Abstract
In this chapter, the dynamical behaviors of discrete-time fast terminal sliding mode control systems are studied. Based on Euler’s discretization, the approximate discrete-time model is obtained. Using a recursive analysis method, the boundedness for the steady states of the discrete-time system is established. Theoretical analysis shows that the discrete-time fast terminal sliding mode control method can offer a higher output tracking precision than the discrete-time linear sliding mode control method. As an application of the proposed theoretical results, the control problem for the DC-DC buck converters via discrete-time fast terminal sliding mode control is investigated. Simulation results are given to demonstrate the effectiveness of the proposed method.
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Drazenovic, B.: The invariance conditions in variable structure systems. Automatica 5, 287–295 (1969)
Utkin, V.I.: Sliding Modes in Control Optimization. Springer (1992)
Edwards, C., Spurgeon, S.: Sliding Mode Control: Theory and Applications. Taylor and Francis, London (1998)
Perruquetti, W., Barbot, J.P. (eds.): Sliding Modes Control in Engineering. Marcel Dekker, New York (2002)
Man, Z., Paplinski, A.P., Wu, H.R.: A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators. IEEE Transactions on Automatic Control 39(12), 2464–2469 (1994)
Yu, X., Man, Z.: Model reference adaptive control systems with terminal sliding modes. International Journal of Control 64, 1165–1176 (1996)
Wu, Y., Yu, X., Man, Z.: Terminal sliding mode control design for uncertain dynamic systems. Systems and Control Letters 34(5), 281–287 (1998)
Yu, X., Man, Z.: Multi-input uncertain linear systems with terminal sliding-mode control. Automatica 34(3), 389–392 (1998)
Yu, X., Man, Z.: Fast terminal sliding-mode control design for nonlinear dynamical systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 49(2), 261–264 (2002)
Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM Journal on Control and Optimization 38(3), 751–766 (2000)
Sarpturk, Z., Istefanopulos, Y., Kaynak, O.: On the stability of discrete time sliding mode control systems. IEEE Transactions on Automatic Control 32(10), 930–932 (1987)
Yu, X., Wang, B., Li, X.: Computer-controlled variable structure systems: The state of the art. IEEE Transactions on Industrial Informatics 8(2), 197–205 (2012)
Xia, X., Zinober, A.S.I.: Delta-modulated feedback in discretization of sliding mode control. Automatica 42(5), 771–776 (2006)
Galias, Z., Yu, X.: Euler’s discretization of single input sliding-mode control systems. IEEE Transactions on Automatic Control 52(9), 1726–1730 (2007)
Yu, X., Wang, B., Galias, Z., Chen, G.: Discretization effect on equivalent control-based multi-input sliding-mode control systems. IEEE Transactions on Automatic Control 53(6), 1563–1569 (2008)
Su, W.C., Drakunov, S.V., Ozguner, U.: An O(T 2) boundary layer in sliding mode for sampled-data systems. IEEE Transactions on Automatic Control 45(3), 482–485 (2000)
Levant, A.: Finite differences in homogeneous discontinuous control. IEEE Transactions on Automatic Control 52(7), 1208–1217 (2007)
Yu, X., Xu, J.-X., Hong, Y., Yu, S.: Analysis of a class of discrete-time systems with power rule. Automatica 43(3), 562–566 (2007)
Abidi, K., Xu, J., She, J.: A discrete-time terminal sliding-mode control approach applied to a motion control problem. IEEE Transactions on Industrial Electronics 56(9), 3619–3627 (2009)
Galias, Z., Yu, X.: Dynamical behaviors of discretized second-order terminal sliding-mode control systems. IEEE Transactions on Circuits and Systems-Part II: Express Briefs 59(9), 597–601 (2012)
Janardhanan, S., Bandyopadhyay, B.: On discretization of continuous-time terminal sliding mode. IEEE Transactions on Automatic Control 51(9), 1532–1536 (2006)
Li, S., Du, H., Yu, X.: Discrete-time terminal sliding mode control systems based on Euler’s discretization. IEEE Transactions on Automatic Control 59(2), 546–552 (2014)
Qian, C., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Transactions on Automatic Control 46(7), 1061–1079 (2001)
Tan, S.C., Lai, Y.M., Tse, C.K.: Sliding Mode Control of Switching Power Converters. CRC Press (2011)
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Du, H., Yu, X., Li, S. (2015). Dynamical Behaviors of Discrete-Time Fast Terminal Sliding Mode Control Systems. In: Yu, X., Önder Efe, M. (eds) Recent Advances in Sliding Modes: From Control to Intelligent Mechatronics. Studies in Systems, Decision and Control, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-18290-2_5
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DOI: https://doi.org/10.1007/978-3-319-18290-2_5
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