Repetitive Control Research For Low-frequency Linear Vibration Table System

Low-frequency linear vibration table is an important testing device to calibrate the error model of inertial systems and instruments. In order to provide acceleration inputs within the known accuracy for inertial systems and instruments, the low- frequency vibration table should be with lower acceleration distortion. However, disturbances existing in the low-frequency linear vibration table will make its acceleration distortion worse. Therefore, how to reject or eliminate the disturbances is a serious problem to be solved. For low-frequency linear vibration table driven by permanent magnet linear synchronous motor, the disturbance forces are mainly friction force and force ripple. Considering the operating mode of the table is reciprocating motion, thus the input signal of it is periodic, and thus the disturbance force is also periodic function. On the other hand, repetitive learning control strategy has "repeated in learning" feature, which makes it very suitable for tracking periodic signals or suppress periodic disturbances. Thus, it is of great practical and theoretical significance to the research on the low-frequency linear vibration table based on the repetitive control.As a main participant, the author took part in and has completed 985 Subject Construction Project entitled"Low-frequency Linear Vibration Table"of Harbin Institute of Technology, and based on that, several repetitive control methods are proposed in this dissertation to improve the precision of low frequency linear vibration table. The main contents are as follows:First, we introduce the control system structure of the low-frequency linear vibration table. According to the required performance specifications, the model parameters of each module except for the controller's are given. Based on that, the current loop controller, velocity loop controller and position loop controller are designed, respectively. A series of experiments is conducted to test each module of the realized low-frequency linear vibration table control system. Moreover, the tracking error and acceleration distortion is tested. Experimental results are given to verify the effectiveness of the system design.Considering the reference input signal and disturbances of low-frequency linear vibration table system are periodic, a discrete-time repetitive control approach is proposed to improve the tracking performance of the system. First, the stability and the convergence performance of the tracking error of the discrete-time repetitive control system are analyzed, and based on this condition, a criteria is given to choose the parameter of the controller. Then, the time-delay element of the discrete-time repetitive controller is in series with lead compensation; the tracking/rejecting performance of the resulting discrete-time repetitive control system is analyzed, and a criterion is given to choose the parameter of the lead compensation element.Considering that the system model exists parametric uncertainties and the friction force exists non-parametric uncertainties, an adaptive repetitive learning control law is proposed based on function approximation technique. First, by using the function approximation technique, the non-parameter uncertainties of the friction force is transformed into the linear combination of orthogonal function. Then, the unknown parameters of system model and the linear combination are estimated based on the adaptive mechanism; the repetitive learning component is used to improve the tracking/rejection performance of the periodic input signal/disturbance force. According to the Lyapunov stability theory, an adaptive repetitive learning control scheme that guarantees the stability and the convergence of position tracking error of the system is designed.Considering that the system model exist parameters uncertainty and the friction force exist non-parametric uncertainty, an adaptive repetitive learning control law is proposed based on function approximation technique. First, by using the function approximation technique, the non-parameter uncertainties of the friction force is transformed into the linear combination of orthogonal function. Then, the unknown parameters of system model and the linear combination are estimated based on the adaptive mechanism; the repetitive learning component is used to improve the tracking/rejection performance of the periodic input signal/disturbance force. According to the Lyapunov stability theory, an adaptive repetitive learning control scheme that guarantees the stability and the convergence of position tracking error of the system is designed.Considering that there exist model parameter and non-parameter uncertainty, and unknown disturbances in low frequency linear vibration table, an adaptive repetitive learning control law is proposed based on fuzzy basis function network (FBFN). FBFN is used to estimate the system non-parametric uncertainties and unknown disturbances, which changes the identification problem from identifying the original non-parametric uncertainties and unknown disturbances to identifying the coefficients of FBFN. The adaptive component is used to the unknown parameters of system model and fuzzy rule. The adaptive repetitive learning control law designed by Lyapunov stability theory guarantees the system stability and the tracking performance.Considering the adaptive repetitive controller mentioned above containing many control parameters, it is tedious to obtain the suitable controller parameters by try and error method. Thus, a design method of the repetitive control system based on the integral sliding mode is proposed to reduce the controller parameters obtained by try and error method, and compensate the uncertainty of the system. First, the linear motor driven system is extended to an uncertain system with mismatching uncertainties. The repetitive control system is obtained through introducing the repetitive controller and state feedback controller to the uncertain system. Then, the repetitive control system is converted to a time-delay system, and a sufficient condition of system stability is derived in terms of a linear matrix inequality (LMI), and based on this condition, the problem of designing the low-pass filter and the state feedback controller is converted to a nonlinear matrix inequality problem. By using generalized singular value minimization algorithm, an iterative algorithm is presented to calculate the larger cut-off angular frequency of a low-pass filter and the parameters of the state feedback controller.