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Energy Shaping for Tracking Control of 4-DOF Crane

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In this paper the nonlinear tracking control methodology is proposed for 4–DOF (degree of freedom) overhead crane system using energy shaping. The 4–DOF underactuated overhead crane system has an extra DOF compared with the popular 3–DOF variant. The 4-DOF crane modeling represents strong state coupling and more complicated system dynamics which makes it challenging control problem. The control methodology begins with the first step of decoupling the crane dynamics into two subsystems using collocated partial feedback linearization. The passivating outputs of the modified subsystems are identified which are further utilized for energy shaping to obtain the nonlinear state feedback control law which effectively achieves the objective of trajectory tracking with fast elimination of payload swings. The energy shaping procedure obviates the need for solving PDEs to derive the control law. The trajectory tracking control law represents generalization of the position regulation problem. The simulation results are presented to validate the control law and superior performance is demonstrated over the existing control methodologies.
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Tracking; Energy Shaping Control; Crane System; Underactuated

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S. Ning, F. Yongchun and X. Zhang, Energy coupling output feedback control of 4–DOF underactuated cranes with saturated inputs, Automatica, 49(5), pp. 1318-1325, 2013

J. H. Yang and K. S. Yang, Adaptive coupling control for overhead crane systems, Mechatronics, vol. 17, no. 2/3, pp. 143–152, 2007.

W. Wang, J. Yi, D. Zhao and D. Liu, Design of a stable sliding-mode controller for a class of second-order underactuated systems, IEE Control Theory and Applications, 151(6), pp. 683–690, 2004.

H. Lee, Modeling and control of a three-dimensional overhead cranes, ASME Journal of Dynamic Systems, Measurement, and Control, 120(4), pp. 471–476, 1998

G. Bartolini, A. Pisano and E. Usai, Second-order sliding-mode control of container cranes, Automatica, 38(10), 1783–1790, 2002.

C. Chang and K. Chiang, Fuzzy projection control law and its application to the overhead crane, Mechatronics, 18(10), 607–615, 2008.

W. Singhose, D. Kim and M. Kenison, Input shaping control of double pendulum bridge crane oscillations, ASME Journal of Dynamic Systems,Measurement, and Control, 130(3), pp. 1–7, 2008.

R. Liu, S. Li and S. Ding, Nested saturation control for overhead crane systems, Transactions of the Institute of Measurement and Control, 34(7), 862–875, 2012.

Y. Fang, W. Dixon, D. Dawson and E. Zergeroglu, Nonlinear coupling control laws for an underactuated overhead crane system, IEEE/ASME Transactions on Mechatronics, 8(3), 418–423, 2013.

A. Bloch, N. Leonard and J. Marsden, Controlled Lagrangians and the stabilization of mechanical systems, IEEE Trans. Automat. Contr., Vol. 45, No. 12, 2000.

J. A. Acosta, R. Ortega, A. Astolfi and A. M. Mahindrakar, Interconnection and damping assignment passivity–based control of mechanical systems with underactuation degree one, IEEE Trans. Automat. Contr.,Vol. 50, No. 12, 2005.

A.K. Kamath, N.M. Singh, F. Kazi and R. Pasumarthy, Dynamics and control of 2D spidercrane: a controlled Lagrangian approach, IEEE conference on decision and control, pp. 3596–3601, 2010.

F. Kazi, R. Banavar, P. Mullhaupt and D. Bonvin. Stabilization of a 2d-spidercrane mechanism using damping assignment passivity- based control. In Proceedings of the 17th IFAC World Congress, pp. 3155– 3160, Seul, Korea, 2008.

I. Sarras, F. Kazi, R. Ortega and R. Banavar, Total energy-shaping IDAPBC control of the 2D-spidercrane, IEEE Conf. Decision Control, pp. 1122–1127, 2010.

M.S. Park, D. Chwa and S.K. Hong, Antisway Tracking Control of Overhead Cranes With System Uncertainty and Actuator Nonlinearity Using an Adaptive Fuzzy Sliding-Mode Control, IEEE Transactions on Industrial Electronics, Vol. 55, No. 11, pp. 3972–3984, 2008.

D. Chwa, Nonlinear tracking control of 3-D overhead cranes against the initial swing angle and the variation of payload weight, IEEE Transactions on Control Systems Technology, 17(4), 876–883, 2009.

H. Lee, Y. Liang and D. Segura, A sliding-mode antiswing trajectory control for overhead cranes with high speed load hoisting. ASME Journal of Dynamic Systems, Measurement, and Control, 128(4), pp. 842–845, 2006.

H. Lee, Y. Liang and D. Segura, A new approach for the antiswing control of overhead cranes with high-speed load hoisting, Int. J. Control, vol. 76, no. 15, pp. 1493-1499, Oct. 2003.

Y. Fang, B. Ma, P. Wang and X. Zhang, A motion planning based adaptive control method for an underactuated crane system, IEEE Transactions on Control Systems Technology, 20(1), pp. 241–248, 2012.

C. Makkar, G. Hu, W. Sawyer and W. Dixon, Lyapunov-based tracking control in the presence of uncertain nonlinear parameterizable friction, IEEE Trans. Automat. Contr., vol. 52, no. 10, pp. 1988–1994, 2007.

N. Sun, Y. Fang, Y. Zhang and B. Ma, A novel kinematic coupling-based trajectory planning method for overhead cranes, IEEE/ASME Transactionson Mechatronics, 17(1), pp. 166–173, 2012.

Lagerev, A.V., Lagerev, I.A., Milto, A.A., Tool for preliminary dynamics and stress analysis of articulating cranes, (2014) International Review on Modelling and Simulations (IREMOS), 7 (4), pp. 644-652.

Lagerev, A., Lagerev, I., Milto, A., Preliminary Dynamics and Stress Analysis of Articulating Non-Telescoping Boom Cranes Using Finite Element Method, (2015) International Review on Modelling and Simulations (IREMOS), 8 (2), pp. 223-226.

R. Mehra, S. Satpute, F. Kazi and N.M. Singh, Geometric–PBC based Control of 4–DOF Underactuated Overhead Crane System, The 21st International Symposium on Mathematical Theory of Networks and Systems, 2014.

S. Satpute, R. Mehra, F. Kazi and N.M. Singh, Geometric–PBC Approach for Control of Circular Ball and Beam System, 21st International Symposium on Mathematical Theory of Networks and Systems, 2014.


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