City Research Online

Abstract

Where the mathematical model is not a faithful representation of the real system, such as when, due to the lack of knowledge of the physical world "hidden uncertainties" in the system are not accounted for by the mathematical model, the use of the classical least squares approach to the estimation of constant unknown parameters of the model may not be adequate. The structural deficiencies of the model may be compensated for by the use of the smoothed least squares proposed by earlier workers who suggested that the identification of uncertain dynamic systems may be achieved by the joint solution of a parameter estimation problem to estimate constant model parameters and a smoothing problem to compensate for structural deficiencies.

These two approaches; the classical least squares and the smoothed least squares have been used to identify the models of a simulated mixing tank system and a pilot plant vaporiser system. The concept of "parameterisation" which evolved from further elaboration on the smoothed least sequares technique whereby the proposed uncertainty is expressed as time-varying functions whose coefficients are estimated by the smoothing problem, has been implemented on the models of the two systems. Use was made of Chebychev polynomials and sine waves to approximate for the time-varying uncertainty.

The effects of the weightings of the errors between system and model responses and the time-varying uncertainty and its nominal trajectory on the performances of the two techniques have been evaluated.

Finally, critical evaluation of the performances of the classical least squares and the smoothed least squares
techniques with regard to the estimated values of the constant model parameters has been made.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments:	School of Science & Technology > Department of Computer Science School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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