Stability of self‐tuning control based on Lyapunov function

The overall stability of a self-tuning controller for discrete-time systems is proved by using the Lyapunov function in this paper, for minimum and a class of non-minimum phase systems. The self-tuning controller utilizes a recursive estimate algorithm for the controller parameters based on the generalized minimum variance criterion. Previously, the stability had been proved in the case of minimum phase systems. A new type of self-tuning controller for the discrete-time system with delay in control input is also studied which is named the generalized minimum variance criterion-β equivalent control, and its stability is proved. The simulation is done to evaluate the performance of the proposed self-tuning controller. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  Björn Wittenmark,et al.  On Self Tuning Regulators , 1973 .

[2]  Choon Yik Tang,et al.  On discrete variable structure control with switching sector , 1999 .

[3]  Katsuhisa Furuta.  VSS-Type Self-Tuning Control-ß Equivalent Control Approach , 1993, 1993 American Control Conference.

[4]  C. Y. Chan,et al.  Servo-systems with discrete-variable structure control , 1991 .

[5]  K. Furuta.  Sliding mode control of a discrete system , 1990 .

[6]  K. Furuta,et al.  Discrete-time VSS represented by input-output relation , 1996, Proceedings. 1996 IEEE International Workshop on Variable Structure Systems. - VSS'96 -.

[7]  Katsuhisa Furuta,et al.  Selftuning, Sliding Mode And Adaptive Control for Direct Drive Motor , 1988, Proceedings.14 Annual Conference of Industrial Electronics Society.

[8]  P. Gawthrop.  On the stability and convergence of a self-tuning controller , 1980 .

[9]  Katsuhisa Furuta,et al.  Frequency-domain criteria of robust stability: Discrete-time and continuous-time systems, a unified approach , 1995 .

[10]  Choon Yik Tang,et al.  Discrete Variable Structure Control for Linear Multivariable Systems , 2000 .

[11]  E. A. Misawa,et al.  Discrete-Time Sliding Mode Control: The Linear Case , 1997 .

[12]  David W. Clarke,et al.  Self-tuning control of nonminimum-phase systems , 1984, Autom..

[13]  P. Ramadge,et al.  Discrete-time multivariable adaptive control , 1979 .

[14]  Katsuhisa Furuta,et al.  VSS type self-tuning control , 1993, IEEE Trans. Ind. Electron..

[15]  A. Morse.  Towards a unified theory of parameter adaptive control. II. Certainty equivalence and implicit tuning , 1992 .