This paper deals with a frequency-weighted model reduction for single-input, single-output systems combining the linear least-squares (LS) method with firefly algorithm (FA). The reduced-order model is determined by minimizing the integral of the magnitude squared of the frequency-weighted transfer function error. | Journal of Automation and Control Engineering Vol. 3, No. 3, June 2015 Frequency-weighted Model Reduction Using Firefly Algorithm Tomohiro Hachino, Koichi Tanigawa, Hitoshi Takata, Seiji Fukushima, and Yasutaka Igarashi Kagoshima University, Kagoshima, Japan Email: hachino@, k4123590@, {takata, fukushima, igarashi}@ Abstract—This paper deals with a frequency-weighted model reduction for single-input, single-output systems combining the linear least-squares (LS) method with firefly algorithm (FA). The reduced-order model is determined by minimizing the integral of the magnitude squared of the frequency-weighted transfer function error. The denominator parameters and time delay of the reducedorder model are represented by the positions of the fireflies and searched for by the FA, while the numerator parameters are estimated by the linear LS method for each candidate of the denominator parameters and time delay. All the best parameters and the time delay of the reducedorder model are obtained through the search by the fireflies. Simulation results show that the accuracy of the proposed method is comparable to that of the genetic algorithm (GA)based model reduction algorithm, with smaller computational burden. Index Terms—model reduction, frequency-weighting, separable least-squares, firefly algorithm I. INTRODUCTION Since many practical systems are of high-order, the problem of approximating high-order systems by loworder models is one of the important problems in system theory. The use of a good approximated low-order model reduces the computational burden to implement system analyses, simulations and control designs. Model reduction algorithms have been developed using a number of approaches [1]-[12].One of the popular approaches is the optimal modelreduction. In this approach, the reduced-order model is generally determinedso that a quadratic cost, ., the integral of the magnitude squared of the transfer .
