optimization methods for control allocation, J. Guid., Control, Dyn., vol. 25, no. 4, pp , 2002.

8 JI et al.: STUDY ON POSITION MOORING SYSTEM DESIGN FOR THE VESSEL MOORED BY MOORING LINES 2831 [5] T.I.Fossen,Marine Control System Guidance, Navigation, Rigs and Underwater Vehicle, Trondheim, Norway: Marine Cybernetics, [6] K. H. Im, D. Chwa, and J. Y. Choi, Multi input multi output nonlinear autopilot design for ship to ship missiles, Int. J. Control, Autom., Sys., vol. 4, no. 2, pp , [7] V. P. Bui and Y. B. Kim, Development of constrained control allocation for ship berthing by using autonomous tugboats, Int. J. Control, Autom., Sys., vol. 9, no. 6, pp , [8] V. P. Bui and Y. B. Kim, Design of sliding mode controller for ship position control, J. Inst. Control, Robot. Sys.,vol.17,no.9,pp , [9] S. W. Ji, V. P. Bui, B. Balachandran, and Y. B. Kim, Robust control allocation design for marine vessel, Ocean Eng., vol. 63, pp , [10] S.-R. Oh, J. Sun, Zhen Li, E. A. Celkis and D. Parsons, System identification of a model ship using a mechatronic system, IEEE/ASME Trans. Mechatronics, vol. 15, no. 2, pp , Apr [11] S. Formentin, D. Berretta, N. Urbano, I. Boniolo, P. D. Filippi, and E. M. Savaresi, A parking assistance system for small-scale boats, IEEE/ASME Trans. Mechatronics, vol. 18, no. 6, pp , Dec [12] J. Strand, A. Sorensen and T. Fossen, Design of automatic thruster assisted position mooring system for ship, Int. J. Model, Identification Control, vol. 19, no. 2 pp , [13] O.M. Aamo and T. Fossen, Finite element modeling of mooring lines, Math. Comput. Simul., vol. 53, pp , [14] O.M. Aamo and T. Fossen, Controlling line tension in thruster assisted mooring systems, in Proc. IEEE Int. Conf. Control Appl.,1999,pp [15] T. D. Nguyen and A. Sorensen, Switching control for thruster-assisted position mooring, Control Eng. Practice, vol. 17, no. 9, pp , [16] M. S. Triantafyllow, Cable mechanics with marine application, Dept. Ocean Eng., Massachusetts Inst. Technol., Cambridge, MA, USA, [17] H. Kawai, Y. B. Kim and Y. Choi, Measurement of a container crane spreader under bad weather conditions by image restoration, IEEE Trans. Instrum. Meas., vol. 61, no. 1, pp , Jan Sang-Won Ji received the B.S. degree in mechanical system engineering and the M.S. and Ph.D. degrees in control and mechanical engineering, all from Pukyong National University, Busan, Korea, in 2004, 2006, and 2009, respectively. He is currently working with Pukyong National University as a Research Fellow. His research interests include fluid power system design and control. Myung-Soo Choi received the B.S. and M.S. degrees in maritime engineering from National Fisheries University of Pusan, Busan, Korea, in 1992 and 1994, respectively, and the Ph.D. degree in control and mechanical engineering from Pukyong National University, Busan, in He is currently a Professor with the Department of Maritime Police Science, Chonnam National University, Yeosu, Korea. His research interests include mechanical vibration and optimum design. Young-Bok Kim (M 96 SM 10) received the B.S. and M.S. degrees in maritime engineering from National Fisheries University of Pusan, Busan, Korea, in 1989 and 1991, respectively, and the Ph.D. degree from Kobe University, Kobe, Japan, in He is currently a Professor with the Department of Mechanical System Engineering, Pukyong National University. He has held visiting position at the Department of Mechanical Engineering, University of Maryland, College Park, MD, USA ( ). His research interests include control theory and application with dynamic ship positioning and crane control system design, etc. Dr. Kim is a member of the American Society of Mechanical Engineers.