Robust adaptive repetitive learning control for low-frequency linear vibration table system

Due to the elimination of mechanical transmission mechanisms, permanent-magnet linear synchronous motors (PMLSM) as the driving part for low-frequency linear vibration table were more sensitive to disturbances and parameters uncertainties. Furthermore, significant nonlinear effects (e. g. friction and force ripple) worsen their motion precision. Aiming at these problems, a robust adaptive repetitive learning control scheme was presented to improve the precision of low-frequency linear vibration table. The control algorithm consisted of an adaptive control, an integral sliding mode control and a repetitive learning control. The adaptive control was used to estimate and compensate unknown model parameters; The integral sliding mode control could stabilize the low-frequency linear vibration table system and suppress aperiodic disturbance; The repetitive learning control was used to restrain the periodic disturbance and improve the tracking performance of periodic position signals. The robust adaptive repetitive learning control law designed by using Lyapunov theory guaranteed the system stability and the position tracking performance. The simulation results demonstrate the robust adaptive repetitive learning control scheme can provide the better tracking performance and improve the acceleration distortion for low-frequency linear vibration table.