Automatic control of a class of non-linear processes

Kerr, Charles N (1964) Automatic control of a class of non-linear processes. PhD thesis, University of Glasgow.

Abstract

The class of nonlinear process presented in this study is characterised by a differential equation involving products both of the output variable with derivatives of the input, and of derivatives of the output with the input. It is described as output-dependent since its dynamic behaviour at a mean, operating, output level changes with that level, and it is shown that the nuclear reactor on an accepted approximation is of this class. The processes studied each incorporate a gain element of either of two types, the gains of which are functions of the process output. There is a progressive development from the gain elements to selected first-order, and thence to second-order, controlled processes. Extensive use is made of phase-plane techniques in the study, as well as other forms of analysis transformations due to Poincare are introduced and applied with effect to the behaviour at infinity in the phase plane, and repeated applications of the Direct Method of Lyapunov produce successively improved definitions of the limits of operation for stable responses. Some of these applications display new approaches to the use of the Direct Method. The stability behaviour of each system following large step changes in input is clearly indicated by diagrams, which it is shown may not be obtained by a locally-linearised treatment involving the concept of a roots-surface. In particular, the controlled nuclear reactor on the above-mentioned approximation is shown to be stable following step inputs of reactivity of any magnitude in either direction.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: G DS Maclellan
• Keywords: Nuclear engineering, Applied mathematics
• Date of Award: 1964
• Depositing User: Enlighten Team
• Unique ID: glathesis:1964-73333
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 14 Jun 2019 08:56
• Last Modified: 14 Jun 2019 08:56
• URI: https://theses.gla.ac.uk/id/eprint/73333