Optimal PID Control System of a Piezoelectric Microospitioner

This paper develops the control system of a piezoelectric micropositioner with an optimal PID control approach. In the control system development, the piezoelectric micropositioner is actuated by a voltage amplifier which is implemented by a linear operational amplifier with a compensator cascaded and the optimal PID control approach for trajectory tracking is developed from an approximated second-order linear model of the piezoelectric micropositioner. To obtain the approximated second-order linear model, an algorithm performed in a computer is taken to automatically identify the continuous-time transfer function from Bode diagrams. From the second-order linear model, the PID controller whose parameter values are determined theoretically by an optimal linear quadratic regulation (LQR) method is developed. By using the optimal PID control approach to trajectory tracking of the piezoelectric micropositioner, the high-performance tracking responses can be obtained. Experimental results from the piezoelectric micropositioner with the optimal PID control are illustrated to show the validity of the proposed control method for practical applications.