Tracking control of a 3-dimensional piezo-driven micro-positioning system using a dynamic Prandtl–Ishlinskii model

Abstract

A controller composed of a feed-forward loop based on a novel dynamic Prandtl–Ishlinskii (P-I) model and a PID feedback control loop is developed to support a 3-dimensional piezo-driven micro-positioning system for high-bandwidth tracking control. By considering the dynamic characteristics of the power amplifier, the dynamic P-I model can accurately describe the rate-dependent hysteresis of piezoelectric stack actuators (PSAs). To ensure that the hysteresis model is independent of system load, the P-I hysteresis operator in that model characterizes the relationship between the output force and the input voltage of PSAs. The dynamics equation of the mechanical is established by using the cutoff modal method. The feedforward control is designed based on the dynamic hysteresis model to reduce the rate-dependent hysteresis. The PID control is incorporated with the feedforward control to increase the tracking accuracy. Experimental results indicate that the controller can overcome the hysteresis efficiently and preserve good positioning accuracy in 1–100 Hz bandwidth. Just by introducing the dynamic characteristics of the power amplifier, which can be expressed as a first-order differential equation, the P-I model can accurately describe the rate-dependent hysteresis of the PSA, which provides a simple method to describe and control piezoelectric actuators and piezo-driven systems in a wide frequency.