Sliding mode controlled variable speed power combination function reaching law

The invention belongs to the technical field of automatic control, provides a segmented variable-speed power reaching law aiming at the problems that the reaching rate of sliding mode control is low and buffeting is generated, and introduces a nonlinear function to design parameter items of a variable-speed power combination function according to the characteristics of a fast reaching law and a power reaching law. The reaching law ensures that the system has the characteristic of rapid convergence in each stage, so that the system can realize rapid convergence in each stage in the reaching process and has the characteristic of fixed-time convergence. When the system has model uncertainty and external interference, the reaching law can enable a sliding mode variable to be converged to a steady-state error boundary within finite time. The method is applied to stability control of a trolley inverted pendulum system, and the effectiveness and superiority of the method are verified through simulation results and n