Abstract:The composite control method based on the singular perturbation method is presented for aimed at the problem of trajectory tracking and vibration suppression of one-link flexible manipulator. The dynamic model of the one-link flexible manipulator was established by the assumed mode method and the Lagrange equations. Then, the coupled dynamic equations were decomposed into slow (rigid) and fast (flexible) sub-systems based on the singular perturbation method. The controller of slow sub-system was designed using proportion integration differential (PID) control and sliding mode control (SMC) for vibration suppression introduced by control input, and the linear quadratic regulator (LQR) optimal control method was used to design fast sub-system controller for realizing simple linear state feedback control law. The numerical simulation results show that the method can not only realize the trajectory tracking of one-link flexible manipulator, but also has a good result on the vibration reducing of flexible manipulators. In addition the controller of slow sub-system designed by using the method of combining SMC with PID control can reduce the input chattering in the traditional SMC, and has a better control effect.