Precision Motion Control of a Piezoelectric Actuator via a Modified Preisach Hysteresis Model and Two-Degree-of-Freedom H-Infinity Robust Control

Abstract

The nonlinear hysteresis phenomenon can occur in piezoelectric-driven nanopositioning systems and can lead to reduced positioning accuracy or result in a serious deterioration of motion control. The Preisach method is widely used for hysteresis modeling; however, for the modeling of rate-dependent hysteresis, where the output displacement of the piezoelectric actuator depends on the amplitude and frequency of the input reference signal, the desired accuracy cannot be achieved with the classical Preisach method. In this paper, the Preisach model is improved using least-squares support vector machines (LSSVMs) to deal with the rate-dependent properties. The control part is then designed and consists of an inverse Preisach model to compensate for the hysteresis nonlinearity and a two-degree-of-freedom (2-DOF) H-infinity feedback controller to enhance the overall tracking performance with robustness. The main idea of the proposed 2-DOF H-infinity feedback controller is to find two optimal controllers that properly shape the closed-loop sensitivity functions by imposing some templates in terms of weighting functions in order to achieve the desired tracking performance with robustness. The achieved results with the suggested control strategy show that both hysteresis modeling accuracy and tracking performance are significantly improved with average root-mean-square error (RMSE) values of 0.0107 μm and 0.0212 μm, respectively. In addition, the suggested methodology can achieve better performance than comparative methods in terms of generalization and precision.

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“…Researchers have recently proposed numerous hysteresis models for piezoelectric actuators. These models primarily include the Preisach model [22][23][24], the Prandtl-Ishlinskii (P-I) model [25], the Krasonselskii-Pokrovskii (K-P) model [26], and the Bouc-Wen (B-W) model [27]. However, the models mentioned above are static models, and their accuracy tends to decrease as the input signal frequency increases.…”