Dynamic inversion-based hysteresis compensation using extended high-gain observer

Abstract

We consider the tracking problem for an uncertain nonlinear single-input-single-output system satisfying the minimum-phase assumption, preceded by an unknown hysteresis operator. This is a widely used model for smart material-actuated systems, such as piezo-based nanopositioning systems. Existing hysteresis compensation methods typically require explicit hysteresis models, which tend to be high-dimensional operators and entail significant complexity in model identification and inversion. We propose an output feedback-based hysteresis compensation approach for this class of systems using dynamic inversion and extended high-gain observers. With mild assumptions on the hysteresis nonlinearity properties, the system can be represented as an uncertain, nonaffine, nonlinear system containing a hysteretic perturbation. Dynamic inversion is used to deal with the nonaffine input, uncertainties, and the hysteretic perturbation, where the latter two are estimated using an extended high-gain observer. Analysis of the closed-loop system under output feedback shows that the tracking error converges to a small neighborhood near the origin, which can be made arbitrarily small via a proper choice of time-scale parameters of dynamic inversion and the observer, respectively. Simulation results are presented to show the interplay between these two parameters. Finally, experiments conducted on a commercial nanopositioner confirm the theoretical analysis and demonstrate that the proposed method delivers performance comparable to several competing methods, all of which require an explicit hysteresis inversion operator.