Adaptive Control Based on an Extended Kalman Filter for Hammerstein System-Application to Piezoelectric Actuators

In this paper, a new control scheme is proposed based on an Extended Kalman Filter (EKF) used as an observer to estimate both state and variable gain of a Hammerstein system. The nonlinear Hammerstein system consists of a static nonlinearity followed by a dynamic linear part, where we consider the static nonlinearity as a variable gain. Then, an adaptive PID control algorithm is designed to auto-tune the control gain of the controller through the gain estimation. Experiments have been carried out on a piezoelectric actuator (unimorph) commonly adopted in microrobotic applications. A Hammerstein model is applied to describe the piezoelectric hysteresis behaviour. Performances of our proposed control scheme are verified through simulation and experimentally compared to a conventional PID control algorithm.