Cyclic Control: Problem Formulation and Stability Analysis

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.