Pawley, Anthony John Robert (1969) Aspects of self-adaptive control using parameter perturbation techniques. PhD thesis, University of Warwick.

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Abstract

This thesis is concerned with the performance of a method of simultaneous identification and optimization of a control system, employing a parameter perturbation technique.
The work is divided into four parts:
(i) The evaluation of several techniques for the identification and gain-estimation of plants having one "input" and one "output", in the presence of noise, where the "input is a controllable parameter, and the "output" is a criterion of the cost of the plant, which is some function of the plant variables. The slope of the cost-function is then given by the "gain" of the plant.
(ii) The optimization of plants having more than one dynamic path between input and output.
(iii) The optimization of multi-parameter plants.
(iv) A general consideration of optimization strategies.

The first part of the thesis is based on the well known
technique of obtaining the step response of a plant by applying a pseudo-random binary sequence (or "chain code") at the input, crosscorrelating this with the output, and integrating. A technique equivalent to this, using a multiplier and running-averager, is analysed, and it is shown that significant errors can be caused by any
d.c. -- bias inherent in the plant output. The performance of the system when band-limited noise is present at the output of the plant is determined, and it is found that if the parameters of the identification process are chosen so as to reduce the variance of the gain-estimate to a minimum, the error due to d.c.-bias may be large. Practical results are given, which support the theory.
An alternative scheme is considered which enables the d.c. error to be effectively removed. Various methods of implementing this scheme in practice are proposed for use with and without a digital process-control computer. The scheme is analysed under the same noise conditions as before. The signal and noise components of the gain-estimate are evaluated in terms of the parameters of the system, and a design procedure for the choice of optimal values for these parameters is formulated. A method of gain-estimation using sine-wave perturbations is then analysed under similar noise conditions, and compared with the chain-code method.

The second part of the work is devoted to the optimization of plants having more than one dynamic path between input and output, with a different cost-function in each path. It is shown that the estimated position of the optimum varies with perturbation frequency when using sine-wave perturbation, or chain-codes. The theory is supported by the experimental analysis of a simplified model based on a steam-generating plant.

In the third part, various methods of identification of multichannel plants are considered, based on the use of chain-codes. The extent of cross-coupling between channels is examined, and ways of reducing this are evaluated. It is found that the best solution is to use time-shifted versions of the same chain-code, applied to the different inputs of the plant. Practical methods of implementing this are discussed, and a multi-channel optimization program is built up for use with an on-line digital computer. The performance of this program is evaluated for a four-parameter system simulated on an analog computer, with and without compensation for the effect that previous changes in parameter have on the estimate of the gradient of the cost-function.

In the last part of the thesis, the basic limitations on speed of optimization are investigated. Various strategies for rapid hill-climbing are discussed, and a technique for minimizing the number of optimization steps is developed.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General)
Library of Congress Subject Headings (LCSH):	Perturbation (Mathematics), Control theory, Engineering -- Statistical methods, Mathematical optimization, Adaptive control systems, System theory
Official Date:	April 1969
Dates:	Date Event April 1969 Submitted
Institution:	University of Warwick
Theses Department:	School of Engineering
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Ng, K. C.
Sponsors:	Science Research Council (Great Britain)
Extent:	xv, [150] leaves.
Language:	eng

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