Tuning PID control parameters for micro-piezo-stage by using grey relational analysis

The materials used in piezo-actuators, which ferroelectric, demonstrate inherent hysteresis behavior in an applied electric field. Unfortunately, this behavior typically results in control problems, with severe inaccuracy and degraded tracking performance. This work focuses on the control of the piezoelectric positioning stage. The hysteresis function is expressed as an external disturbance. Grey relational analysis is proposed to examine the sensitivity of the tuning of the PID parameters for such system, to achieve the desired performance. Accordingly, the PID parameters can be tuned to handle uncertain information. The experimental results of the proposed grey relational approach also indicate that developing a low-cost, reliable, automatic, less time-consuming controller than conventional PID control for a piezoelectric positioning stage is technically and economically feasible. Hence, the results obtained using this proposed methodology can be applied to various mechanical systems, such as positioning control subjected to external disturbances.