Tóm tắt Trong bài báo này, một hệ thống điều khiển chống lắc cho hệ cần cẩu trên biển được trình bày. Hệ cần cẩu này được sử dụng để vận chuyển container qua lại từ tàu chở container có trọng tải lớn được neo đậu trên biển và tàu được trang bị cần cẩu. Mục tiêu điều khiển là triệt tiêu hoàn toàn dao động lắc của container trong quá trình bốc dỡ dưới tác động của sóng biển tác động lên các con tàu. Phương pháp điều khiển được đề nghị là sự kết hợp giữa bộ điều khiển chống lắc thông thường và việc bù chuyển động của tàu. Sự kết hợp này đảm bảo container được vận chuyển đến vị trí qui định. Kết quả thực nghiệm được trình bày nhằm đánh giá tính khả thi của phương án điều khiển. Abstract: In this paper, a method to control the pendulum motion of an offshore container crane is discussed. The offshore container crane is used to loadunload containers between a huge container ship (called the “ mother ship”) and a smaller ship mounted cranes (called the “mobile harbor”). The control objective during loadunload container is to control the pendulum motion (i.e., “sway”) of the load in the presence of the mobile harbor motions (heave, roll, and pitch) induced by wave to keep the spreader at the desire position. Experiment results are provided to demonstrate the ability of the proposed control metho
Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 231 Mã bài: 47 Bộ điều khiển chống lắc cho cần cẩu container hoạt động trên mặt biển A pendulation control system of an offshore container crane Quang Hieu Ngo 1 ,*, Trungtinh Tran 1 , and Keum-Shik Hong 2 1 College of Technology, Can Tho University, Vietnam (Email: {nqhieu, tttinh}@ctu.edu.vn) 2 School of Mechanical Engineering, Pusan National University, Korea (Email: kshong@pusan.ac.kr) Tóm tắt Trong bài báo này, một hệ thống điều khiển chống lắc cho hệ cần cẩu trên biển được trình bày. Hệ cần cẩu này được sử dụng để vận chuyển container qua lại từ tàu chở container có trọng tải lớn được neo đậu trên biển và tàu được trang bị cần cẩu. Mục tiêu điều khiển là triệt tiêu hoàn toàn dao động lắc của container trong quá trình bốc dỡ dưới tác động của sóng biển tác động lên các con tàu. Phương pháp điều khiển được đề nghị là sự kết hợp giữa bộ điều khiển chống lắc thông thường và việc bù chuyển động của tàu. Sự kết hợp này đảm bảo container được vận chuyển đến vị trí qui định. Kết quả thực nghiệm được trình bày nhằm đánh giá tính khả thi của phương án điều khiển. Abstract: In this paper, a method to control the pendulum motion of an offshore container crane is discussed. The offshore container crane is used to load/unload containers between a huge container ship (called the “mother ship”) and a smaller ship mounted cranes (called the “mobile harbor”). The control objective during load/unload container is to control the pendulum motion (i.e., “sway”) of the load in the presence of the mobile harbor motions (heave, roll, and pitch) induced by wave to keep the spreader at the desire position. Experiment results are provided to demonstrate the ability of the proposed control method. 1. Introduction Container cranes are widely used to transfer containers and other objects from and to various locations in ports and at container terminals. In recent years, with the rapid growth of the world logistics industry and the rises in competition and costs, ship companies have resorted to making container ships larger. The largest container ship having the capacity 13,800 TEU (twenty-foot equivalent unit) was launched by Samsung Heavy Industries, a Korean company, in 2008. Now, the designs of 16,000-TEU-class ships have been completed and are waiting for an order. It is predicted that by the 2020s, super large, 18,000 TEU container ships will be in operation. To keep up with ever-increasing ship sizes, container cranes have to become larger, faster, and higher, necessitating, in turn, efficient controllers that can both guarantee fast turnover times and meet stringent safety requirements. Despite these improvements, one problem has remained for small container terminals and ports: they cannot accommodate, owing to their relatively shallow water, the larger container ships. To solve this problem, special crane- equipped ships (“mobile harbor (MH)”) capable of operating on the open sea have been introduced. Fig. 1 shows a mobile harbor that loads containers to and unloads them from a mega container ship in open sea. A small ship has a container crane and is connected to a container vessel by a mooring system. The vessel is assumed to be fixed on the ocean. It is not affected by the sea wave because of its mass. The mooring system between the crane ship and the vessel imposes constraint oscillations on the crane ship. Thus, only three motions of the crane ship are considered: heaving, rolling and