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

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. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, an output feedback-based hysteresis compensation approach is proposed for uncertain nonlinear systems with an unknown hysteresis operator. The nonaffine input, uncertainties, and hysteretic perturbation are handled by dynamic inversion and extended high-gain observers. The convergence of the tracking error in the closed-loop system under output feedback is analyzed. Simulation and experimental results demonstrate the performance of the proposed method.