Dynamic modeling and displacement control of the piezoelectric actuator

The dynamic model and displacement control of piezoelectric actuators which are commercially available materials for managing extremely small displacements in the range of sub-nanometer are presented. Piezoceramics have electromechanical characteristics that transduce energy between the electrical and mechanical domains. However, they have hysteresis between the input voltage and output displacement, and this behavior is very demanding and complicated. In this paper, we propose a method of designing the control algorithm, and present the dynamic modeling equations which represent the hysteretic behavior between input voltage and output displacement. For this process, the piezoelectric actuator is treated as second-order linear dynamic system and system constants are determined by the system identification method. And, a classical PID controller is designed and used to regulate the output displacement of the actuator. To evaluate the performance of the proposed method, numerical simulation results were presented.