Robust micro-positionnig control of a 2DOF piezocantilever based on an extended-state LKF

Abstract This paper presents a control scheme regarding to improve the performances of a piezoelectric actuator (PEA) for precise positioning tasks. The piezoelectric actuator exhibits strong nonlinear disturbances for 1- and 2-DOF motion, i.e. input-dependent hysteresis, creep and cross-couplings. These unwanted phenomena undeniably compromise the final precision of the targeted tasks (micromanipulation) and therefore it should be conveniently considered during the controller synthesis. In this regard, the dynamic equation is also split into a nominal model and a uncertain model including parametric uncertainties. We propose to use simultaneously a the discrete linear extended-state linear Kalman filter (ES-LKF), to estimate the aforementioned disturbances and the velocity, and Lyapunov-based controller to guarantee asymptotic stability while meeting the actuator limits. The proposed strategy permits to perform accurate positioning, for regulation and trajectory-tracking tasks, without a prior knowledge of parametric and unmodeled uncertainties. Real-time experiments were carried out with circular trajectories to demonstrate the efficiency of the proposed approach.