LuGre Friction Model Based Adaptive Control With Functional Approximation Compensation for a Piezoelectric-Actuating Table

Since the piezoelectric actuators have the disadvantages of small travel and hysteretic behavior, a long range friction actuating mechanism was designed. The piezoelectric material is used to generate high frequency oscillation for actuating a finger tip which contacted with a slide to induce the back and forth motion. The LuGre friction model is chosen to simulate the dynamics of this friction actuating mechanism. However, this piezoelectric actuating system has obvious nonlinear and time-varying dead-zone offset control voltage due to the static friction and preload. It is difficulty to establish an accurate dynamic model for model-based precision control design. Hence, the functional approximation (FA) scheme is employed to compensate the system modeling error. The Laypunov-like design strategy is adopted to derive the adaptive laws and the system stability criterion. Different trajectories tracking control are planned to investigate the motion control performance and the steady state error of this adaptive controller. The dynamic experimental results of the proposed controller are compared with that of a model-based PID controller.