Efficient tuning of linear multivariable controllers using iterative feedback tuning

Iterative feedback tuning is a direct tuning method using closed-loop experimental data. The method is based on numerical optimization and in each iteration an unbiased gradient estimate is used. Due to these unbiased gradient estimates, the method converges to a stationary point of the control criterion provided the closed loop signals remain bounded throughout the iterations. In this contribution, it is shown how such unbiased estimates can be obtained for multivariable linear time-invariant systems. Particular attention is given to the issue of keeping the experiment time to a minimum and several efficient algorithms are presented. It is shown that, for tuning an arbitrary linear time-invariant multivariable controller with nw inputs and nu outputs, 1+nuA—nw experiments are sufficient in each iteration of the algorithm. For disturbance rejection, an alternative algorithm is proposed which requires nu+nw experiments. As an illustration, the method is applied to a simulation model of a gas turbine engine.

[1]  A. Talkin,et al.  Adaptive servo tracking , 1961 .

[2]  V. Rajaraman,et al.  A parameter-perturbation adaptive control system , 1961 .

[3]  K. Narendra,et al.  An adaptive procedure for controlling undefined linear processes , 1964 .

[4]  K. Narendra,et al.  Multiparameter self-optimizing systems using correlation techniques , 1964 .

[5]  P. Parks,et al.  Liapunov redesign of model reference adaptive control systems , 1966 .

[6]  Lennart Ljung,et al.  Theory and Practice of Recursive Identification , 1983 .

[7]  Lennart Ljung,et al.  Adaptive control based on explicit criterion minimization , 1985, Autom..

[8]  V. Wertz,et al.  Adaptive Optimal Control: The Thinking Man's G.P.C. , 1991 .

[9]  Lennart Ljung,et al.  Information contents in identification data from closed-loop operation , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[10]  Brian D. O. Anderson,et al.  A new approach to adaptive robust control , 1993 .

[11]  S. Gunnarsson,et al.  A convergent iterative restricted complexity control design scheme , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[12]  Håkan Hjalmarsson.  Model Free Tuning of Controllers : Experience with Time-Varying Linear Systems , 1995 .

[13]  M. Gevers,et al.  Iterative weighted least-squares identification and weighted LQG control design , 1995, Autom..

[14]  Michel Gevers,et al.  Model-free Tuning of a Robust Regulator for a Flexible Transmission System , 1995, Eur. J. Control.

[15]  Håkan Hjalmarsson,et al.  For model-based control design, closed-loop identification gives better performance , 1996, Autom..

[16]  L. Ljung,et al.  Asymptotic Variance Expressions for Closed-Loop Identification and Their Relevance in Identification for Control , 1997 .

[17]  J. Sjoberg,et al.  Nonlinear controller tuning based on linearized time-variant model , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[18]  Håkan Hjalmarsson,et al.  Control of nonlinear systems using iterative feedback tuning , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[19]  Svante Gunnarsson,et al.  Iterative feedback tuning: theory and applications , 1998 .

[20]  Håkan Hjalmarsson.  Iterative Feedback Tuning , 1998 .

[21]  Bo Wahlberg,et al.  A primal-dual interior-point method for iterative feedback tuning , 1999 .