Gravitational search algorithm-based design of fuzzy control systems with a reduced parametric sensitivity

Abstract

This paper proposes the design of fuzzy control systems with a reduced parametric sensitivity making use of Gravitational Search Algorithms (GSAs). The parametric variations of the processes lead to sensitivity models. Objective functions expressed as integral quadratic performance indices, which depend on the control error and squared output sensitivity functions are suggested. GSAs are employed to minimize the objective functions in the appropriately defined optimization problems. This paper also suggests a GSA with improved search accuracy. The new GSA is characterized by the modification of the denominator in the expression of the force acting on an agent from the other agent; the denominator depends not only on the Euclidian distance between the two agents but also on the position of the latter: A design method for Takagi–Sugeno proportional-integral fuzzy controllers (PI-FCs) is proposed. The PI-FCs are dedicated to a class of processes characterized by second-order linear or linearized models with an integral component. Two discrete-time sensitivity models of the fuzzy control systems are derived. An example dealing with the angular position control of direct current (DC) servo system laboratory equipment validates the new controller design. A set of real-time experimental results illustrates the fuzzy control system performance.