Extremum seeking control with adaptive disturbance feedforward

This paper presents an extension to the classical gradient-based extremum seeking control for the case when the disturbances responsible for changes in the extremum of a selected performance function are available for measurement. Based on these additional measurements, an adaptive extremum seeking disturbance feedforward is designed that approximates the unknown, static mapping between the disturbances and the optimal inputs. For this purpose, orthogonal, multivariate Tchebyshev polynomials are used. The feedforward enables the extremum seeking to be conducted in the proximity of the extremum thus yielding improvements both in terms of accuracy and increased convergence speed compared to the traditional scheme. Simulation results given for a turbine driven electrical generator system demonstrate the benefits of the presented design.