Inversion-free feedforward hysteresis control using Preisach operator

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.