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

Abstract

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.

Application of Modeling and Control Approaches of Piezoelectric Actuators: A Review

“…There have been continuous efforts in improvisation of the existing hysteresis model, such as the modified P-I model [134,135] and the modified Preisach model [136,137] for better compensation of dynamic nonlinearity. Furthermore, the neural network-based models [138,139], fuzzy logic models [140,141], and support vector machinebased models [142,143] have also proved to help model the hysteretic characteristics of the piezoelectric actuators. Based on the understanding of the above-described modeling approaches, implementing a particular model majorly depends on rate-dependent or rate-independent behavior.…”

Hysteresis Modelling and Feedforward Control of Piezoelectric Actuator Based on Simplified Interval Type-2 Fuzzy System

“…The Prandtl-Ishlinskii model [14][15][16][17] was widely investigated for describing the rate-independent and rate-dependent, symmetric and asymmetric hysteresis. Preisach model [18,19], Duhem model [20], fuzzy system [21,22] and neural networks [23] were also presented to characterizing hysteresis. Regarding control strategies, feedback control algorithms incorporating feedforward control were mainly developed, such as finite-time learning control [24], iterative control [25,26], internal model-based feedback control [17] and fuzzy control [27].…”