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Technical Briefs

Optimal H-Based Linear-Quadratic Regulator Tracking Control for Discrete-Time Takagi–Sugeno Fuzzy Systems With Preview Actions

[+] Author and Article Information
Hui Zhang

Center for Automotive Research,
Department of Mechanical and Aerospace Engineering,
The Ohio State University,
930 Kinnear Road,
Columbus, OH 43212
e-mail: huizhang285@gmail.com

Yang Shi

e-mail: yshi@uvic.ca

Bingxian Mu

e-mail: bxmu@uvic.ca
Department of Mechanical Engineering,
University of Victoria,
P.O. Box 3055, STN CSC,
Victoria, BC, V8W 3P6, Canada

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT AND CONTROL. Manuscript received January 23, 2012; final manuscript received March 7, 2013; published online May 13, 2013. Assoc. Editor: Qingze Zou.

J. Dyn. Sys., Meas., Control 135(4), 044501 (May 13, 2013) (5 pages) Paper No: DS-12-1029; doi: 10.1115/1.4024007 History: Received January 23, 2012; Revised March 07, 2013

This paper investigates the optimal tracking control problem for discrete-time Takagi–Sugeno (T–S) systems. The control signal has three components: preview control for the previewable reference signal, integral control for the tracking error, and the state-feedback control for the plant. The optimization objective is a quadratic form of the tracking error and the control signal. By using the augmentation technique, the tracking controller design problem is converted into a design problem of the state-feedback controllers for augmented T–S fuzzy systems. The quadratic optimization objective is equivalent to the two-norm (in fact, the square of the two-norm) of a controlled output. Assuming that the external inputs of the augmented systems are l2 bounded, the H performance index is employed to investigate and optimize the controller design. The controller gains can be obtained by solving a sequence of linear matrix inequalities (LMIs). An example on electromechanical system shows the efficacy of the proposed design method.