pitching motions. In the process of loading/unloading containers, the longitudinal and lateral motions of the trolley (especially when starting or stopping, along with wave-induced ship movement) impart a pendulum motion to the suspended container [1]. This type of motion can not only lead to a potentially serious damage, but also prolong the time required for precise positioning of the load. Although an MH crane can perform anti-swing control in the conventional approach [2-13], it still needs to compensate non-negligible, relative rotations. Because both the MH ship and the 232 Quang Hieu Ngo, Trungtinh Tran and Keum-Shik Hong VCM2012 container ship are heaving, rolling, and pitching in the waves, the trolley have to move to compensate for the ship motions so that the spreader can land on the top of the containers, which its position is considered as a fix position on the container ship. The trolley of the offshore container crane is redesign so that it can suppress both longitudinal and lateral sway motions and compensate for the ship motions. The structure of the trolley consists of two stages. First stage is the main trolley and is used to move the container from the vessel to the crane ship or vice Fig. 1. Loading/unloading of containers at a mobile harbor in an open sea. versa. Second stage has a relative motion with the main trolley in two perpendicular directions. The sway motions of the load are suppressed by using these relative motions. This paper represents the inaugural work of mobile harbor studies. Here, for the first time, the necessity of a new mechanism for the mobile harbor is identified, and treated, from a control point of view. The motion of the trolley is used not only eliminating the sway motion but also compensating for the ship motions to keep the spreader at the desire position. Therefore, the control law includes the sway suppression and the ship motions compensation. The paper is organized as follows. In Section 2, the system dynamics of an offshore container crane are provided. In Section 3, an anti-sway control law is proposed, and corresponding trajectories is introduced. In Section 4, experiment results are discussed. Finally, conclusions are drawn in Section 5. 2. Problem formulation To develop a mathematical model of the whole system, three coordinate systems are introduced in Fig. 2. The first one is the global coordinate, O 0 x 0 y 0 z 0 . The second one is the crane ship coordinate, O s x s y s z s , with the origin at the center of gravity of the ship. The last coordinate is the trolley coordinate, O t x t y t z t , which is fixed on the main trolley. Using these coordinates, the mathematical model can be derived as follow [14]. ,)()(),()( uqGqqDqqqCqqM (1) where ,sinsin ,coscos , ,0,0,, , 0 0 0 , , 00 00 00 00 ,,,, , 0 0 0 0 ,,,, 4114 3113 11 434241 34333231 242321 141312 4241 3231 2221 1211 4321 444241 333231 242322 141311 lmmm lmmm mmm ff ccc cccc ccc ccc dd dd dd dd gggg mmm mmm mmm mmm yx p p pt T yx T T u qqC D qG qM q Fig. 2. Introduced coordinate frames: reference (mother ship), ship, and trolley. Mother ship Mo bile harbor (Small ship) Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 233 Mã bài: 47 .cossin ,cossin2 cossincos2 sinsinsin2 ,cossin ,cossin ,cossin ,sincoscos2 cossincos2 ,sincos ,sinsinsinsincos coscossin ,sinsinsin coscossin ,sin ,cossinsincos ,cossinsincos ,sin2 , ,cos , ,coscos cossinsin ,sincossin 2 43 42 41 2 34 2 33 32 31 24 23 21 14 13 12 2 44 22 33 22 4224 3223 lmc lm lm lmc lmc lmc lmc lm lmc lmc lmlm lmc lm lmc mmc lmlmc lmlmc mmc lmm lmm mmm lm lmmm lmmm p p p p p p p p p p pp p p p pt pp pp pb p p pt p p p m t and m p are the masses of the trolley and the load, respectively. x and y represent the position of the connection point between the main rope and the trolley in the trolley coordinate frame. l denotes the rope length, h is the crane height, and define the longitudinal and lateral sway angles of the load in the reference coordinate frame. z is the heave motion (displacement) of the ship in the reference coordinate frame. and are the rolling and pitching angular displacements of the ship, respectively, in the reference coordinate frame. 3. Pendulation control system The conventional control systems for container crane are given as follow: , , kekekf kekekf ypyydyy xpxxdxx (2) where k dx , k px , k , k dy , k py , and k are the control gains, dx xxe and dy yye are position errors in x and y directions. x d and y d are desire positions of the trolley. During loading/unloading process, the ship motions impart to the sway motion of the payload even thought the main trolley has been moved to the desire position. The control objective in this situation is to keep the payload in the small acceptable region, which is predetermined by a global desire position (X d and Y d ). Without loss of generality, X d and Y d are assumed to be constants. In practical, the trolley must move following trajectories to keep the payload in the desire region. The trajectories can be obtained due to the ship motions as follow. . cos sin , cos cossinsinsin hY y hyX x d d d d (3) The objective of the control law must be minimize the position error while tracking the trajectory (3), and suppressing the sway motion, and . The control diagram is given in Fig. 3. 