Hysteresis Modeling of Piezoelectric Actuators Based on a T-S Fuzzy Model

Piezoelectric actuators (PEAs) have been widely used in aerospace, electronic communication and other high-accuracy manufacturing fields because of their high precision, low power consumption, fast response, and high resolution. However, piezoelectric actuators have very complicated hysteresis nonlinearity, which greatly affects their positioning and control accuracy. Particularly in the field of active vibration control, the control accuracy of piezoelectric actuators is easily affected by noise points. To address the problem, this paper proposes a hyperplane probability c-regression model (HPCRM) algorithm to establish its T-S fuzzy model of hysteresis nonlinearity. Firstly, an improved fuzzy c regression clustering algorithm is proposed to identify the antecedent parameters of T-S fuzzy model. This algorithm not only divides the fuzzy space better but also effectively avoids the influence of noise points generated by the external environment during data acquisition. Secondly, a new type of hyperplane membership function is introduced to solve the problem that the traditional Gaussian membership function does not match the hyperplane clustering algorithm. Finally, the accuracy of the modeling method is confirmed by several comparative experiments. Experimental results show that the proposed method is more precise than the traditional fuzzy c-regression models (FCRM) and probability c-regression models (PCRM) under the sine signals of 5 Hz–100 Hz.