Model order reduction of high order LTI system using particle swarm optimisation

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, Particle Swarm Optimisation (PSO). PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order 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 second order reduced stable model from a stable seventh and fifth order original system with minimum error bound.