Output control in linear systems : a transfer-function approach

Publisher Website
Google Scholar
Abstract
The paper presents a transfer-function approach to the output control problem in linear systems in which the commands to be tracked v(t) and the disturbances to be rejected w(t) are represented by specified functions of time with unknown coefficients. For single-variable plants, it is shown that a necessary and sufficient condition for output control is that the poles of the controller include the poles of V(s) and W(s) ; and the controller exists provided the plant control-zeros do not coincide with the poles of V(s) and W(s). The controller is decomposed, into the ‘ regulator’ and the ‘ stabilizer’, where the regulator achieves steady-state output control and the stabilizer ensures closed-loop stability. For multivariable plants, output control is achieved by means of a decentralized control structure consisting of a number of local single-variable controllers. In this structure, the poles of each local output controller must include the poles of all V(s) and (s) ; and the controllers exist provided the transmission zeros of the plant do not coincide with the poles of any V(s) or W(s). The local controllers are decomposed into the ‘ local regulators ’ and the ‘ local stabilizers ’, and the local stabilizers exist provided the plant has no unstable fixed modes. The controllers discussed in this paper are robust in the sense that output control is achieved for arbitrary variations in the plant parameters and in the stabilizer parameters provided the closed-loop stability is maintained. Three numerical examples are discussed.