Frequency domain properties of reset systems with multiple reset anticipations

A reset controller is a controller that operates most of the time as a linear system, except when some condition holds. The typical reset condition is the zero crossing of the tracking error signal, e(t) = 0. At this moment, the controller performs a zero resetting action on its state. It has been shown that reset control is able to overcome fundamental linear limitations. This article studies, within a frequency-domain framework, the generalisation of reset control systems based on including some anticipation on the reset condition.This has a favourable phase lead effect. The paper discusses different reset anticipations schemes, including multiple reset actions in the same period, computes Fourier harmonics and describing function of general reset controllers and shows explicitly the overcoming of frequency-domain limitations (Bode´s gain-phase relation).