On Horowitz's contributions to reset control

Abstract

SUMMARYHistory shows that Prof. Isaac Horowitz was often ahead of the curve in his feedback control research, especially in developing quantitatively driven design procedures. In some topics, his work was so out of line with the main stream that it has received virtually no recognition from the control community until a few decades later. In this paper, we present recent research that was directly motivated by Horowitz's pioneering work on reset controllers in the 1970s. Reset controllers are linear controllers that reset some of their states to zero when their inputs reach a threshold. Horowitz motivated their use by showing that with qualitative design, they can exhibit better performance trade-offs than those in linear, time-invariant systems. This paper supports and advances his thinking by presenting recent theoretical and experimental results on reset control.

H<inf>2</inf> performance analysis of reset control systems

“…These results have been extended in [11] to a sufficient criterion for BIBO (bounded input bounded output) stability, and later to the so-called H β -condition [12]. The possible advantages of reset controllers over linear ones have been shown both in simulations [9], [13] and experiments [7], [11], [14]. A clear overview of this work for general reset systems is provided in [15].…”

“…Subsequently, in [6], a first order reset element (FORE) was introduced, together with a controller design procedure based on frequency domain techniques. An overview of these results is given in [7].…”

Mid-frequency Disturbance Rejection of HDD Systems

“…In recent years, reset control system attracts more and more attentions because of its nice frequency property which indicates its capability of overcoming linear control constraints. See [3][4][5][6] for instance. A reset controller is a linear controller with part of its state being reset to zero when its input crosses zero.…”

Towards -stability of discrete-time reset control systems via dissipativity theory

“…Horowitz's contributions to reset control system are shown in [13]. During the last decade, several works have been devoted to reset control system and they have been summarised in [1].…”