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Vol: 53(67) No: 4 / December 2008 Shifted Switching Plane Design for Second Order Systems with Velocity and Input Signal Constraints Aleksandra Nowacka-Leverton Institute of Automatic Control, Technical University of Lódź, 18/22 Stefanowskiego St., 90-924 Lódź, Poland, e-mail: ola.nowacka@gmail.com, web: http://zneiap.p.lodz.pl Andrzej Bartoszewicz Institute of Automatic Control, Technical University of Lódź, 18/22 Stefanowskiego St., 90-924 Lódź, Poland, e-mail: andrzej.bartoszewicz@p.lodz.pl Keywords: variable structure systems, sliding mode control, time-varying switching lines, reaching phase elimination Abstract In this paper a new sliding mode control (SMC) algorithm for second order systems subject to input signal and velocity constraints is presented. The proposed method ensures the reaching phase elimination and furthermore, it guarantees fast and monotonic tracking error convergence to zero without violating the input signal and velocity constraints. The presented algorithm employs a time-varying switching line. At the initial time t = t0 the switching line passes through the representative point of the system in the error state space. Afterwards, the line moves with a constant velocity and a constant angle of inclination to the origin of the space and having reached the origin it stops moving. By this means insensitivity of the system with respect to external disturbance and model uncertainty from the very beginning of the control action is ensured. The parameters of the line are selected in such a way that introduced control quality criterion – integral absolute error (IAE) – is minimized. References [1] A. Bartoszewicz, “A comment on ‘A time–varying sliding surface for fast and robust tracking control of second-order uncertain systems’,” Automatica, vol. 31, 1995, vol. 31, pp. 1893 – 1895. [2] A. Bartoszewicz, “Time-varying sliding modes for second-order systems,” IEE Proceedings, Control Theory and Applications, vol. 143, 1996, pp. 455 – 462. [3] A. Bartoszewicz and A. Nowacka: “Sliding mode control of the third order system subject to velocity acceleration and input signal constraints,” International Journal of Adaptive Control and Signal Processing. vol. 21, 8-9, 2007, pp. 779 – 794. [4] A. Bartoszewicz and A. Nowacka-Leverton: “SMC without the reaching phase – the switching plane design for the third order system,” IET Proceedings, Control Theory and Applications, vol. 1, 5, 2007, pp. 1461 – 1470. [5] S.B. Choi, C.C. Cheong and D.W. Park: “Moving switching surface for robust control for second-order variable structure systems,” International Journal of Control, vol. 58, 1993, pp. 229 – 245. [6] S.B. Choi and D.W. Park: “Moving switching surface for fast tracking control for second-order dynamic systems,” Transaction of the ASME Journal of Dynamic Systems, Measurement, and Control, vol. 116, 1994, pp. 154 – 158. [7] S.B. Choi, D.W. Park and S. Jayasuriya: “A time-varying sliding surface for fast and robust tracking control of second-order systems,” Automatica, vol. 30, 1994, pp. 899 – 904. [8] R.S. DeCarlo, S. Żak and G. Mathews: ”Variable structure control of nonlinear multivariable systems: a tutorial,” Proceedings of the IEEE, vol. 76, 1988, pp. 212 – 232. [9] C. Edwards, E. Fossas Colet and L. Fridman (editors): “Advances in variable structure and sliding mode control,” Series: Lecture Notes in Control and Information Sciences, vol. 334, 2006. [10] J.Y. Hung, W. Gao and J.C. Hung, “Variable structure control: a survey,” IEEE Transactions on Industrial Electronics, vol. 40, 1993, pp. 2 – 22. [11] E. Misawa and V. Utkin (editors): “Variable structure systems,” Special issue: Transactions of the ASME — Journal of Dynamic Systems, Measurement, and Control, vol. 122, 2000, pp. 585 – 819. [12] J.J. Slotine and W. Li Applied Nonlinear Control, Prentice-Hall International Editions, 1991. [13] S. Tokat, I. Eksin and M. Guzelkaya: “A new design method for sliding mode controllers using a linear time-varying sliding surface,” Proceedings of the Institution of Mechanical Engineers Part I – Journal of Systems and Control Engineering, vol. 216, 6, 2002, pp. 455 – 466. [14] S. Tokat, I. Eksin, M. Guzelkaya and M.T. Soylemez: “Design of a sliding mode controller with a nonlinear time-varying sliding surface,” Transactions of the Institute of Measurement and Control, vol. 25, 2, 2003, pp. 145 – 162. [15] V. Utkin (editor): “Sliding mode control,” Special issue: International Journal of Control vol. 57, 1993, pp. 1003–1259 [16] V. Utkin, “Variable structure systems with sliding modes,” IEEE Transactions on Automatic Control, vol. 22, 1977, pp. 212 – 222. [17] V. Utkin, J. Guldner and J. Shi: Sliding mode control in electromechanical systems, Taylor & Francis, London, 1999. [18] A. Zinober (editor): Variable Structure and Lyapunov Control. Springer-Verlag, London, 1994. |