Control Oriented Modeling of Distributed Systems—The Question of Control System Stability

Abstract

Distributed systems dynamics is described by partial differential equations (PDE), i.e., the model is of infinite order. For control system synthesis such a model ought to be reduced. This paper presents the original analytical solutions for critical controller gain in the output feedback control of processes described by parabolic PDE. Numerical analysis using different reduced models leads to the same results. The solution to the problem of locating the positive zero of the first-order nonminimum phase system (which is the lowest order model for approximation of this particular distributed system) is given. The concept and method are of general interest and can be useful in control system design for different systems with distributed parameters.