Design of Two-Loops Extremum Seeking System by Means of Localization Method

G.A. Frantsuzova (Russia)


Extremum seeking; Nonlinear dynamic plant;Localization method; Two-loops system; Outputderivatives feedback; Gradient proportional controller.


This work introduces an approach for extremum seeking control system design based on a localization method. It is considered a class of plants that is represented as a combination of a nonlinear input dynamics and a static nonlinearity with an extremum. The feature of this paper consists in the offered design approach of two-loops system where the internal subsystem includes a dynamic part of plant. The controller for this subsystem is based on the localization method and uses the derivatives of a output variable. It allows to ensure processes according to linear desirable model. The external contour contains the stabilized dynamic part ("equivalent" linear dynamics) and static nonlinear map. Then it is offered to organize gradient proportional controller in the external scheme contour. The parameters of the internal and external controllers are designed by means of poles assignment in the linear closed-loop system. In this case, seeking of the set-point (extremum value of the nonlinear output static map) is occured to required dynamic quality. The offered approach to system design is illustrated with a brief simulation study.

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