Two-Cascade Extremum Seeking Systems for Nonlinear Non-Stationary Plants

Abstract

The controller synthesis problem for an automatic extremum-seeking system in the case of SISO plants is considered. The plant model can be represented as a serial connection of a nonlinear dynamic component and a static quality function with a certain minimum or maximum value. It is proposed for the individual plant components to organize two separate cascades with the different processes rates in the system. The controller synthesis procedures for each loop are presented. At the first stage, it is suggested to stabilize the processes in the inner contour by means of a controller based on the localization method or to organize a sliding mode in it. Such controllers allow to suppress the perturbations and nonlinear characteristics of the plant dynamic part, as well as to provide the required properties to the inner cascade. In order to the extremum seeking in the outer control loop, it is recommended to use a typical I-controller. The extremum seeking process is corresponded to the first-order linear differential equation. The main differences between the two extremum systems types are shown, depending on the inner loop controller type. The presented numerical simulation results of the two systems types in MatLab illustrate their basic properties.