4. Experimental results 4.1 Experiment model Experiment model using in the paper includes a 6-degree-of-freedoms (6DOFs) platform to generate the ship motions induced by random waves and a 3-dimensional (3D) crane. The 3D crane is placed on the top of the 6DOFs platform as shown in Fig. 4. The Marine System Simulator (MSS) [15] is used to simulate the ship motions induced by random waves. The 6DOFs platform is control to follow the simulation data from MSS. An inertial measurement unit (IMU), a MTi sensor from XSENS, measures real-time motions of the platform. Fig. 5 presents the roll motion of the platform with simulation result and the measurement result from IMU. , , z ,,, yx Fig. 3. Control diagram. 234 Quang Hieu Ngo, Trungtinh Tran and Keum-Shik Hong VCM2012 Fig. 4. Experiment model including 6DOFs platform and 3D Crane. 4.2 Results The control gains in (2) are tuned by controlling the trolley to desire position without the ship motions. Fig. 6 shows the trolley position and the sway angle in Y direction. The trolley reaches the desire position and suppresses the sway angle well. Fig. 9 presents the position of the payload with free motion (without control), sway control without tracking the trajectories (3), and sway control with tracking trajectories (3). Without tracking, the payload moves in the large region even thought the sway control is applied. With tracking, the position of the payload is in the small region (-0.04m, 0.04m). This result seems good in the experiment conditions by using the conventional control law. However, the new control law must be designed to improve performance before it can be implemented in the practice. 0 20 40 60 80 100 120 140 160 180 200 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Time [sec] Pitchl motion of the ship [rad] Simulation result from MSS Platform's motion (a) Pitch motion of the ship 0 20 40 60 80 100 120 140 160 180 200 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Time [sec] Roll motion of the ship [rad] Simulation result from MSS Platform's motion (b) Roll motion of the ship 0 20 40 60 80 100 120 140 160 180 200 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Time [sec] Error [rad] Roll motion Pitch motion (c) Error between simulation and replicated motion in the platform Fig. 5. Comparison of the ship motions in Sea State 3 (simulation vs. replicated motion in the platform). 0 1 2 3 4 5 6 7 8 9 10 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time [sec] Trolley position [m] (a) Trolley position. Tuyển tập công trình Hội nghị Cơ điện tử toàn quốc lần thứ 6 235 Mã bài: 47 0 1 2 3 4 5 6 7 8 9 10 -0.1 -0.05 0 0.05 0.1 Time [sec] Sway angle [rad] (b) Sway angle. Fig. 6. Control perfomance of the crane with out ship motions. -0.1 -0.05 0 0.05 0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Payload position in X [m] Payload position in Y [m] (a) -0.1 -0.05 0 0.05 0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Payload position in X [m] Payload position in Y [m] (b) -0.1 -0.05 0 0.05 0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Payload position in X [m] Payload position in Y [m] (c) Fig. 7. Position of the payload in XY plane in case of free motion (a), sway control with out tracking (b), and sway control with tracking (c). 5. Conclusions The conventional control has been applied for the offshore container crane. The control law suppresses the sway motion and tracks the trajectory to keep the payload in the acceptable region. The experiment has been performed to demonstrate the proposed idea for position tracking and sway suppression. However, for perfect suppression of the sway motion of the payload, the control algorithm should be improved. References [1] Q. H. Ngo and K S. Hong, “Sliding mode control of an offshore container crane,” IEEE/ASME Trans. Mechatron., vol. 6, no. 5, pp. 662-668, 2012. [2] K. L. Sorensen, W. Singhose, and S. Dickerson, “A controller enabling precise positioning and sway reduction in bridge and gantry cranes,” Control Eng. Practice, vol. 15, no. 7, pp. 825-837, 2007. [3] K. T. Hong, C. D. Huh, and K S. Hong, “Command shaping control for limiting the transient sway angle of crane systems,” Int. J. Control Autom. Syst., vol. 1, no. 1, pp. 43-53, 2003. [4] K S. Hong, B. J. Park, and