An Improved Water Swirl Algorithm Approach for Formulation of Lower Order Model of Multivariable Linear Time Invariant Continuous System

In this paper an Improved Water Swirl Algorithm (IWSA) approach is used for formulation of lower order Multi Input Multi Output (MIMO) model for a given absolutely stable higher order MIMO Continuous system in transfer function form. Water Swirl Algorithm (WSA) is a swarm based optimization technique that mimics the way by which water finds a drain in a sink. It observes the flowing and searching behavior of water for drain and proposes a suitable strength update equations to locate the optimum solution iteratively from the initial randomly generated search space. The sink holding the water particle represents the boundary conditions limiting the search space. The strength of a water particle is governed by three components namely, Inertia, Cognitive and Social. Water is an inevitable substance in the nature for all the livings. In the proposed Improved WSA, the cognitive component of water particle is spitted into good experience component and worst experience component. Due to the inclusion of worst experience component, the particle can bypass the previously visited worst position and try to occupy the best position. A weighted average method is proposed in this paper to reduce the higher order model formulation to lower order form. Integral square error is used as an indicator for selecting the lower order model. An average scheme has been proposed for commonizing the denominators of the individual lower order approximants so that a lower order MIMO model can be declared in the transfer function matrix form. The proposed methodology is illustrated with an example.