Abstract
This paper deals with a new method for model order reduction of linear continuous time interval system. This new method is based on the Kharitonov’s theorem, the Stability equation method and the error minimization by Differential Evolution. The reduced order interval model is determined by using Kharitonov’s polynomials, which make use of the Kharitonov’s theorem and general form of the stability equation method for denominator, while the numerator is obtained by minimizing the integral square error between the transient responses of original and reduced order models using Differential Evolution algorithm. This method generates stable reduced order interval system if the original higher order system is stable and retains the steady-state value. The proposed method is illustrated with the help of typical numerical example considered from the literature.
Highlights
The original system model is fairly complex and is of higher order
Differential Evolution (DE) is employed to minimize the objective function ’J‘, which is the error between the original higher order system and the reduced order system
The four kth order reduced Kharitonov’s transfer function denominators are obtained by using stability equation method and the numerators are obtained by minimizing integral square error using Differential Evolution Algorithm
Summary
The original system model is fairly complex and is of higher order. The understanding of the behavior of the system is difficult due to complexity. Among these various model order reduction methods for stability preservation available in the literature, the stability equation method is one of the most popular techniques The advantage of this method is that it preserves stability in the reduced model, if the original higher-order system is stable, and retains the first two time-moments of the system. In [17] and [18], the linear interval systems reduction techniques are presented using the Kharitonov’s theorem to generate stable reduced order linear interval models. In [19], a reduction technique for linear interval systems using Kharitonov’s polynomials and Routh Approximation is presented to generate a stable reduced order interval model. The stability is guaranteed for the reduced order system if the original higher order system is stable and the responses matching between original higher order system and the reduced order model
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