Research On The Design And Application Of Second-order Sliding Mode Extremum Seeking Control Method

Extremum seeking control(ESC)is a non-model-based adaptive control method which can solve operating point tracking or optimization problems in control systems.It has the advantages of simple structure and low computational cost and is adaptive to the unknown and uncertainty of practical systems.Sliding mode extremum seeking control(SMESC)is a main class of extremum seeking control,which maintains the advantage of robustness in sliding mode control.However,the chattering phenomenon and steady-state oscillation in SMESC have a negative impact on the performance of the method and limit the application in actual systems.In order to eliminate the chattering and steady-state oscillation in SMESC,a novel second-order extremum seeking control scheme is proposed and a non steady-state oscillation strategy is designed correspondingly in this paper.The rigorous analysis and verification of the proposed method are also given.The main results are as follows.Firstly,the basic principle and convergence of SMESC are analyzed.Based on the analysis,the reasons of the chattering and steady-state oscillation in SMESC are explained respectively,which provides the research ideas and theoretical basis for next improvement of the classical SMESC.Secondly,in order to solve the problem of chattering fundamentally,this paper proposes a novel second-order sliding mode extremum control scheme based on twisting algorithm.The proposed scheme eliminates the chattering in virtue of the feature of highorder sliding mode controller.The rigorous proof of convergence for the proposed scheme is presented and the relationship between parameters and convergence performance is discussed.The analysis for steady-state oscillation stage of the proposed scheme is also given to facilitate further improvement.Furthermore,the simulation shows the efficiency of eliminating the chattering.Thirdly,based on the common causes of steady-state oscillation in both classical SMESC and second-order SMESC,a non-steady-state oscillation control strategy is designed first for the classic SMESC so that the convergence performance can be further improved.In the strategy,the gradient is employed to adjust online reference signal to maintain the system on the sliding mode without oscillation.Then,we expand the control strategy into the proposed second-order method with considering its own characteristics.Consequently,the formed non-steady-state oscillation second-order sliding mode extremum seeking control scheme can suppress the chattering,eliminates the steady-state oscillation and improve the convergence accuracy while ensuring the original convergence speed.And the ability of eliminating the steady-state is fully verified by simulation.Finally,the proposed non steady-state oscillation second-order extremum seeking control scheme is applied to the fuel cell system to solve the maximum power point tracking problem.The control system with extremum seeking control scheme is built in Simulink.The comparison experiments with classical SMESC verify the efficiency and superiority of the proposed scheme.