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Fault tolerant control for uncertain time-delay systems based on sliding mode control. (English) Zbl 1180.93087
Summary: Fault tolerant control for uncertain systems with time varying state-delay is studied in this paper. Based on sliding mode controller design, a fault tolerant control method is proposed. By means of the feasibility of some Linear Matrix Inequalities (LMIs), a delay dependent sufficient condition is derived for the existence of a linear sliding surface which guarantees quadratic stability of the reduced-order equivalent system restricted to the sliding surface. A reaching motion controller, which can be seen as a fault tolerant controller, can retain the stability of the closed loop system in the present of uncertainties, disturbances and actuator fault is designed. A numerical simulation shows the effectiveness of the approach.

MSC:
93D09 Robust stability
34K35 Control problems for functional-differential equations
93C23 Control/observation systems governed by functional-differential equations
93B40 Computational methods in systems theory (MSC2010)
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References:
[1] Cheng C., Zhao Q.: Reliable control of uncertain delayed systems with integral quadratic constraints. IEE Proc. Control Theory Appl. 151 (2004), 790-796
[2] Edwards, Ch., Tan C. P.: Fault tolerant control using sliding mode observers. Conference on Decision and Control. Tlantis, Paradise Island, 2004, pp. 5254-5259
[3] Gouaisbaut F., Dambrine, M., Richard J. P.: Robust control of delay systems: a sliding mode control design via LMI. Systems Control Lett. 46 (2002), 219-230 · Zbl 0994.93004 · doi:10.1016/S0167-6911(01)00199-2
[4] Hu K. J., Basker V. R., Crisalle O. D.: Sliding mode control of uncertain input-delay systems. Proc. American Control Conference. Philadelphia 1998, pp. 564-568
[5] Koshkouei A. J., Zinober: Sliding mode time-delay systems. Proc. IEEE International Workshop on Variable Structure Systems, Tokyo 1996, pp. 97-101
[6] Kreindle E., Jameson A.: Conditions for nonnegatives of portioned matrices. IEEE Trans. Automat. Control 17 (1972), 147-148
[7] Kyeong T., Yeu S. K.: Sliding mode observer based fault detection and isolation in descriptor systems. American Control Conference, Anchorage 2002, pp. 4543-4548
[8] Li X., Decarlo R. A.: Memoryless sliding mode control of uncertain time-delay systems. Proc. American Control Conference, Arlington 2001, pp. 4344-4350
[9] Liu G. Y., Li Y. C.: Active fault tolerant control with actuation reconfiguration. IEEE Trans. Aerospace and Electronic Systems 40 (2004), 1110-1117
[10] Mahmoud M. S. N.F.A.-M.: Quadratic stabilization of continuous time systems with state-delay and norm-bounded time-delay uncertainties. IEEE Trans. Automat. Control 39 (1994), 2135-2139 · Zbl 0925.93585 · doi:10.1109/9.328812
[11] Niu Y., Lam J., Wang, X., Ho W. W. C.: Sliding mode control for nonlinear state-delayed systems using neural network approximation. IEE Proc. Control Theory Appl. 150 (2003), 233-239
[12] Niu J. L. Y., Wang, X., Ho D. W. C.: Observer-based sliding mode control for nonlinear state-delayed systems. Internat. J. Systems Sci. 35 (2004), 139-150 · Zbl 1059.93025 · doi:10.1080/00207720410001671732
[13] Parlakci M. N. A.: Robust stability of uncertain time-varying state-delayed systems. IEE Proc. Control Theory Appl. 153 (2006), 469-477
[14] Petersen I. R.: A stabilization algorithm for a class of uncertain linear systems. Systems Control Lett. 8 (1987), 351-357 · Zbl 0618.93056 · doi:10.1016/0167-6911(87)90102-2
[15] Tan, Ch. P., Edwards C.: Multiplicative fault reconstruction using sliding mode observers. Proc. 5th Asian Control Conference 2004, pp. 957-962
[16] Wang J. Z., Ma L.: A robust fault detection and isolation method via sliding mode observer. Proc. 5th World Congress on Intelligent Control and Automation, Hangzhou 2004, pp. 1727-1730
[17] Xia Y. J.: Robust sliding-mode control for uncertain time-delay systems: An LMI approach. IEEE Trans. Automat. Control 48 (2003), 1086-1092 · Zbl 1364.93608
[18] Xiong Y., Saif M.: Robust and nonlinear fault diagnosis using sliding mode observers. IEEE Conference on Decision and Control, Orlando 2001, pp. 567-572
[19] Yan X.-G., Edwards C.: Robust sliding mode observer-based actuator fault detection and isolation for a class of nonlinear systems. 44th IEEE Conference on Decision and Control, Seville 2005, pp. 987-992 · Zbl 1168.93324 · doi:10.1080/00207720701778395
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