High-speed tracking control of piezoelectric actuators using an ellipse-based hysteresis model

In this paper, an ellipse-based mathematic model is developed to characterize the rate-dependent hysteresis in piezoelectric actuators. Based on the proposed model, an expanded input space is constructed to describe the multivalued hysteresis function H[u](t) by a multiple input single output (MISO) mapping Gamma:R(2)-->R. Subsequently, the inverse MISO mapping Gamma(-1)(H[u](t),H[u](t);u(t)) is proposed for real-time hysteresis compensation. In controller design, a hybrid control strategy combining a model-based feedforward controller and a proportional integral differential (PID) feedback loop is used for high-accuracy and high-speed tracking control of piezoelectric actuators. The real-time feedforward controller is developed to cancel the rate-dependent hysteresis based on the inverse hysteresis model, while the PID controller is used to compensate for the creep, modeling errors, and parameter uncertainties. Finally, experiments with and without hysteresis compensation are conducted and the experimental results are compared. The experimental results show that the hysteresis compensation in the feedforward path can reduce the hysteresis-caused error by up to 88% and the tracking performance of the hybrid controller is greatly improved in high-speed tracking control applications, e.g., the root-mean-square tracking error is reduced to only 0.34% of the displacement range under the input frequency of 100 Hz.