Tracking control of hysteretic piezoelectric actuator using adaptive rate-dependent controller

Abstract

With the increasing popularity of actuators involving smart materials like piezoelectric, control of such materials becomes important. The existence of the inherent hysteretic behavior hinders the tracking accuracy of the actuators. To make matters worse, the hysteretic behavior changes with rate. One of the suggested ways is to have a feedforward controller to linearize the relationship between the input and output. Thus, the hysteretic behavior of the actuator must first be modeled by sensing the relationship between the input voltage and output displacement. Unfortunately, the hysteretic behavior is dependent on individual actuator and also environmental conditions like temperature. It is troublesome and costly to model the hysteresis regularly. In addition, the hysteretic behavior of the actuators also changes with age. Most literature model the actuator using a cascade of rate-independent hysteresis operators and a dynamical system. However, the inertial dynamics of the structure is not the only contributing factor. A complete model will be complex. Thus, based on the studies done on the phenomenological hysteretic behavior with rate, this paper proposes an adaptive rate-dependent feedforward controller with Prandtl-Ishlinskii (PI) hysteresis operators for piezoelectric actuators. This adaptive controller is achieved by adapting the coefficients to manipulate theweights of the play operators. Actual experiments are conducted to demonstrate the effectiveness of the adaptive controller. The main contribution of this paper is its ability to perform tracking control of non-periodic motion and is illustrated with the tracking control ability of a couple of different non-periodic waveforms which were created by passing random numbers through a low pass filter with a cutoff frequency of 20 Hz.