Model Reduction Through Parameter Estimation in the s-Domain

3 Model Reduction Through Parameter Estimation in the s-Domain 

Quite often we are face with the task of reducing the order of a transfer function without losing essential dynamic behavior of the system. Many methods have been proposed for model reduction, however quite often with unsatisfactory results. A reliable method has been suggested by Luus (1980) where the deviations between the reduced model and the original one in the Nyquist plot are minimized. 

The poles of the transfer function (roots of the denominator) are at -1, -l j, -3, -4, -5, -8 and -10. Let us assume that we seek a third order system that follows as closely as possible the behavior of the high order system. Namely, consider 

The constant in the numerator can always be chosen to preserve the steady state gain of the transfer function. As suggested by Luus (1980) the 5 unknown parameters can be obtained by minimizing the following quadratic objective function 

In this problem you are asked to determine the unknown parameters using the dominant zeros and poles of the original system as an initial guess. LJ optimization procedure can be used to obtain the best parameter estimates. 

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