Dynamical analysis and stabilizing control of inclined rotational translational actuator systems. (English) Zbl 1463.93199

Summary: Rotational translational actuator (RTAC) system, whose motions occur in horizontal planes, is a benchmark for studying of control techniques. This paper presents dynamical analysis and stabilizing control design for the RTAC system on a slope. Based on Lagrange equations, dynamics of the inclined RTAC system is achieved by selecting cart position and rotor angle as the general coordinates and torque acting on the rotor as general force. The analysis of equilibria and their controllability yields that controllability of equilibria depends on inclining direction of the inclined RTAC system. To stabilize the system to its controllable equilibria, a proper control Lyapunov function including system energy, which is used to show the passivity property of the system, is designed. Consequently, a stabilizing controller is achieved directly based on the second Lyapunov stability theorem. Finally, numerical simulations are performed to verify the correctness and feasibility of our dynamical analysis and control design.


93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C10 Nonlinear systems in control theory
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[1] Spong, M. W.; Siciliano, B.; Valavanis, K. P., Underactuated mechanical systems, Control Problems in Robotics and Automation, 135-150 (1998), London, UK: Springer, London, UK
[2] Reyhanoglu, M.; van der Schaft, A.; McClamroch, N. H.; Kolmanovsky, I., Dynamics and control of a class of underactuated mechanical systems, IEEE Transactions on Automatic Control, 44, 9, 1663-1671 (1999) · Zbl 0958.93078
[3] Fantoni, I.; Lozano, R., Nonlinear Control for Underactuated Mechanical Systems (2002), London, UK: Springer, London, UK
[4] Wan, C.-J.; Bernstein, D. S.; Coppola, V. T., Global stabilization of the oscillating eccentric rotor, Nonlinear Dynamics, 10, 1, 49-62 (1996)
[5] Bupp, R. T.; Bernstein, D. S.; Coppola, V. T., A benchmark problem for nonlinear control design, International Journal of Robust and Nonlinear Control, 8, 4-5, 307-310 (1998)
[6] Jankovic, M.; Fontaine, D.; Kokotović, P. V., TORA example: cascade- and passivity-based control designs, IEEE Transactions on Control Systems Technology, 4, 3, 292-297 (1996)
[7] Bupp, R. T.; Bernstein, D. S.; Coppola, V. T., Experimental implementation of integrator backstepping and passive nonlinear controllers on the RTAC testbed, International Journal of Robust and Nonlinear Control, 8, 4-5, 435-457 (1998)
[8] Lee, C.-H.; Chang, S.-K., Experimental implementation of nonlinear TORA system and adaptive backstepping controller design, Neural Computing and Applications, 21, 4, 785-800 (2012)
[9] Tsiotras, P.; Corless, M.; Rotea, M. A., An L2 disturbance attenuation solution to the nonlinear benchmark problem, International Journal of Robust and Nonlinear Control, 8, 4-5, 311-330 (1998)
[10] Petres, Z.; Baranyi, P.; Hashimoto, H., Approximation and complexity trade-off by {TP} model transformation in controller design: a case study of the {TORA} system, Asian Journal of Control, 12, 5, 575-585 (2010)
[11] She, J.; Zhang, A.; Lai, X.; Wu, M., Global stabilization of 2-DOF underactuated mechanical systems—an equiavlent-input-disturbance approach, Nonlinear Dynamics, 69, 1-2, 495-509 (2012)
[12] Burg, T.; Dawson, D., Additional notes on the TORA example: a filtering approach to eliminate velocity measurements, IEEE Transactions on Control Systems Technology, 5, 5, 520-523 (1997)
[13] Escobar, G.; Ortega, R.; Sira-Ramírez, H., Output-feedback global stabilization of a nonlinear benchmark system using a saturated passivity-based controller, IEEE Transactions on Control Systems Technology, 7, 2, 289-293 (1999)
[14] Celani, F., Output regulation for the {TORA} benchmark via rotational position feedback, Automatica, 47, 3, 584-590 (2011) · Zbl 1216.93062
[15] Gao, B. T., Dynamical modeling and energy-based control design for TORA, Acta Automatica Sinica, 34, 9, 1221-1224 (2008)
[16] Avis, J. M.; Nersesov, S. G.; Nathan, R. a. .; Muske, K. R., A comparison study of nonlinear control techniques for the RTAC system, Nonlinear Analysis, 11, 4, 2647-2658 (2010) · Zbl 1214.93052
[17] Gao, B.; Zhang, X.; Chen, H.; Zhao, J., Energy-based control design of an underactuated 2-dimensional TORA system, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS ’09)
[18] Gao, B.; Xu, J.; Zhao, J.; Huang, X., Stabilizing control of an underactuated 2-dimensional tora with only rotor angle measurement, Asian Journal of Control, 15, 5, 1477-1488 (2013)
[19] Ortega, R.; Loria, A.; Nicklasson, P., Passivity-Based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications (1998), Berlin, Germany: Springer, Berlin, Germany
[20] Gao, B.; Bao, Y.; Xie, J.; Jia, L., Passivity-based control of two-dimensional translational oscillator with rotational actuator, Transactions of the Institute of Measurement and Control, 36, 185-190 (2014)
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