Order Reduction of Unstable Systems by Minimizing the Multi Objective Weighted Sum Function ITSE and H∞ Norm with Bat Algorithm

In this work, a method for order reduction of unstable systems by minimizing the multi-objective weighted sum function ITSE and H∞ norm with bat algorithm is investigated. At first, the unstable model is divided into two parts: stable and unstable. Then, the order of reduced model is determined by considering the stable part and using Hankel norm. In the following, a fixed structure with unknown coefficients is considered for a reduced order model. By minimizing the weighted sum multi-objective included ITSE and H∞ norm with bat algorithm, in which the error is the difference between the step response of original system and reduced order model, unknown parameters of the reduced order model are determined. The Routh-Hurwitz criterion has been used to satisfy the stability condition, which is introduced as a constraint in the optimization problem, and thus the unconstrained optimization problem is converted to constrained optimization problem. Finally, the unstable part is joined to the reduced order part. To confirm and demonstrate the capability and efficiency of the proposed method, three large systems have been reduced and compared with some order reduction methods such as balanced truncation and optimal Hankel approximation. The results show the capability of the proposed method over classical methods.