Extremum-Seeking Control for the Adaptive Design of Variable Gain Controllers

In this paper, we experimentally demonstrate an extremum-seeking control strategy for nonlinear systems with periodic steady-state outputs, for the adaptive design of variable-gain controllers. Variable-gain control can balance the tradeoff between low-frequency disturbance suppression and sensitivity to high-frequency noise in a more desirable manner than linear controllers can. However, the optimal performance-based tuning of the variable-gain controller parameters is far from trivial, and depends on the unknown disturbances acting on the system. The extremum-seeking controller only utilizes output measurements of the plant, and can therefore be used to optimally design the parameters of the variable gain controller, without using direct information on the disturbances acting on the system. Experimental results are presented for the performance-optimal tuning of a variable-gain controller applied to a magnetically levitated industrial motion control setup performing tracking motions. The influence of the different parameter choices on the performance of the extremum-seeking controller is illustrated through experiments.