Adaptive repetitive learning control for improvement of acceleration distortion of low-frequency linear vibration table systems

An adaptive repetitive learning control (ARLC) scheme is presented to restrain the friction force, the ripple force and the dead zone characteristics in low-frequency linear vibration table systems. The function approximation technique is employed to transform the dead zone uncertainties into finite combinations of orthonormal basis functions. The control algorithm consists of an adaptive component, a PID component and a repetitive learning component. The adaptive component is used to estimate unknown parameters of finite combinations and those of the friction force model on line. The PID component can stabilize the low-frequency linear vibration table system and suppress aperiodic disturbances. The repetitive learning component is used to restrain the periodic ripple force without knowledge of the plant model and improve the performence of tracking periodic input signals. The ARLC law designed by using the Lyapunov theory guarantees the system stability and the tracking performance. The simulation results demonstrate the proposed scheme can improve the tracking performance and the acceleration distortion for low-frequency linear vibration table systems.