Research On Design And Application Of Extremum Seeking Algorithm Without Steady-state Oscillation

Extremum seeking algorithm (ESA) is an adaptive optimal algorithm which ismode free. The advantage of ESA include the simple principle, less amount ofcomputations and less required knowledge of the controlled object. It can drive andmaintain the controlled object to its extremum only with the information of the inputand output. However, the principle of the ESA determines that the phenomenon of thesteady-state oscillation will emerge inevitably when the ESA works. This greatly limitsthe scope of application of the algorithm. So, in order to eliminate the steady-stateoscillation of the ESA, this dissertation propose a kind of ESA without steady-stateoscillation and studies its stability and its application deeply. The main contribution ofthe dissertation can be summarized as follows:(1) The relationships between the performances and the algorithm parameters areanalyzed deeply for the perturbation-based ESA and the sliding-mode-based ESArespectively. The dissertation also illustrates the reasons for the generation of thesteady-state oscillation for the different ESAs.(2) A pre-demodulation ESA without steady-state oscillation is proposed byadjusting the structure of the classical ESA to make the sinusoidal excitation signalamplitude proportional to the square of the extremum estimation error. The improvedESA can speed up the convergence with large extremum estimation error to shorten thesearch time dramatically, and enlarge the search area to avoid falling to the localextremum effectively. It can also reduce the sinusoidal excitation signal amplitude withsmall extremum estimation error to eliminate the adverse effects of the steady-stateoscillation eventually. Learn from the above idea, a perturbation based ESA base on thesignal after demodulation also be proposed to make the sinusoidal excitation signalamplitude proportional to the absolute of the extremum estimation error. The improvedESA base on the signal after demodulation has a better adaptability for the extremumestimation error.(3) A sliding mode based ESA without steady-state oscillation is proposed bycombining the sliding mode based ESA with the perturbation based ESA withoutsteady-state oscillation through designing a switching law. The algorithm not only hasthe advantage of the sliding mode based ESA, such as a fast convergence androbustness, but also eliminates the steady-state oscillation and improves the preferencegreatly. In addition, a more rigorous and simple proof method of the stability of classicalsliding mode based ESA was given.(4) Finally, the application of the proposed ESA without steady-state oscillation inanti-lock braking system (ABS) is studied. The enormous simulation results illustrate the effectiveness and superiority of the ESA without steady-state oscillation proposed inthis dissertation.