Model order reduction of high order LTI system using Genetic Algorithm

Abstract

Any realistic model will have high complexity; in other words, it will require many state variables to be adequately described. The resulting complexity, i.e. number of first-order differential equations, is such that a simplification or model reduction will be needed in order to perform a simulation in an amount of time which is acceptable for the application at hand, or for the design of a low order controller which achieves desired objectives. Thus in all these cases reduced-order models are needed. The motivation for appropriate MOR is to obtain an accurate model of smaller order which can be easily simulated and implemented in hard ware with ease saving effort, cost and time. This paper proposes a numerically efficient model order reduction method using evolutionary technique, Genetic Algorithm. GA method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. This ISE is very useful in performance evaluation. The simulation result shows the effectiveness of the proposed scheme to obtain the stable 1st, 2nd and 3rd order reduced stable model from a stable 4th order original system with minimum error bound.