M. H. Lee, “Two- stage control for container cranes,” JSME Int. J. Ser. C, vol. 43, no. 2, pp. 273-282, 2000. [5] H. Kawai, Y. B. Kim, and Y. W. Choi, “Anti- sway system with image sensor for container cranes,” J. Mech. Sci. Technol., vol. 23, no. 10, pp. 2757-2765, 2009. [6] D. Chwa, “Nonlinear tracking control of 3-D overhead cranes against the initial swing angle and the variation of payload weight,” IEEE Trans. Control Syst. Technol., vol. 17, no. 4, pp. 876-883, 2009. [7] H. Park, D. Chwa, and K S. Hong, “A feedback linearization control of container cranes: Varying rope length,” Int. J. Control Autom. Syst., vol. 5, no. 4, pp. 379-387, 2007. [8] Y. S. Kim, K S. Hong, and S. K. Sul, “Anti- sway control of container cranes: Inclinometer, observer, and state feedback,” Int. J. Control Autom. Syst., vol. 2, no. 4, pp. 435-449, 2004. [9] Q. H. Ngo, K S. Hong, and I. H. Jung, “Adaptive control of an axially moving system,” J. Mech. Sci. Technol., vol. 23, no. 11, pp. 3071-3078, 2009. [10] C. S. Kim and K S. Hong, “Boundary control of container cranes from the perspective of controlling an axially moving string system,” Int. J. Control Autom. Syst., vol. 7, no. 3, pp. 437-445, 2009. 236 Quang Hieu Ngo, Trungtinh Tran and Keum-Shik Hong VCM2012 [11] H. H. Lee, Y. Ling, and D. Segura, “A sliding mode antiswing trajectory control for overhead cranes with high-speed load hoisting,” J. Dyn. Syst. Meas. Control-Trans. ASME, vol. 128, no. 4, pp. 842-845, 2006. [12] M. S. Park, D. Chwa, and S. K. Hong, “Anti- sway tracking control of overhead cranes with system uncertainty and actuator nonlinearity using an adaptive fuzzy sliding-mode control,” IEEE Trans. Industrial Electronics, vol. 55, no. 11, pp. 3972-3984, 2008. [13] Q. H. Ngo and K S. Hong, “Skew control of a quay container crane,” J. Mech. Sci. Technol., vol. 23, no. 12, pp. 3332-3339, 2009. [14] K S. Hong and Q. H. Ngo, “Dynamics of the container crane on a mobile harbor,” Ocean Engineering, vol. 53, pp. 16-24, 2012. [15] T. I. Fossen and Ø.N. Smogeli, “Nonlinear time-domain strip theory formulation for low- speed manoeuvring and station-keeping,” Model. Identif. Control, vol. 25, no. 4, pp. 201-221, 2004. Quang Hieu Ngo received the B.S. degree in mechanical engineering from Ho Chi Minh City University of Technology, Vietnam, in 2002, the M.S. degree in mechatronics from Asian Institute of Technology, Thailand, in 2007, and the Ph.D. degree in intelligent control and automation from Pusan National University, Korea. He has worked as a lecturer on the College of Technology – Can Tho University from 2002. His current research interests include port automation, control of axially moving systems, sliding mode control, adaptive control, and input shaping control. Trungtinh Tran received the B.Sc. degree and post graduate diploma from Cantho University, Vietnam and University of Professional Education Larenstein, The Netherland, in 1997 and 2001 respectively, the M.S. and Ph.D. degrees from Gyeongsang National University, Korea in 2004 and 2007 respectively. His research interest includes power system expansion planning, transmission expansion planning, power system operation, power system reliability evaluation, power system market, applied fuzzy set theory. Especially, he has been researching electricity market, renewable energy and energy saving. He has worked as a lecturer on the College of Technology – Can Tho University. Keum-Shik Hong received the B.S. degree in mechanical design and production engineering from Seoul National University in 1979, the M.S. degree in mechanical engineering from Columbia University, New York, in 1987, and both the M.S. degree in applied mathematics and the Ph.D. degree in mechanical engineering from the University of Illinois at Urbana-Champaign (UIUC) in 1991. From 1991 to 1992, he was a Postdoctoral Fellow at UIUC. Since Dr. Hong joined the School of Mechanical Engineering at Pusan National University (PNU), Korea, in 1993, he became Professor in 2004. Dr. Hong’s current research interests include nonlinear systems theory, adaptive control, distributed parameter systems control, vehicle control, brain computer interface, and innovative control applications in brain engineering. . toàn quốc lần thứ 6 231 Mã bài: 47 Bộ điều khiển chống lắc cho cần cẩu container hoạt động trên mặt biển A pendulation control system of an offshore container crane Quang Hieu Ngo 1 ,*,. dao động lắc của container trong quá trình bốc dỡ dưới tác động của sóng biển tác động lên các con tàu. Phương pháp điều khiển được đề nghị là sự kết hợp giữa bộ điều khiển chống lắc thông. trình bày. Hệ cần cẩu này được sử dụng để vận chuyển container qua lại từ tàu chở container có trọng tải lớn được neo đậu trên biển và tàu được trang bị cần cẩu. Mục tiêu điều khiển là triệt