Robust-stable quadratic-optimal fuzzy-PDC controllers for systems with parametric uncertainties: A PSO based approach

The present paper shows how robust stable quadratic-optimal fuzzy controllers can be designed using particle swarm optimization (PSO) algorithm, a popular metaheuristic optimization technique. This controller is designed following the Parallel distributed compensation (PDC) technique, employed for Takagi–Sugeno (TS) fuzzy model based control systems, and is termed as a mixed /LMI controller. These controllers are designed to achieve two objectives simultaneously i.e. robust stabilization of the uncertain system with parametric uncertainties in hand and also to achieve desired transient response. The robust stabilization is guaranteed when a set of linear matrix inequalities (LMIs) formulated get satisfied. The controller simultaneously achieves the desired transient performance by minimizing a quadratic finite-horizon integral performance criterion for the nominal dynamical system. The proposed PSO based mixed /LMI controller has been employed for a benchmark dynamical system and it has been demonstrated to achieve better performance than a recently proposed hybrid Taguchi genetic algorithm (HTGA) based approach, implemented for the same problem