Observer and Robust $H_{\infty }$ Control of a 2-DOF Piezoelectric Actuator Equipped With Self-Measurement

This letter introduces a dynamic observer in order to estimate the displacement in a 2-DOF piezoelectric actuator (piezoactuator) devoted to precise positioning and equipped with static self-measurement circuit. Then, the estimated displacement derived by the suggested observer is used as feedback for a robust H
_∞
controller. The 2-DOF piezoactuator is characterized by strong cross-couplings which are accounted for in the observer and in the feedback controller. Experimental results demonstrate the efficiency of the observer as well as the H
_∞
controller. The approach is very interesting for piezoelectric systems where it is difficult to implement sensors for feedback, such as in precise positioning applications at the small scale where measurement technology is still challenging.