Controller Design Based on Decorrelation

Miskovic L., A. Karimi and D. Bonvin. Correlation-Based Tuning of a Restricted-Complexity Controller for an Active Suspension System. European Journal of Control, 2003, Vol. 9(1), 77-83

Karimi A., L. Miskovic and D. Bonvin. Iterative Correlation-Based Controller Tuning: Application to a Magnetic Suspension System. Control Engineering Practice , 2003, 11, 1069-1078

Karimi A., L. Miskovic and D. Bonvin. Iterative Correlation-Based Controller Tuning: Frequency Domain Analysis. 41st IEEE Conference on Decision and Control, Las Vegas, Nevada USA / december 2002, 4215-4220

Karimi A., L. Miskovic and D. Bonvin. Convergence Analysis of an Iterative Correlation-Based Controller Tuning Method. 15th IFAC World Congress, Barcelona, Spain (July 2002), 1546 KARIMI Alireza, MISKOVIC Ljubisa, BONVIN Dominique

A new time-domain methodology for controller tuning using closed-loop data based on the correlation approach is proposed. The main idea is to make the closed-loop output error (the difference between the output of the closed-loop system and a reference model) uncorrelated with the excitation signal. The controller parameters are solution of a correlation equation involving instrumental variables. This equation is solved iteratively using closed-loop data. The conditions for the existence and uniqueness of the solution are being investigated.

For the case where there is at least one solution, the convergence, consistency and accuracy of the estimated controller parameters for different choices of instrumental variables are analyzed. The case of slowly time-varying systems is also considered, for which appropriate recursive algorithms are developed.

For the case where the correlation equation has no solution, two approaches are considered. The first one minimizes a norm of the correlation function, and the bias distribution of the estimates can be analyzed in the frequency domain. This analysis shows the frequency regions in which the performance of the closed-loop system with respect to the reference model is preserved. The second approach consists of dividing the closed-loop output error in two parts: the correlated part and the uncorrelated part with respect to the excitation signal. Then, the objective of the control design is to minimize the infinity norm of the correlated part. For this purpose, the problem is formulated in the form of linear matrix inequalities (LMIs) and solved via convex optimization.

An application of the proposed method to an international benchmark for control design is planned.