×

zbMATH — the first resource for mathematics

Dynamic sliding mode control for a class of systems with mismatched uncertainty. (English) Zbl 1293.93172
Summary: In this paper, a robust stabilization problem for a class of uncertain systems is studied using sliding mode techniques. Matched and mismatched uncertainties are both considered. By employing the sliding surface proposed by C. Edwards and S. K. Spurgeon in [Int. J. Control 62, No. 5, 1129–1144 (1995; Zbl 0849.93012)], the stability of the sliding mode is shown first. Then, an asymptotic observer is established to estimate the system state variable based on a constrained Lyapunov equation, and a variable structure controller is proposed to stabilize the system by exploiting the estimated state and system output. The two major limitations in C. M. Kwan [IEEE Trans Autom Control 41, No. 11, 1691–1693 (1996; Zbl 0875.93056)] are eliminated. Finally, a simulation study based on a simplified model of the HIRM aircraft system is used to illustrate the effectiveness of the results.

MSC:
93B12 Variable structure systems
93D21 Adaptive or robust stabilization
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alvarez, J.; Orlov, I.; Acho, L., An invariance principle for discontinuous dynamic systems withapplication to a Coulomb friction oscillator, ASME J dyn syst measure control, 122, 687-690, (2000)
[2] Burton, J.A.; Zinober, A.S.I., Continuous approximation of variable structure control, Int J syst sci, 17, 876-885, (1986) · Zbl 0599.93029
[3] 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
[4] Edwards, C.; Spurgeon, S.K., Sliding mode stabilisation of uncertain systems using only output information, Int J control, 62, 5, 1129-1144, (1995) · Zbl 0849.93012
[5] Edwards, C.; Spurgeon, S.K., Sliding mode control: theory and application, (1998), Taylor and Francis Ltd London
[6] Filippov, A.F., Differential equations withdiscontinuous right hand sides, mathematics and its applications, (1983), Kluwer Academic Publishers Dordrecht
[7] Huzmezan M. Theory and aerospace applications of constrained model based predictive control. Ph. D Thesis, Department of Engineering, University of Cambridge, UK 1998
[8] Kwan, C.M., On variable structure output feedback controllers, IEEE trans autom control, 41, 11, 1691-1693, (1996) · Zbl 0875.93056
[9] Kwan, C.M., Further results on variable output feedback controllers, IEEE trans autom control, 46, 9, 1505-1508, (2001) · Zbl 1004.93007
[10] Magni, J.F.; Bennani, S.; Terlouw, J., Robust flight control: A design challenge, lecture notes in control and information sciences, 224, (1997), Springer-Verlag Berlin
[11] Orlov, Y.; Dochain, D., Discontinuous feedback stabilization of minimum-phase semilinear infinite-dimensional systems withapplication to chemical tubular reactor, IEEE trans autom control, 47, 8, 1293-1304, (2002) · Zbl 1364.93660
[12] Shu, X.; Rigopoulos, K.; Cinar, A., Vibrational control of an exothermic CSTR: productivity improvement by multiple input oscillations, IEEE trans autom control, 34, 2, 193-196, (1989) · Zbl 0664.93061
[13] Shyu, K.K.; Tsai, Y.W.; Lai, C.K., A dynamic output feedback controller for mismatched uncertain variable structure systems, Automatica, 37, 5, 775-779, (2001) · Zbl 0981.93010
[14] Syrmos, V.L.; Abdallah, C.T.; Dorato, P.; Grigoriadis, K., Static output feedback - a survey, Automatica, 33, 2, 125-137, (1997) · Zbl 0872.93036
[15] Utkin, V.I., Sliding modes and their application to variable structure systems, (1978), Moscow: MIR Publication House · Zbl 0398.93003
[16] Yan, X.G.; Edwards, C.; Spurgeon, S.K., Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback, Automatica, 40, 4, 613-620, (2004) · Zbl 1060.93026
[17] Yan, X.G.; Wang, J.J.; Lü, X.Y.; Zhang, S.Y., Decentralised output feedback robust stabilization for a class of nonlinear interconnected systems withsimilarity, IEEE trans autom control, 43, 2, 294-299, (1998)
[18] Zak, S.H.; Hui, S., On variable structure output feedback controllers for uncertain dynamic systems, IEEE trans autom control, 38, 10, 1509-1512, (1993) · Zbl 0790.93027
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.