Dynamic analysis and optimum control of distributed parameter systems with interaction due to convective flow with chemical reaction

Abstract

In this dissertation, the characteristics of the backflow cell model for flow systems of various holdup and mixing distributions were obtained. These include steady state and transient responses for reactor systems in which the resulting equations are nonlinear due to the reaction rate expression. The primary state variables are concentration, temperature, and coolant temperature which are dependent upon axial position. The Newton-Raphson technique of iteration is shown to be a fast and convenient method of obtaining the solution of the resulting mass and energy balance equations. Also, the frequency response characteristics for small deviations in the state variables around or about the steady state values are obtained by a direct matrix method. Certain transient and frequency responses are compared with experimental data. In all cases, very favorable comparisons are obtained for the responses. The maximum principle of Pontryagin is used in the optimization studies. The temperature profile to maximize the yield of an intermediate product of a chain reaction in a steady state reactor system with axial dispersion is obtained. The state variables for this type of system are described by a two-point boundary value system of differential equations in position. The adjoint variables resulting from the application of the maximum principle to this problem are also defined by a two-point boundary value system. Optimal control specifications for dynamic reactor systems are obtained through the application of the maximum principle and the utilization of gradient methods of convergence to the optimal trajectories. A step-by-step procedure is presented for the use of these equations. The optimization specifications are a single variable type. Also, the possibility of an internal feedback control loop on a second variable is considered. Some examples are presented to illustrate the techniques and the responses that can be expected. The techniques which are presented can be used on a relatively small computer and are fast enough to make on-line dynamic optimization of the control trajectories possible.