Hysteresis compensation of a piezoelectric-stack-actuator-driven (PSA-driven) system using inversion-based models and feedback control

Abstract

This paper compares tracking performances of the inverse hysteresis model-based feedforward compensator and the feedback-feedforward combined controller for the time-varying hysteresis nonlinearity of a piezoelectric-stack-actuator-driven (PSA-driven) system. Three different inverse hysteresis models, including Bouc-Wen, polynomial, and Prandtl-Ishlinskii (PI), are adopted to design feedforward compensator for the PSA-driven compliant system. Particle swarm optimization (PSO) scheme is employed to estimate model parameters of the Bouc-Wen and PI hysteresis models, respectively, whereas the least-mean-square-error based criterion is utilized in identifying the polynomial-based hysteresis model. Although solely feedforward compensation approach seems workable for systems with rate-independent hysteresis or slow tracking trajectories, large modeling errors are inevitable when fast trajectory or rate-dependent hysteresis is facing. To improve tracking performances, conventional PID control is augmented to the feedforward controllers. The resultant scheme is denoted as the feedback-feedforward combined control. To compare control performances of the solely feedforward and feedback-feedforward combined scheme, a number of experiments focusing on sinusoidal trajectories with different frequency have been implemented on the PSA-driven stage system. The results indicate that significant performance improvement can be achieved provided PID control is augmented to the solely feedforward approach. When different hysteresis models are of concerned, PI hysteresis model performs better in either feedforward or combined cases.