Thesis in partial fulfilment of the requirements for the degree of Master of Science, Massachusetts Institute of Technology, USA

S F Bush

Summary

The analysis and control of a continuous process can be approached in two ways. One method analyses the system as closely as possible to obtain equations which describe the process in detail. The second method seeks to find relations between outputs and inputs by statistical correlation methods without enquiring closely about the details of the process. This thesis deals with the use of the first method on the control of a chemical process producing hydrogen from steam and carbon monoxide.

Generally, the first method yields non-linear, partial differential, simultaneous equations. The main burden of this thesis is to obtain approximate solutions of these equations and to obtain them in a form suitable for controller design. A method for getting non-linear solutions has been worked out. The results obtained from this method have been compared with those obtained from considering small perturbations of the dependent variables about their steady state values. Solutions for the perturbations were found in two ways: firstly by an integral series technique, previously applied to the equations of a heat exchanger and extended here to solving linear equations with variable coefficients, and secondly by a lumping procedure which reduces the equations to ordinary differential equations. The result of all these methods are compared with each other and with numerical solutions and there is a short note on the methods which failed.

The reactor is controlled by altering the flow of reactor gas to a heat exchanger heating the incoming gases. In this case, the control problem is not difficult, once the analysis has been done. In this process, the transfer function relating output to input disturbances is easily derived and several means of control suggest themselves.

Finally, there are tentative suggestions for extending the non-linear solutions and for obtaining some precise criteria for deciding which method of analysis is likely to be the best in any given case.