Design And Implementation Of Attracting-law-based Control For Discrete-time Systems

As one of the important equipments for modern industrial production,AC servo system has the characteristics of strong stability,high precision and rapid reponse.However,parameter perturbation and external disturbances have nagative effect on the control performance.Sliding mode control can improve system performance,because of external disturbances that satisfies matching conditions are suppressed.Design methods of discrete-time controllers for servo systems are studied to achieve the accurate tracking of repetitve trajectories and effective suppression of external disturbances in this dissertation,in order to improve the control performance of the servo motors.The main contributons of the dissertation are sumarried as follows:1.A non-switching attracting law is proposed to avoid the system chattering,and the disturbance suppression method is inolved in the attracting law to construct the ideal error dynamics,and at the same time,the discrete controller is designed to complete the tracking task.The specific expressions of the performance indexs including monotonic reduction region,absolute attracting layer,steady-state error band and convergence step number of tracking error are derived,which can be used to describe the transient and steady-state system performance and to tune the controller parameters.Numerical simulations show the effectiveness of the proposed method and the accuracy of performance indexs expressions.2.By using the even function of the tracking error as the variable to replace the proportional coefficient in the attracting law,the parameter self-tuning non-switching attracting law is constructed,including the non-switching variable-speed attracting law and the non-switching fast attracting law.Then the ideal error dynamics is constructed and the discrete controller is designed.Specific expressions for describingsystem tracking performance are derived,which are used for tuning controller parameters.Numerical simulations show the effectiveness of the proposed method and the accuracy of the tracking performance indexs expressions.3.An enhanced-switching attracting law is proposed,and the parameter self-tuning nonlinear function is used to optimize the constant coefficient in the exponential attracting law.Compared with the non-switching attracting law,the proposed method canimprove the convergence speed of thr tracking error,suppress the controller chattering and improve the system steady-state accuracy.The specific expressions that can characterize the system tracking performance are derived and compared with those of the exponential reaching law.Numerical simulations show the effectiveness of the proposed method and the accuracy of the tracking performance indexs expressions.4.The disturbance suppress method is imroved based on the feedback control,and a disturbance differential compensation scheme is proposed for dealing with the unknown disturbance problem is practical systems.The corresponding disturbance compensation can be selected according to the specific form of the reference trajectory to achieve the accurate tracking of the specified trajectory.In addition,for the periodic disturbance in the control system,discrete repetitive control technology is emploved to design the discrete repetitive controller based on the attracting law,and eliminate the influence of periodic disturbance and improve the steady-state tracking accuracy of the system.Numerical simulations show the effectiveness of the proposed method and the accuracy of the performance indexs expressions.5.Experimental verification of the proposed attracting laws on the permanent magnet synchronous motor platform,and the experimental results show that:(1)the accurate tracking of the specified trajectory;(2)the repetitive controller can better sippress the periodic disturbance compared with the feedback controller;(3)compared with the reaching law,the proposed attracting law can ensure the better transient and steady-state system performance;and(4)with the same controller parameters,the enhanced switching attracting law can improve the transient response speed of the system.