×

Design of sliding surface for mismatched uncertain systems to achieve asymptotical stability. (English) Zbl 1201.93108

Summary: The design of an adaptive Sliding Mode Control (SMC) scheme is proposed in this paper for stabilizing a class of dynamic systems with matched and mismatched perturbations. Two methods for designing a novel sliding surface function are introduced first. By utilizing a pseudocontrol input in the sliding surface function, one cannot only suppress the mismatched perturbations in the sliding mode, but also obtain the property of asymptotic stability. Then a sliding mode controller is designed to drive the controlled systems to the designated sliding surface in a finite time. Adaptive mechanism is also embedded in the controller as well as in the sliding surface function designed from the second method to overcome the perturbations, so that the informations of upper bound of perturbations are not required. An application of flight control and experimental results of controlling a servomotor are also given for demonstrating the applicability of the proposed control scheme.

MSC:

93D20 Asymptotic stability in control theory
93C40 Adaptive control/observation systems
93B12 Variable structure systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Utkin, V. I., Variable structure systems with sliding modes, IEEE Trans. Automat. Control, 22, 2, 212-221 (1977) · Zbl 0382.93036
[2] Barmish, B. R.; Leitmann, G., On ultimate boundedness control of uncertain systems in the absence of matching assumptions, IEEE Trans. Automat. Control, 27, 1, 153-158 (1982) · Zbl 0469.93043
[3] Singh, S. N.; Coelho Antônio, A. R., Nonlinear control of mismatched uncertain linear systems and application to control of aircraft, J. Dyn. Syst. Meas. Control Trans. ASME, 106, 3, 203-210 (1984) · Zbl 0557.93038
[4] Liao, T. L.; Fu, L. C.; Hsu, C. F., Output tracking control of nonlinear systems with mismatched uncertainties, Syst. Control Lett., 18, 1, 39-47 (1992) · Zbl 0743.93053
[5] Spurgeon, S. K.; Davies, R., A nonlinear control strategy for robust sliding mode performance in the absence of mismatched uncertainty, Int. J. Control, 57, 5, 1107-1123 (1993) · Zbl 0772.93013
[6] J. Hu, J. Chu, H. Su, SMVSC for a class of time-delay uncertain systems with mismatching uncertainties, IEE Proceeding-Control Theory and Applications, vol. 147(6), 2000, pp. 687-693.; J. Hu, J. Chu, H. Su, SMVSC for a class of time-delay uncertain systems with mismatching uncertainties, IEE Proceeding-Control Theory and Applications, vol. 147(6), 2000, pp. 687-693.
[7] Tao, C. W.; Chan, M. L.; Lee, T. T., Adaptive fuzzy sliding mode controller for linear systems with mismatched time-varying uncertainties, IEEE Trans. Syst. Man Cybern. Part B Cybern., 33, 2, 283-294 (2003)
[8] Kwan, C. M., Sliding mode control of linear systems with mismatched uncertainties, Automatica, 31, 2, 303-307 (1995) · Zbl 0821.93021
[9] Choi, H. H., An explicit formula of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties, Automatica, 34, 8, 1015-1020 (1998) · Zbl 1040.93506
[10] Choi, H. H., Variable structure output feedback control design for a class of uncertain dynamic systems, Automatica, 38, 2, 335-341 (2002) · Zbl 0991.93021
[11] Choi, H. H., An LMI-based switching surface design method for a class of mismatched uncertain systems, IEEE Trans. Automat. Control, 48, 9, 1634-1638 (2003) · Zbl 1364.93330
[12] Chan, M. L.; Tao, C. W.; Lee, T. T., Sliding mode controller for linear systems with mismatched time-varying uncertainties, J. Franklin Inst. Eng. Appl. Math., 337, 2, 105-115 (2000) · Zbl 0981.93012
[13] Kim, K. S.; Park, Y.; Oh, S. H., Designing robust sliding hyperplanes for parametric uncertain systems: a Riccati approach, Automatica, 36, 7, 1041-1048 (2000) · Zbl 0955.93005
[14] Tsai, Y. W.; Shyu, K. K.; Chang, K. C., Decentralized variable structure control for mismatched uncertain large-scale systems: a new approach, Syst. Control Lett., 43, 2, 117-125 (2001) · Zbl 0974.93014
[15] Shyu, K. K.; Tsai, Y. W.; Lai, C. K., A dynamic output feedback controllers for mismatched uncertain variable structure systems, Automatica, 37, 5, 775-779 (2001) · Zbl 0981.93010
[16] Cao, W. J.; Xu, J. X., Nonlinear integral-type sliding surface for both matched and mismatched uncertain systems, IEEE Trans. Automat. Control, 49, 8, 1355-1360 (2004) · Zbl 1365.93068
[17] Yoo, D. S.; Chung, M. J., A variable structure control with simple adaptation laws for upper bounds on the norm of the uncertainties, IEEE Trans. Automat. Control, 37, 6, 860-865 (1992) · Zbl 0760.93014
[18] Chou, C.-H.; Cheng, C. C., Design of adaptive variable structure controllers for perturbed time-varying state delay systems, J. Franklin Inst. Eng. Appl. Math., 388, 1, 35-46 (2001) · Zbl 0966.93101
[19] Chou, C.-H.; Cheng, C. C., A decentralized model reference adaptive variable structure controller for large-scale time-varying delay systems, IEEE Trans. Automat. Control, 48, 7, 1123-1127 (2003)
[20] Hung, J. Y.; Gao, W.; Hung, J. C., Variable structure control: a survey, IEEE Trans. Automat. Control, 40, 1, 2-22 (1993)
[21] Leon, S. J., Linear Algebra with Applications (1999), Prentice-Hall: Prentice-Hall New Jersey
[22] El-Ghezawi, O. M.E.; Zinober, A. S.I.; Billings, S. A., Analysis and design of variable structure systems using a geometric approach, Int. J. Control, 38, 3, 657-671 (1983) · Zbl 0538.93035
[23] Żak, S. H.; Hui, S., On variable structure output feedback controllers for uncertain dynamic systems, IEEE Trans. Automat. Control, 38, 10, 1509-1512 (1993) · Zbl 0790.93027
[24] Khalil, H. K., Nonlinear Systems (2000), Prentice-Hall: Prentice-Hall New Jersey · Zbl 0948.93007
[25] Slotine, J. J.E.; Li, W., Applied Nonlinear Control (1991), Prentice-Hall: Prentice-Hall New Jersey · Zbl 0753.93036
[26] Shyu, K. K.; Tsai, Y. W.; Lai, C. K., Stability regions estimation for mismatched uncertain variable structure systems with bounded controllers, Electron. Lett., 35, 16, 1388-1390 (1999)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.