A Variable Structure MRAC for a Class of MIMO Systems

Authors: Ardeshir Karami Mohammadi

Abstract:

A Variable Structure Model Reference Adaptive Controller using state variables is proposed for a class of multi input-multi output systems. Adaptation law is of variable structure type and switching functions is designed based on stability requirements. Global exponential stability is proved based on Lyapunov criterion. Transient behavior is analyzed using sliding mode control and shows perfect model following at a finite time.

Keywords: Adaptive control, Model reference, Variablestructure, MIMO system.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072076

References:

[1] Chiang-ju, C., King-Chuan, S., A-Chen, W., and Li-Chen, F., (1996), "A Robust MRAC Using Variable Structure Design for Multi variable plants," Automatica, 32,no. 6, pp. 833-848.
[2] Hsu, L., Araujo, A.D., and Costa, R.R., (1994), " Analysis and design of I/O based variable structure adaptive control," IEEE Trans. Automat. Control, pp. 4-21.
[3] Hsu, L., (1990), " Variable structure model reference adaptive control using only I/O measurement: General case," IEEE Trans. Automat. Control, pp. 1238-1243.
[4] Hung, J.Y., Gao, W., Hung, J.C., (1993), " Variable structure control: A survey," IEEE Trans. On Indust. Elect. , Vol. 40, no. 1, pp. 2-22.
[5] Karami mohammadi A., (2004), "Variable Structure Model Reference Adaptive Control, for SIMO Systems, " proceedings of ICCAS2004, August 25-27, Bangkok, Thiland.
[6] Itkis, U., (1976)," control systems of variable structure," John Wiley & sons Inc., New york.
[7] Narandra, K.S., Annaswamy, A.M., (1989), " Stable Adaptive Systems," Prentice-Hall Int. Inc..
[8] Utkin, V.I., (1978), " Sliding modes and their application in variable structure systems," New york: MIR.
[9] Cunha, J. P. V. S., Hsu, L., Costa, R. R., & Lizarralde, F. (2003). Outputfeedback model-reference sliding mode control of uncertain multivariable systems. IEEE Transactions on Automatic Control, 48(12), 2245-2250.
[10] Imai, A. K., Costa, R. R. and Hsu, L., Multivariable MRAC using Nussbaum gain. In proceedings of 2001 International symposium on adaptive and intelligent systems and control.