Optimal Techniques for On-Line Control Systems with an Application to the Control of a Power-Station Boiler

Abstract

The thesis describes the development of techniques for the optimal control of industrial processes by an on-line digital computer. The process model is taken to be a set of linear differential equations describing the behaviour of the process for small displacements about a particular operating point. The design of the control system is based on the minimisation of a performance index which is a quadratic function of the displacements of the system variables. The minimisation is subject to amplitude constraints on the control inputs. An investigation is carried out into the theoretical and practical value of existing techniques for optimal on-line control of systems with constrained inputs. One result of the investigation is a new theoren on the equivalence of single-stage and N-stage optimal control policies. Because of practical limitations of existing methods, a new technique is developed in the thesis. The theoretical value of this technique is considered to be not less than that of any comparable technique, In each case the optimal control policy is derived using the concepts of dynamic programming. The proposed technique involves the exact minimisation of a single-stage performance index at each successive sampling instant, and uses a computational procedure based on the geometrical properties of the index to solve the resulting quadratic programming problem. The method of solution of the control problem is such that most of the difficulties associated with the practical implementation of other methods are removed. A study by simulation is included of the application of these techniques to the dynamic control of a power-station boiler under changing load conditions. Results are given of tests carried out using both digital and hybrid computers. The practical limitations of existing methods are demonstrated, and it is shown that the proposed technique yields system responses which in certain cases show a significant improvement over responses achieved using other methods.