Design a Linear Quadratic Gaussian Controller for Piezo-Positioning Stage

The piezo-positioning stage driven by piezoelectric (PZT) actuators has been widely used in the precision engineering field. Because that in an actual piezo-positioning control system, it is usually difficult to obtain an accurate mathematical model of the controlled object, and there is also the problem of some disturbances in the system, a Linear Quadratic Gaussian (LQG) control system is given. In this control system, an optimal controller for a deterministic linear quadratic regulator problem is obtained by solving a state feedback law equation. A Kalman filter is designed to obtain the best state estimation value of the control system, so as to solve the problem that the state must be measurable and usable for feedback. According to simulation results, the dynamic response and robustness performance of designed LQG control system is given, it obviously seen that the designed control system has no-overshoot, good dynamic characteristics and stability, it can effectively suppress the step disturbance at the output. These indicate that the designed controller is effective and feasible.