Two-Degree-of-Freedom Robust Controller Design Approach for Fuzzy Parametric Uncertain Systems using Particle Swarm Optimization

摘要

In this proposed work, a two-degree-of-freedom robust controller design approach for fuzzy parametric uncertain systems to ensure both the robust stability and performance is proposed. A fuzzy parametric uncertain system is a linear time-invariant uncertain system with fuzzy coefficients. Using nearest approximation, these fuzzy coefficients are approximated into crisp sets called intervals to get an interval system. In the proposed approach, the robust stability is determined by utilizing the newly developed stability conditions of interval systems. Consequently, these stability conditions are used to derive a set of inequalities in terms of controller parameters and these inequalities are solved to obtain a robust stabilizing controller with the help of particle swarm optimization for an unstable fuzzy parametric uncertain system. Finally, the required system performance is achieved by synthesizing a pre-filter using the frequency-domain method. The proposed method has the advantage of having less computational complexity and easy implementation on a digital computer. The viability of the proposed approach is illustrated through a numerical example of its successful implementation. The efficacy of the proposed approach is also evaluated against the available method in the literature and the simulation results were successfully implemented for robust stability and performance of fuzzy parametric uncertain systems.