Tunnung PID control gains for micro piezo-stage in using grey relational analysis

Due to the requirements of the nanometer resolution in displacement, high stiffness, and fast response, piezo-actuators are used often in high-precision positioning applications. However, the materials of the piezo-actuators are ferroelectric, they fundamentally exhibit hysteresis behavior in the response to an applied electric field. This research focuses on the controlling of the piezoelectric positioning stage. In order to study the sensitivity of tuning the PID parameters to achieve the desired performance, the grey relational analysis has been proposed. Therefore, by tuning the PID parameters, the proposed controller owns the capability in handling such uncertain information. The experimental results of the proposed grey relational methodology also show that it is technically and economically feasible to develop a low-cost, reliable, automatic, less time-consuming controller for piezoelectric positioning stage. Hence, the results of this proposed methodology can be practicable to various mechanical systems, such as positioning control subjected to external disturbances.