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Research Papers

LMI Based Sliding Mode Surface Design With Mixed H2/H Optimization

[+] Author and Article Information
Shirin Valiloo

e-mail: sh.valiloo@gmail.com

Mohammad J. Khosrowjerdi

e-mail: khosrowjerdi@sut.ac.ir

Mohammad Salari

e-mail: salari@gmail.com

Department of Electrical Engineering,
Sahand University of Technology,
P.O. Box 51335-1996, Sahand,
Tabriz, Iran

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 24, 2013; final manuscript received September 22, 2013; published online October 15, 2013. Assoc. Editor: Srinivasa M. Salapaka.

J. Dyn. Sys., Meas., Control 136(1), 011016 (Oct 15, 2013) (9 pages) Paper No: DS-13-1167; doi: 10.1115/1.4025553 History: Received April 24, 2013; Revised September 22, 2013

In this paper sliding mode surface design is concerned with multi objective optimization for nonlinear continuous-time systems in the presence of matched and mismatched uncertainties and disturbances. In order to reduce the effect of uncertainties and disturbances on sliding motion, this problem is formulated as a well-motivated mixed H2/H optimization problem and a constructive algorithm based on linear matrix inequality (LMI) is proposed. We also give an LMI-based sliding mode control law to direct the system trajectories onto the designed sliding surface. Finally, using a numerical example, we show the effectiveness of proposed method.

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Figures

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Fig. 1

Disturbance signal w(t)

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Fig. 2

System closed loop behavior using H2 approach and θ = 1. Top: sliding surface value σ = Cx; bottom: states x(t).

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Fig. 3

System closed loop behavior using mixed H2/H approach and θ = 1. Top: sliding surface value σ = Cx; bottom: states x(t).

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Fig. 4

Control effort u for θ = 1. Top: using H2 approach; bottom: using mixed H2/H approach.

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Fig. 5

System closed loop behavior using H2 approach and θ = 10. Top: sliding surface value σ = Cx; bottom: states x(t).

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Fig. 6

System closed loop behavior using mixed H2/H approach and θ = 10. Top: sliding surface value σ = Cx; bottom: states x(t).

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