Design And Application Of Discrete Sliding Mode Repetitive Controller Based On Improved Reaching Law

In the actual industrial production,the systems with repetitive control tasks is more common.At the same time,with the widespread application of computers in the field of control,the research of discrete systems has attracted more and more attention.In these systems,there may be unknown disturbances such as parameter disturbance,external disturbance and un-modeled dynamic disturbance.With the increasingly strict requirements for product accuracy in industrial production,it is of great theoretical and practical significance to propose a high-precision control tracking method for systems with repetitive characteristics and unknown disturbances.In this paper,the parabolic function is embedded in the exponential approximation law according to the continuous and uninterrupted characteristics of the parabolic function at 0 and ±1,and the improved reaching law is obtained.The sliding mode controller is deduced and simulated with the server motor model.the results show that the discrete sliding mode controller is designed based on improved reaching law of quasi sliding mode with narrower,reduced the system oscillation,to improve control accuracy.Discrete repetition time of single input single output system,will get the discrete sliding mode controller combined with repetitive control method,discrete sliding mode repetitive controller,the existing system of the single cycle interference analysis of convergence performance,deduce the monotone convergence layer,absolute convergence layer,steady-state error and using the servo motor model simulation,the simulation results show that the discrete sliding mode,under the influence of the repetitive controller system near the convergence to the quasi sliding mode with the second cycle,quasi sliding mode changes over parameters,belt width and quasi sliding mode can converge to a very small bandwidth.In addition,in the existence of multiple periodic interference system,based on improved discrete reaching law to design mold repetitive controller,and the child repetitive controller in parallel to form a discrete sliding mode cycle more repetitive controller,the existence of multiple periodic disturbance system,convergence analysis of absolute convergence layer,the steady-state error is deduced with steps and approach,the simulation results show that the cycle in discrete sliding mode under the influence of the repetitive controller,the system quickly converge to the sliding mode surface,near the bandwidth and quasi sliding mode can converge to a small,minimal turbulence.Simulation results of linear servo motor demonstrate the effectiveness of the proposed algorithm.Finally,real experiments are carried out to verify that the vibration experiments of piezoelectric actuators and the repeated operation experiments on multi-cylinder hydraulic system all prove the effectiveness of the proposed discrete sliding mode repeating controller for the tracking control problem of the repeated system.In this paper,based on the research of discrete time repeating system,the controller is designed based on the improved approach law,and the sliding mode control method is combined with the repeated control method to obtain the sliding mode repeating controller,which improves the control accuracy.On this basis,for systems with multi-period disturbances,the designed sub-repetitive controllers are overlapped to obtain the final controller,which improves the convergence speed and control quality.Experiments on piezoelectric actuators show the effectiveness of the proposed algorithm.In the application of multi-cylinder hydraulic system,the problem of repetitive operation in hydraulic operation is solved,and the research area of repetitive control is expanded.