Reduction of Higher-Order Linear Time-Invariant SISO Continuous Systems to Its Lower-Order Model Employing an Improved Water Swirl Algorithm

Abstract

Abstract This paper proposes a new version of the water swirl algorithm (WSA), namely, improved water swirl algorithm for lower-order model formulation of single-input–single-output (SISO) continuous systems. The 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 drains and proposes suitable strength update equations to locate the optimum solution iteratively from the initial randomly generated search space. The strength of a water particle is governed by three components, namely, inertia, a cognitive component, and a social component. In the proposed improved WSA, the cognitive component of a water particle is split into a good-experience component and worst-experience component. Because of the inclusion of the 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. The result shows good performance of the improved WSA in solving SISO continuous system problems, as compared to other existing techniques. The proposed method is illustrated through numerical examples from the literature.