Ultra-precise tracking control of piezoelectric actuators via a fuzzy hysteresis model

In this paper, a novel Takagi-Sugeno (T-S) fuzzy system based model is proposed for hysteresis in piezoelectric actuators. The antecedent and consequent structures of the fuzzy hysteresis model (FHM) can be, respectively, identified on-line through uniform partition approach and recursive least squares (RLS) algorithm. With respect to controller design, the inverse of FHM is used to develop a feedforward controller to cancel out the hysteresis effect. Then a hybrid controller is designed for high-performance tracking. It combines the feedforward controller with a proportional integral differential (PID) controller favourable for stabilization and disturbance compensation. To achieve nanometer-scale tracking precision, the enhanced adaptive hybrid controller is further developed. It uses real-time input and output data to update FHM, thus changing the feedforward controller to suit the on-site hysteresis character of the piezoelectric actuator. Finally, as to 3 cases of 50 Hz sinusoidal, multiple frequency sinusoidal and 50 Hz triangular trajectories tracking, experimental results demonstrate the efficiency of the proposed controllers. Especially, being only 0.35% of the maximum desired displacement, the maximum error of 50 Hz sinusoidal tracking is greatly reduced to 5.8 nm, which clearly shows the ultra-precise nanometer-scale tracking performance of the developed adaptive hybrid controller.