An Adaptive Takagi–Sugeno Fuzzy Model-Based Predictive Controller for Piezoelectric Actuators

Piezoelectric actuators (PEAs) are widely used in the nanopositioning applications due to their high stiffness, fast response, and ultrahigh precision. However, PEAs inherently have the hysteresis nonlinearity which can dramatically degrade the tracking performance. This paper proposes an adaptive Takagi-Sugeno (T-S) fuzzy model-based predictive controller with a parallel distributed control structure. Compared to the previous results, the proposed controller does not require the inverse hysteresis model of PEAs, and is easy to be calculated because the predictive subcontroller for each T-S fuzzy rule has an explicit form. Meanwhile, the parameters in the T-S fuzzy model can be online adjusted according to the real-time tracking error feedback, and the offline training accuracy of the T-S fuzzy model is no longer a serious concern. In addition, some physical constraints of the proposed controller can be well handled. To verify the proposed method, experiments are conducted on a commercial PEA product, and experiment results show that the proposed method has a satisfactory tracking performance. Furthermore, comparisons with some existing controllers are made and the proposed adaptive fuzzy model-based predictive controller outperforms these controllers.

I. Introduction

Recently, nanopositioning has been drawing considerable attention in the modern manufacturing. Because of the properties of high stiffness and fast response, piezoelectric actuators (PEAs) have been widely used as a core component in many practical nanopositioning applications, such as the micromanipulator [1] and ultraprecision mechanism [2]. However, the undesired inherent “hysteresis nonlinearity” can greatly deteriorate the positioning performance of PEAs. Hysteresis, one of the dominant nonlinear characteristics of PEAs, is a kind of memory effect where the current displacement of PEAs is affected not only by its current control effort but also by its past displacements [3]. Furthermore, the dynamics of PEAs is also relevant to the frequency of its control input (called rate-dependent property). When the frequency of the control input changes, the dynamical behavior of PEAs has a visible variation. Because of these particular phenomena, how to control PEAs with a desired precision becomes a challenging task.