Research And Application Of Adaptive Recursive Terminal Sliding Mode Control Based On Positive Semi-definite Barrier Function

Nowadays,sliding mode control has attracted more and more attention because of its fast response,strong robustness,and can effectively deal with uncertainties and disturbances.Which has been applied to many control systems.The main research area of this paper is high-order sliding mode combined with barrier function.Compared with the traditional sliding mode,the high-order sliding mode solves the inherent chattering problem of the traditional sliding mode,and can better improve the steady-state accuracy.The barrier function does not need to require the knowledge of the upper bound of the disturbance,and can avoid the overestimation of the control gain.Combining the advantages of both has become a hot topic in current research.In this article,a novel second-order fast nonsingular terminal sliding mode control method based on positive semi-definite barrier function is proposed.Which combines the advantages of positive semi-definite barrier function,second-order sliding mode and fast nonsingular terminal sliding mode.This method gets rid of the dependence on the initial condition of the sliding variable.The adaptive adjustment of the controller gain in a lower amplitude mode is realized,meanwhile,the sliding variable and the systematic error(also its derivative)converge to a predefined region without the knowledge of the perturbation upper bound in a chattering free mode.Secondly,a novel positive semi-definite barrier function based adaptive recursive terminal sliding mode control for a class of uncertain nonlinear systems with actuator saturation is proposed.Which combines the advantages of positive semi-definite barrier function,adaptive recursive terminal sliding mode.In the presence of actuator saturation and external disturbances,the proposed control method not only improve the convergence performance and control accuracy of the system,but also better prevent actuator saturation.In addition,in order to prevent the problem of excessive positive semi-definite barrier function gain caused by sudden large disturbances,a modified barrier function gain form which can vary with the disturbance amplitude is also proposed,therefore the overestimation of the gain which may be difficult to achieve in reality is effectively avoided.The control method is further optimized.Finally,the joint debugging of MATLAB and Lab VIEW is used to test the real object of the multi-cylinder hydraulic press,which proves the effectiveness of the proposed control strategy in the actual system.In Summary,the three control methods proposed in this paper can make the sliding variable and the systematic error(also its derivative)converge to a predefined region in a finite time.And the stability analysis of the above three control strategies is carried out in detail,which proves the feasibility of the algorithm,and can be better applied to the actual system,further promoting the research and development of sliding mode control.