Graduate Thesis Or Dissertation
 

Critical evaluation of Ouyang's model reduction method

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  • A model reduction method for stable, linear, time-invariant, continuous systems is critically studied. This method, proposed by Prof. Ouyang, is based on the concept of power dispersion and the least-squared estimation technique. The reduced models obtained by this method retain the stability of the stable, high order original systems and give no steady-state error between both the reduced model and the original system. Systems having repeated poles or complex poles are discussed in this thesis. The simulations of a number of examples show that the 2nd order reduced models can give good approximations to the 4th order original systems studied here whose poles are wholly or partially located on the negative real axis of the s-plane. But, the results also show that unsatisfactory approximations occur for original systems having 2 pairs of conjugate complex poles. Ouyang did not point out how to select the retained poles for the reduced model when the original systems have negative power dispersion components. New methods for selecting the reduced model poles are proposed for original systems having negative power dispersion components. The methods are based on selecting reduced model poles to obtain a best fit to the original system output autocorrelation function. Some examples are given to demonstrate the effectiveness of the new methods. The results obtained by new methods show that power dispersion method is still valuable. By selecting the poles due to largest positive power dispersion, the reduced model can be determined for the case of the systems having negative power dispersion component.
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