Controllability Studies of Chemical Processes Based on the Concept of Passivity

Abstract

This article presents an approach on controllability of nonlinear chemical processes based on passivity. The proposed method extents on the concept of Maya-Yescas and Aguilar (2003). The method divides the model system into controllable and uncontrollable parts. A controller can be designed by setting the controllable part equal to zero, so-called the perfect controller. For uncontrollable part, the storage and the supply rate functions are defined by implementing the same perfect controller to analyze the stability. If the uncontrollable part has the Kalman-Yacubovich-Popov (KYP) property, it is guaranteed to be stable and, therefore, the overall system would be controllable. The applications of proposed method are illustrated with two examples: 1) the four available control structures of heat exchanger network for one hot stream and two cold streams; and 2) the two process variables of continuous fermentation. The simulation results imply that the stability and the steady state of uncontrollable part can be considered only as the Lie derivative of a storage function. This technique can be extended to other nonlinear chemical processes as a tool for selecting the best input-output pairing to design the control structure.