EFFECT OF EXCITATION FREQUENCY IN PERTURBATION-BASED EXTREMUM SEEKING METHODS

In perturbation-based extremum-seeking methods, an excitation signal is added to the input, and the gradient, computed from the correlation between the input and output variations, is forced to zero. It is shown here that the distance between the optimum and solution reached by the perturbation method is proportional to the square of the frequency of excitation and does not go to zero with the amplitude of the excitation. However, for Wiener/Hammerstein approximations, the error will indeed go to zero with the excitation amplitude. Simulation results on a simple reaction system are used to illustrate the concepts presented in this work.