Modeling and Control of Piezoelectric Hysteresis: A Polynomial-Based Fractional Order Disturbance Compensation Approach

Piezoelectric hysteresis is a critical issue that significantly degrades the motion accuracy of piezo-actuated nanopositioners. Such an issue is difficult to be precisely modeled and compensated for, primarily due to its asymmetric, rate, and input amplitude-dependent characteristics. This article proposes a novel method to deal with this challenge. Specifically, a polynomial-based fractional order disturbance model is proposed to accommodate and characterize the complex hysteresis effect. In this model, the rate dependence is captured by a general method of implementing curve fitting in Bode magnitude plot. The inverse model for control purposes is immediately available from the original one. The proposed method does not require expensive computational resources. In fact, this article shows that this controller can be easily implemented in an analog manner, which brings the advantages of high bandwidth and low cost. Extensive modeling and tracking experiments are carried out to demonstrate the effectiveness of the proposed method. It is shown that the piezoelectric hysteresis nonlinearity can be significantly suppressed over a wide bandwidth.