Velocity control of hyperbolic partial differential equation systems with single characteristic variable

This work addresses the problem of controlling a flow system described by a set of first-order partial differential equations with a single characteri stic variable. The manipulated input variable is the characteristic flow ve locity of the system while the controlled output is any function of the sta te variables in the outlet stream. Extending ideas and concepts from geomet ric control theory for ordinary differential equation systems, the notion o f input/output linearization is used as a basis for the controller design. The method of characteristics is used to establish properties of the system dynamics. Because of the presence of a deadtime, the nonlinear system beha ves in a manner analogous to linear systems having quasirational transfer f unctions. It is shown that the zero dynamics is marginally stable. Two type s of controller designs are considered. Because of the nature of the zero d ynamics, a continuous-time controller is shown to-induce oscillations, maki ng it unsuitable for practical use. A novel alternative controller is propo sed that will induce a discrete-time linear input/output response in the cl osed loop. The discrete control action is taken at variable intervals of ti me equal to the residence time of the fluid entering the system at the star t of that interval. The control methodology is implemented on a nonisotherm al plug flow reactor and its performance and robustness are evaluated throu gh simulations. (C) 1998 Elsevier Science Ltd. All rights reserved.