Displacement Control of Piezoelectric Actuator using the PID Controller and System Identification Method

The piezoelectric actuators are electromechanical device and transduce energy between the electrical and mechanical domains, and they are commercially available materials for managing extremely small displacements in the range of sub-nanometer. Due to their simplicity, high stiffness, low wear and tear, and fast response, they are used for high precision mechanical and electrical engineering applications. However, piezoceramics are dielectric material and they suffer from hysteretic behavior inherent to nonlinear dielectric materials. This characteristic is electrical behavior and affects the micro adjustment and control. To determine the dynamic modeling equations which represent the hysteretic behavior between input voltage and output displacement, we performed the model reduction. This paper, the piezoelectric actuator is treated as second-order liner dynamic system. And the system identification method which deals with the problem of building mathematical models of dynamic systems based on observed data collected from system is used to determine the system constants. A classical PID controller is designed and used to regulate the output displacement, and the PID controller gains which minimize the system error are selected by optimization technique. In this paper, dynamic modeling and controller design method of piezoelectric actuator were presented. For this process, we utilized the system identification method and a classical PID controller. Numerical simulation and experimental test results demonstrate that the hysteresis characteristic between input voltage and output displacement is clearly modeled and endpoint displacement of actuator can be controlled.