General Design Method And Application Of Second-order Sliding Mode Extremum Seeking Control

Extremum seeking control(ESC)is a model-free adaptive control method,which has simple principle,low computation cost and great real-time performance.Among the existing extremum seeking methods,the sliding mode extrmum seeking control(SMESC)has gained wide attentions in recent decades with its good robustness and controllable convergence speed.However,as the classical SMESC schemes based on the traditional first-order sliding mode theory,the chattering phenomena and steady-state oscillation problems caused by sliding mode control itself will affect the performance of these methods to a certain extent,and limit their application in practical systems.In order to eliminate chattering phenomena,scholars have proposed the second-order SMESC(2-SMESC)method.However,the combination of second-order sliding mode control and extremum seeking problems will increase the difficulty of system design.In order to apply more kinds of classical second-order sliding mode control laws to ESC and make full use of the characteristics of various methods,a general structure of 2-SMESC is proposed in this paper,by the way,the general design method of the controller and the corresponding steady-state oscillation suppression strategy are also given.The sliding chattering and steady-state oscillation problems are thoroughly solved with our design.The main contents of this paper are summarized as following.Firstly,the convergence analysis of the classical first-order SMESC is given and the causes of chattering and steady-state oscillation in SMESC are pointed out respectively,which lays a solid foundation for the following research.Secondly,aiming at the problem that the existing 2-SMESC lacks a general design framework and the theoretical analysis is too complex,a general framework of 2-SMESC is proposed in this paper.By giving the necessary assumptions,standard form of sliding mode surface and the stability conditions,a unified control method is given,with it,we can directly apply many existing second-order sliding mode control laws to ESC.Through the redesign of the existing twisting algorithm and the new design of the algorithm with a prescribed convergence law and the super-twisting algorithm,the universality and validity of the proposed design method are fully verified.Thirdly,aiming at the steady-state oscillation which still exist in the proposed 2-SMESC,we make a deep analyzation of the common causes of the steady-state oscillation between the proposed method and the classical first-order method,and a steady-state oscillation suppression strategy based on the characteristics of sliding mode control is designed.When the system enters the steady-state stage,the oscillation amplitude can be reduced by adjusting the sliding surface parameters online.The simulation results indicate that,without affecting the original convergence speed of the method,the purpose of suppressing the steady-state oscillation is achieved and the convergence accuracy of the method is improved as well.Finally,the proposed 2-SMESC under the steady-state oscillation suppression strategy is applied to the maximum power point tracking(MPPT)problem of the alternator based energy conversion system.The whole control system is built under Simulink environment and verified by simulation.Compared with the control effect under the classical MPPT method,the practicability and superiority of the improved method are verified.