Control system design for nano-positioning using piezoelectric actuators

This paper presents a systematic control system design for nano-positioning of a piezoelectric actuator (PEA). PEAs exhibit hysteresis nonlinearity, which can dramatically limit the application and performance of linear feedback control theory. Thus the hysteresis is compensated for based on the Maxwell resistive capacitor (MRC) model first. Then a proportional plus integral (PI) controller and a proportional double integral plus lead compensation (PII&L) controller are designed for the hysteresis-compensated PEA to account for model uncertainty, disturbance, and noise. The robust stability of both controllers is proved. The effectiveness of the proposed control scheme is demonstrated experimentally. Both controllers achieve fast precise positioning. The 2% settling times for the PI controller and the PII&L controller are 1.5 ms and 4.7 ms, respectively. The positioning resolution is upto 1 nm for both controllers.