High-Precision Tracking of Piezoelectric Actuator Using Iterative Learning Control and Direct Inverse Compensation of Hysteresis

TLDR

Rate‑dependent hysteresis in piezoelectric actuators hampers precise motion control, and existing inverse‑compensation methods depend heavily on accurate hysteresis models, motivating a more robust approach. This study proposes a control strategy that integrates iterative learning control with a direct inverse hysteresis compensator, assuming a Hammerstein model of the actuator to simultaneously mitigate nonlinearities and uncertainties. The method employs a Hammerstein representation, uses ILC as a feedforward scheme that exploits prior input–output data to refine tracking, and is evaluated on polynomial, triangular, and step trajectories. Experimental results demonstrate that within five iterations the combined ILC–inverse approach reduces root‑mean‑square, relative, and maximum absolute tracking errors far below those achieved by a PI controller or a PI controller with inverse compensation.

Abstract

Rate-dependent hysteretic nonlinearity, which is an inherent characteristic of piezoelectric actuators (PEAs), causes a significant challenge in precise motion control of piezoelectric nanopositioning stages. In this paper, by assuming that the model of PEA takes a Hammerstein structure, a novel control strategy that combines iterative learning control (ILC) and the direct inverse of hysteresis is proposed to compensate for both nonlinearities and uncertainties of system simultaneously. Different from those existing direct inverse compensation methods whose control performance highly relies on the accuracy of the hysteresis model, the proposed control strategy is more robust by adding an additional ILC loop. Since ILC is essentially a feedforward control scheme that fully utilizes the input and output information in previous iterations, the tracking precision can be improved promptly in the iteration domain. Comparative experiments are performed to test the efficacy of the proposed algorithm for polynomial, triangular, and step signals. Results show that it is superior to pure proportional–integral (PI) controller and even PI controller combined with inverse compensator in the sense that the root mean square, relative, as well as maximal absolute errors of output tracking have been decreased remarkably within five iterations.