Masters Theses

Date of Award

6-1980

Degree Type

Thesis

Degree Name

Master of Science

Major

Chemical Engineering

Major Professor

Duane D Bruns

Committee Members

Charlie F Moore, George C Frazier

Abstract

Several methods are available for mathematical prediction of the oscillatory characteristics of a system under nonlinear feedback control. Of these methods, Tsypkin's analysis which treats relay controller exactly has been found to offer superior predictions when applicable. These procedures, in particular Tsypkin's method, have essentially been presented for only single-input/ single-output systems. Because Tsypkin's analysis has been successfully tested in several studies, and its applicability experimentally demonstrated for single-input/ single-output processes, this thesis extends the mathematical formalisms to encompass multi-input/ multi-output process utilizing relay as a control element.

This new theory has general application in nonlinear system analysis. The specific motivation in this research is the stabilization of chemical reaction systems at an unstable steady state condition where control may be desirable. For mathematical tractibility and ease of demonstration, the classical literature example of the lumped-parameter nonisothermal process undergoing a first order exothermic reaction was chosen as a specific example. The reactor's concentration and temperature were the controlled output variables which were manipulated with the reactor's input flow rate and coolant temperature respectively. Treatment of this reactor model with relay controllers gave birth to the new control theory for multi-input/multi-output control systems.

The prediction of the reactor's oscillatory response near an unstable steady state using two relays according to the new theory was compared to the exact response of the process via nonlinear simulation for several sets of relay design parameters. In all cases of control demonstration, sustained oscillation of all control loops of the system ( a condition necessary for the application of the new theory) was possible only when the control bandwidth of each controller was restricted within some range of values. A failure to comply to this restriction always resulted in loss of control, and, consequently, in a break down of the new theory application.

The nonlinear simulation results compared well with the new theory results especially at small values of control bands where small amplitude oscillations of the system about an unstable steady state always resulted. In such control restriction, the system approximated a linear process, a condition exploited in the development of the new theory, the analysis and the simulation results agreed very well. But at large control bands, poor comparisons often resulted, an indication that the process was becoming more nonlinear.

Thus the new control theory is applicable for control of multivariable processes when restrictions are placed on control bands of each feed back loop, and when, with reasonable choice of other control parameters, small amplitude oscillation of the system about an unstable steady state condition is ensured.

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