Modeling and Identification of the Rate-Dependent Hysteresis of Piezoelectric Actuator Using a Modified Prandtl-Ishlinskii Model

Piezoelectric actuator (PEA) is an ideal microscale and nanoscale actuator because of its ultra-precision positioning resolution. However, the inherent hysteretic nonlinearity significantly degrades the PEA’s accuracy. The measured hysteresis of PEA exhibits strong rate-dependence and saturation phenomena, increasing the difficulty in the hysteresis modeling and identification. In this paper, a modified Prandtl-Ishlinskii (PI) hysteresis model is proposed. The weights of the backlash operators are updated according to the input rates so as to account for the rate-dependence property. Subsequently, the saturation property is realized by cascading a polynomial operator with only odd powers. In order to improve the efficiency of the parameter identification, a special control input consisting of a superimposition of multiple sinusoidal signals is utilized. Because the input rate of such a control input covers a wide range, all the parameters of the hysteresis model can be identified through only one set of experimental data, and no additional curve-fitting is required. The effectiveness of the hysteresis modeling and identification methodology is verified on a PEA-driven flexure mechanism. Experimental results show that the modeling accuracy is on the same order of the noise level of the overall system.