Robust performance enhancement using disturbance observers for hysteresis compensation based on generalized Prandtl-Ishlinskii model

This paper presents an approach employing disturbance observers (DOBs) to enhance the performance of inverse-based hysteresis compensation based on the generalized Prandtl-Ishlinskii model in feedback control reference-tracking applications. It is first shown that the error resulting from inexact hysteresis cancelation is an L_∞-bounded signal. Hence, a DOB is designed to cancel its effect and improve the closed loop robust tracking performance in the presence of plant uncertainty. The design of the DOB makes use of an equivalent internal model-based estimation of exogenous disturbances, where the internal model dynamics is designed to have at least one of its eigen-values at the origin. The synthesis is then formulated as an H_∞ weighted-sensitivity optimization for static output feedback (SOF) gain of a Luenberger observer. A linearization heuristic is then implemented to solve the bilinear-matrix-inequality (BMI) constrained semi-definite program (SDP) for a (sub)optimal static gain. Simulation results indicate that tracking performance is indeed improved using the combined inversion-based compensation and the DOB.