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References

Takagi, T., and Sugeno, M., 1985, “Fuzzy Identification of Systems and its Applications to Modeling and Control,” IEEE Trans. Syst. Man Cybern., 15(1), pp. 116–132. [CrossRef]
Gao, H., Zhao, Y., and Chen, T., 2009. “H∞ Fuzzy Control of Nonlinear Systems Under Unreliable Communication Links,” IEEE Trans. Fuzzy Syst., 17(2), pp. 265–278. [CrossRef]
Tanaka, K., and Wang, H. O., 2001, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach, Wiley, New York.
Lin, C., Wang, Q.-G., and Lee, T. H., 2006, “H∞ Output Tracking Control for Nonlinear Systems via T–S Fuzzy Model Approach,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern., 36(2), pp. 450–457. [CrossRef]
Elsayed, A., and Grimble, M. J., 1989, “A New Approach to the H∞ Design of Optimal Digital Linear Filters,” IMA J. Math. Control Inf., 6(2), pp. 233–251. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2012, “On H∞ Filtering for Discrete-Time Takagi-Sugeno Fuzzy Systems,” IEEE Trans. Fuzzy Syst., 20(2), pp. 396–401. [CrossRef]
McEneaney, W. M., 1998, “Robust/H∞ Filtering for Nonlinear Systems,” Syst. Control Lett., 33(5), pp. 315–325. [CrossRef]
Zhang, H., and Shi, Y., 2012, “Observer-Based H∞ Feedback Control for Arbitrarily Time-Varying Discrete-Time Systems With Intermittent Measurements and Input Constraints,” J. Dyn. Syst., Meas., Control, 134(6), p. 061008. [CrossRef]
Apkarian, P., and Gahinet, P., 1995, “A Convex Characterization of Gain-Scheduled H∞ Controllers,” IEEE Trans. Autom. Control, 40(5), pp. 853–864. [CrossRef]
Grigoriadis, K. M., and Watson, J. T., 1997, “Reduced-Order H∞ and L2-L∞ Filtering via Linear Matrix Inequalities,” IEEE Trans. Aerosp. Electron. Syst., 33(4), pp. 1326–1338. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2012, “Robust Equalisation for Inter Symbol Interference Communication Channels,” IET Signal Process., 6(2), pp. 73–78. [CrossRef]
Palhares, R., and Peres, P., 2000, “Robust Filtering With Guaranteed Energy-To-Peak Performance—An LMI Approach,” Automatica, 36(6), pp. 851–858. [CrossRef]
He, S., and Liu, F., 2010, “Robust Peak-To-Peak Filtering for Markov Jump Systems,” Signal Process., 90(2), pp. 513–522. [CrossRef]
Fridman, E., Shaked, U., and Xie, L., 2003, “Robust H∞ Filtering of Linear Systems With Time-Varying Delay,” IEEE Trans. Autom. Control, 48(1), pp. 159–165. [CrossRef]
Zhang, H., and Shi, Y., 2013, “Parameter-Dependent H∞ Filtering for Linear Time-Varying Systems,” J. Dyn. Syst., Meas., Control, 135(2), p. 021006. [CrossRef]
Zhang, J., Xia, Y., and Shi, P., 2009, “Parameter-Dependent Robust H∞ Filtering for Uncertain Discrete-Time Systems,” Automatica, 45(2), pp. 560–565. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2011, “Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems,” IEEE Trans. Ind. Electron., 58(12), pp. 5396–5405. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2012, “Robust H∞ PID Control for Multivariable Networked Control Systems With Disturbance/Noise Attenuation,” Int. J. Robust Nonlinear Control, 22(2), pp. 183–204. [CrossRef]
Åström, K. J., and Hägglund, T., 2001, “The Future of PID Control,” Control Eng. Pract., 9(11), pp. 1163–1175. [CrossRef]
Cohen, A., and Shaked, U., 1997, “Linear Discrete-Time H∞-Optimal Tracking With Preview,” IEEE Trans. Autom. Control, 42(2), pp. 270. [CrossRef]
Kojima, A., and Ishijima, S., 1999, “LQ Preview Synthesis: Optimal Control and Worst Case Analysis,” IEEE Trans. Autom. Control, 44(2), pp. 352–357. [CrossRef]
Takaba, K., 2000, “Robust Servomechanism With Preview Action for Polytopic Uncertain Systems,” Int. J. Robust Nonlinear Control, 10(2), pp. 101–111. [CrossRef]
Zattoni, E., 2008, “Perfect Elimination of Regulation Transients in Discrete-Time LPV Systems via Internally Stabilizable Robust Controlled Invariant Subspaces,” IEEE Trans. Autom. Control, 53(6), pp. 1509–1515. [CrossRef]
Wang, H. O., Tanaka, K., and Griffin, M. F., 1996, “An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues,” IEEE Trans. Fuzzy Syst., 4(1), pp. 14–23. [CrossRef]
Guerra, T. M., and Vermeiren, L., 2004, “LMI-Based Relaxed Nonquadratic Stabilization Conditions for Nonlinear Systems in the Takagi-Sugeno's Form,” Automatica, 40(5), pp. 823–829. [CrossRef]
Zhang, H., Shi, Y., and Saadat Mehr, A., 2011, “Robust Non-Fragile Dynamic Vibration Absorbers With Uncertain Factors,” J. Sound Vib., 330(4), pp. 559–566. [CrossRef]
Gao, H., Zhao, Y., Lam, J., and Chen, K., 2009, “H∞ Fuzzy Filtering of Nonlinear Systems With Intermittent Measurements,” IEEE Trans. Fuzzy Syst., 17(2), pp. 291–300. [CrossRef]
de Oliveira, M. C., Bernussou, J., and Geromel, J. C., 1999, “A New Discrete-Time Robust Stability Condition,” Syst. Control Lett., 37(4), pp. 261–265. [CrossRef]
Pipeleers, G., Demeulemaere, B., Swevers, J., and Vandenberghe, L., 2009, “Extended LMI Characterizations for Stability and Performance of Linear Systems,” Syst. Control Lett., 58(7), pp. 510–518. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Scheme of tracking control with preview and integral compensation

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