Reliability-based optimal controller design for systems with probabilistic uncertain parameters using fuzzy limit state function

Abstract

In this paper, a fuzzy rule-based system (FRS) has been used for optimal reliability-based robust controller design for a two-mass-spring system with probabilistic uncertainties in its parameters. In this way, a multiobjective uniform-diversity genetic algorithm (MUGA) is first used to find a Pareto front of two-mass-spring system in a deterministic approach. This paper considers a two-mass-spring system under an impulse input. Two conflicting objective functions in this model include settling time of the second mass and control effort exerted on the first mass. Consequently, such Pareto front is then obtained for a two-mass-spring system with probabilistic uncertainties in its parameters using the probabilities of failure of those objective functions through a Monte Carlo simulation approach. It is shown that the FRS system removes the difficulty of selecting suitable crisp values and obligation due to a defining limit state function. Besides, the multiobjective Pareto optimization of such robust controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust controllers can be compromisingly chosen from the Pareto frontiers.