Disturbance observer-based control with hysteresis identification in piezoelectric deformable mirrors

Piezoelectric deformable mirrors are complex systems with a reflective face-sheet and underlying actuators. The inherent hysteresis phenomenon in piezoelectric materials introduces nonlinearity and delay, rendering conventional control methods inappropriate for deformable mirror actuation. This study presents a disturbance observer-based controller with the generalised Bouc-Wen hysteresis parameter identification algorithm. Analytical proofs establish fixed-time stability for the observer and controller. A key feature of the proposed disturbance observer is the convergence of the estimated hysteresis to the actual value after a prescribed settling time, which facilitates precise hysteresis parameter identification. This is based on a data clustering technique, unlike most previous works. The proposed controller has the capability of hysteresis compensation and reference tracking in the piezoelectric deformable mirror actuators. Numerical simulation results are present to evaluate the tracking performance of the controller in the presence of random wavefront, the convergence of disturbance to the actual value in the fixed time, and identification of hysteresis parameters.