Robust Sliding Mode Control of Class of Linear Uncertain Saturated Systems

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This paper proposes a new design approach of continuous sliding mode control of linear systems in presence of uncertainty and saturation. The saturation constraint is reported on inputs vector and uncertainty being norm bounded reported on both dynamic and control matrices. In a first step, the design of the sliding surface is formulated as a pole assignment of linear uncertain and saturated system in a specific region through convex optimization. The solution to this problem is therefore numerically tractable via linear matrix inequalities (LMI) optimization, which leads to the development of a continuous and non-linear control law. In a second step, an approximation on the trajectory deviation of the uncertain saturated system compared to the ideal behavior is proposed to provide robustness of the nonlinear control. Finally, the validity and the applicability of this approach are illustrated by a multivariable numerical example of a robot pick and place.
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Sliding Mode Control; Norm Bounded Uncertainty; Saturation; Robustness

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S.V. Emelyanov, Automatic Control Systems of Variable Structure (Moscow, Nauka, 1967).

U. Itkis, Control Systems of Variable Vtructures (Wiley, New York, 1976).

V.I. Utkin, Sliding Modes and their Applications in Variable Structure Systems, IEEE Transactions on Automatic Control, Vol. 22: 279, 1977.

C.M. Dorling and A.S.I. Zinober, Two Approaches to Hyperplane Design Multivariable Variable Structure Control Systems, I. J. of Control, Vol. 44 (Issue 1):65-82, 1986.

A.S.I. Zinober, An Introduction to Sliding Mode Variable Structure Control, Lecture Notes in Control and Information, Springer-Verlag, 1994.

Abiri Ebrahim, Rashidi Farzan, Application of Virtual Flux-Direct Power Control for VSC Based HVDC Systems, (2009) International Review of Electrical Engineering (IREE), 4 (6), pp. 1204-1209.

Afshari H., Nazari M., Davari M., Gharehpetian G. B., Dynamic Voltage Restorer with Sliding Mode Control at Medium Voltage Level, (2010) International Review of Electrical Engineering (IREE), 5 (2), pp. 409-415.

D. Arzelier, J. Bernussou,, and G. Garcia, Pole Assignment of Linear Uncertain Systems in a Sector Via a Lyapunov-Type Approach, IEEE Trans. on Automatic Control, Vol. 38(Issue 7):1128-1131, 1993.

E.P. Ryan and M. Corless, Ultimate Boundedness and Asymptotic Stability of a Class of Uncertain Dynamicall Systems Via Continuous and Discontinuous Feedback Control, IMA Journal of Mathematics and Control Information, Vol. 1:223-242, 1984.

A. Sellami, D. Arzelier, R. M’hiri, J. Zrida, A Sliding Mode Control Approach for Systems Subjected to a Norm-Bounded Uncertainty, International Journal of Robust and Nonlinear Control, Vol. 17(Issue 4):327-346, 2007.

Sarcheshmah M. Sadeghi, Seifi A. R., A New Fuzzy Power Flow Analysis Based on Uncertain Inputs, (2009) International Review of Electrical Engineering (IREE), 4 (1), pp. 122-128.

P. Hippe, Windup Prevention for Stable and Unstable MIMO Systems, International Journal of Systems Science, Vol. 37(Issue 2):67-78, 10 February 2006.

Manoel Gomes da Silva Jr, Romeu Reginatto and Sophie Tarbouriech, Anti-Windup Design Guaranteed Regions of Stability for Discrete-Time Linear Systems with Saturating Controls, Revista Controle & automaçao, Vol. 14(Issue 1), jan., Fev e Março 2004.

M.L. Corradini and G. Orlando, Linear Unstable Plants with Saturating Actuators: Robust Stabilization by a Time Varying Sliding Surface, Automatica, Vol. 43:88-94, 2007.

Haijun Fang, Zongli Lin and Tingshu Hu, Analysis of Linear Systems in the Presence of Actuator Saturation and L2-Disturbances, Automatica Vol. 40:1229-1238, 2004.

Wolfgang Reinelt, Control of Multivariable Systems with Hard Contraints, Technical reports from the Automatic Control group in LinkÖping, available at the, Report N°.: LiTH-ISY-R-2348.

B. Torchani, A. Sellami, R. M'hiri, G. Garcia, Control of saturated systems with sliding mode, 16th IEEE International Conference on Electronics, Circuits, and Systems~ICECS2009~, pp. 567-570, Hammamet, Tunisia, 2009.

Mounir Klai, Stabilisation des systèmes linèaires continus contraints sur la commande par retour d’état et de sortie saturés, Ph.D.dissertation, Paul sabatier Univ., Toulouse, 1994.

C.A. Woodham and A.S.I.Zinober, Eigenvalue Placement in a Specified Sector for Variable Structure Control Systems, I.J.of Control, Vol. 57(Issue 5):1021-1037, 1986.


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