Inversion-free feedforward hysteresis control using Preisach operator

TL;DR

This paper presents a novel inversion-free feedforward hysteresis control method using the Preisach model, achieving high bandwidth and accuracy by employing a high-gain integral loop with hysteresis in negative feedback.

Contribution

The paper introduces a new control scheme that eliminates the need for inversion in hysteresis compensation using the Preisach operator, enabling theoretically infinite bandwidth.

Findings

Loop error tends to zero with high feedback gain.

The control bandwidth can be theoretically infinite with continuous Preisach output.

Numerical examples validate the proposed control method.

Abstract

We introduce a new inversion-free feedforward hysteresis control using the Preisach model. The feedforward scheme has a high-gain integral loop structure with Preisach hysteresis operator in negative feedback. This allows obtaining a dynamic quantity which corresponds to the inverse hysteresis output, as the loop error tends towards zero for a sufficiently high feedback gain. By analyzing the loop sensitivity function with hysteresis that acts as a state-varying phase lag, we demonstrate the achievable bandwidth and accuracy of the proposed control method. Remarkable fact is that the control bandwidth is theoretically infinite, provided the Preisach operator in feedback can be implemented in a way to ensure the $\mathcal{C}^0$ continuous hysteresis output. Numerical control examples with the Preisach hysteresis model in differential form are presented.