Cyclic Control: Problem Formulation and Stability Analysis

Abstract

This paper considers the problem of controlling rotating machinery with actuators and sensors fixed in inertial space. Such a problem arises in control of charging and fusing stages in the xerographic process, drilling and milling machines, and turbo machinery. If a rotating device is represented as a set of discrete wedges, the resulting system can be conceptualized as a set of plants (wedges) with a single actuator and sensor. In such architecture, each plant can be controlled only intermittently, in a stroboscopic manner. This leads to the problem of cyclic control (CC) considered in this paper. Specifically, the problem of stabilizability in CC architecture is considered, and the resulting stabilizability conditions are compared with those in the usual, permanently acting control (PAC). In this regard, it is shown that the domain of asymptotic stability under CC is an open disc in the open left half plane (OLHP), rather than the OLHP itself, and the controller gains that place the closed loop poles at the desired locations under CC are N times larger than those under PAC, where N is the number of wedges. The results are applied to temperature stabilization of the fusing stage of a xerographic process.

Cyclic Control: Reference Tracking and Disturbance Rejection

“…The problem of stabilizability of (5) under feedback controllers (7), (9), and (10) (with r = d = 0) was addressed in [3]. Here, for the sake of completeness, we cite the results used for the analysis of reference tracking and disturbance rejection.…”

“…As shown in [3], the proof of this theorem is based on a simplification of the monodromy matrix of (17) that can be…”

“…In [3], both CC and PAC systems without references or disturbances were formalized. Here, we model PAC and CC systems with references and disturbances.…”

“…Section III describes the approach used throughout this paper. Section IV reviews the results on stabilizability of CC systems derived in [3]. Section V presents our results on reference tracking and disturbance rejection.…”

“…In [3], the problem of stabilizability in CC is analyzed and the losses due to CC, as compared with PAC, are quantified. However, the problems of reference tracking and disturbance rejection, which are central to our illustration, were not addressed.…”