Nonlinear compensation control scheme for acceleration distortion of low-frequency linear vibration table system

An adaptive repetitive learning control scheme based on the fuzzy basis function network (FBFN) is presented to restrain model uncertainties and external disturbances in low-frequency linear vibration table system. FBFN is used to estimate model uncertainties and external disturbances, which change the identification problem from identifying model uncertainties and disturbances to identifying the coefficients of FBFN. The control algorithm consists of an adaptive component and a repetitive learning component. The adaptive component is used to estimate weight coefficients of FBFN. To attenuate chattering effectively, the discontinuous control is approximated by an adaptive PI control structure. Due to the bound of the discontinuous control term being assumed to be unknown, an adaptive mechanism is used to estimate this bound. The repetitive learning component is used to improve the tracking performance of periodic input signals. The adaptive repetitive learning control law designed by using Lyapunov theory guarantees the system stability and the position tracking performance. The simulation results demonstrate the adaptive repetitive learning control scheme can improve the tracking performance and acceleration distortion for low-frequency linear vibration table.