Order reduction by minimizing integral square error and H∞ norm of error


1 Department of Electrical Engineering, Firoozkooh Branch, Islamic Azad university, firoozkooh, Iran

2 Electrical Engineering Department, Shahid Bahonar University of Kerman, Kerman, Iran


In this paper, a new alternative method for order reduction of high order systems is presented based on optimization of multi objective fitness function by using Harmony Search algorithm. At first, step response of full order system is obtained as a vector, then, a suitable fixed structure considered for model order reduction which order of original system is bigger than fixed structure model. Parameters of model order reduction are determined by minimizing the multi objective fitness function where the fitness function is conducted with integral square error and H norm of error.  The harmony search algorithm is applied for minimizing the multi objective fitness function. To assure the stability, the Routh criterion is applied for specifying the stability conditions. This stability condition is considered as constraints in optimization problem. To present the accuracy y of the proposed method, three test systems are reduced. The obtained results show that the proposed approach performs very well.