×

zbMATH — the first resource for mathematics

Sliding mode parameter adjustment for perturbed linear systems with actuators via invariant ellipsoid method. (English) Zbl 1214.93026
Summary: A methodology for the design of sliding mode controllers for perturbed quasi-linear systems in the presence of actuators is presented. This technique is based on the invariant ellipsoid method and given in terms of the solution of a set of linear matrix inequalities. The provided methodology allows the design of the controller parameters ensuring global convergence of the states to a suboptimal ellipsoidal region around the origin even in the presence of both matched and unmatched uncertainties/disturbances. A benchmark example illustrates a good workability of the suggested technique.

MSC:
93B12 Variable structure systems
93C05 Linear systems in control theory
93C73 Perturbations in control/observation systems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Utkin, Sliding Modes in Control and Optimization (1992)
[2] Utkin, Sliding Mode Control in Electromechanical Systems (1999)
[3] Hui, Robust output feedback stabilization of uncertain dynamic systems with bounded controllers, International Journal of Robust and Nonlinear Control 3 (2) pp 115– (1993) · Zbl 0783.93095
[4] Edwards, Sliding Mode Control: Theory and Applications (1998)
[5] Hsu, Model-reference output-feedback sliding mode controller for a class of multivariable nonlinear systems, Asian Journal of Control 5 (4) pp 543– (2009)
[6] Andrade-Da Silva, Sliding-mode output-feedback control based on LMIs for plants with mismatched uncertainties, IEEE Transactions on Industrial Electronics 56 (9) pp 3675– (2009)
[7] Boyd, Linear Matrix Inequalities in Systems and Control Theory (1994) · Zbl 0816.93004
[8] Poznyak, Advanced Mathematical Tools for Control Engineers, Volume 1: Deterministic Techniques (2008) · Zbl 1145.93001
[9] Balandin, Synthesis of Control Laws Based on LMI (in Russian) (2007)
[10] Castanos, Analysis and design of integral sliding manifolds for systems with unmatched perturbations, IEEE Transactions on Automatic Control 51 (5) pp 853– (2006) · Zbl 1366.93094
[11] Choi, Sliding-mode output feedback control design, IEEE Transactions on Industrial Electronics 55 (11) pp 4047– (2008)
[12] Fridman, An averaging approach to chattering, IEEE Transactions on Automatic Control 46 (8) pp 1260– (2001) · Zbl 1007.93010
[13] Fridman, Singularly perturbed analysis of chattering in relay control systems, IEEE Transactions on Automatic Control 47 (12) pp 2079– (2002) · Zbl 1364.93491
[14] Kurzhanski, Ellipsoidal Calculus for Estimation and Control (1996)
[15] Blanchini, Set invariance in control-a survey, Automatica 35 (11) pp 1747– (1999) · Zbl 0935.93005
[16] Nazin, Rejection of bounded exogenous disturbances by the method of invariant ellipsoids, Automatic Remote Control 68 (3) pp 467– (2007) · Zbl 1125.93370
[17] Polyak, Suppression of bounded exogenous disturbances: Output feedback, Automatic Remote Control 69 (5) pp 801– (2008) · Zbl 1156.93338
[18] Polyakov A Poznyak A Minimization of the unmatched disturbances in the sliding mode control systems via invariant ellipsoid method 1122 1127
[19] Choi, Variable structure output feedback control design for a class of uncertain dynamic systems, Automatica 38 (2) pp 335– (2002) · Zbl 0991.93021
[20] Xiang, An ILMI approach to robust static output feedback sliding mode control, International Journal of Control 79 (8) pp 959– (2006) · Zbl 1102.93007
[21] Cardim, Variable-structure control design of switched systems with an application to a DC-DC power converter, IEEE Transactions on Industrial Electronics 56 (9) pp 3505– (2009)
[22] Filippov, Differential Equations with Discontinuous Right-hand Sides (1988) · Zbl 0664.34001
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.