On the application of multi-parameter extremum seeking control

In many control applications the best set point for operation is not known a priori, and yet, controller design tools tend to focus on regulation to known set points and reference trajectories. This paper presents and analytically verifies techniques for online optimization of set points. The main contributions of this paper include a new control law for multiple parameter set-points and a proof of exponential stability for the averaged system. Methodologies for implementing this control law in a discrete time setting are discussed. The application of this new algorithm to a magnetically suspended flywheel is detailed. The extremum seeking controller is used to minimize vibrations and the results of twenty runs compared with the expected physical model of the process. The fit is poor enough to justify the use of the online optimizer proposed.