Fractional reset control

Abstract

Reset control is a nonlinear control technique that consists in resetting to zero the value of the integrals in a controller, whenever their input becomes zero. Fractional reset control is the application of reset control to a fractional controller. This is done both to force the control action to oscillate around zero, preventing it from having a nonzero average, and to improve the phase margin of the open loop, while keeping the slope of the gain plot of the controller’s Bode diagram. This paper presents numerical values for the describing functions obtained with fractional reset control applied to controller s α , \({\alpha \in {\rm I}\kern -1.6pt{\rm R}}\). Three different ways of implementing fractional derivatives are employed: one based upon the Grunwald–Letnikoff definition, one based upon the Riemann–Liouville definition, and the Crone approximation. It is found that the describing function depends significantly on the way fractional derivatives are implemented.