Beyond the Waterbed Effect: Development of Fractional Order CRONE Control with Non-Linear Reset

TL;DR

This paper introduces a novel CRONE reset control method that combines fractional order control with non-linear reset techniques to improve robustness and performance beyond traditional waterbed effect limitations.

Contribution

The paper develops a new CRONE reset control approach that integrates non-linear reset control with fractional order design, overcoming fundamental robustness-performance trade-offs.

Findings

Achieves better reference-tracking and noise attenuation.

Provides stability conditions for CRONE reset controllers.

Validated on a nanometre precision stage.

Abstract

In this paper a novel reset control synthesis method is proposed: CRONE reset control, combining a robust fractional CRONE controller with non-linear reset control to overcome waterbed effect. In CRONE control, robustness is achieved by creation of constant phase behaviour around bandwidth with the use of fractional operators, also allowing more freedom in shaping the open-loop frequency response. However, being a linear controller it suffers from the inevitable trade-off between robustness and performance as a result of the waterbed effect. Here reset control is introduced in the CRONE design to overcome the fundamental limitations. In the new controller design, reset phase advantage is approximated using describing function analysis and used to achieve better open-loop shape. Sufficient quadratic stability conditions are shown for the designed CRONE reset controllers and the control design is validated on a Lorentz-actuated nanometre precision stage. It is shown that for similar phase margin, better performance in terms of reference-tracking and noise attenuation can be achieved.