In this paper, A fuzzy rule-based system (FRS), has been used for optimal reliability-based multi-objective Pareto design of robust PI controllers for a first-order system with time delay having parameters with probabilistic uncertainties. The objective functions that have been considered are, namely, the probabilities of failure of settling time (PTs) and of maximum overshoot (Pos) in the reliability-based design optimization (RBDO) approach. In this way, Pareto front of optimum controllers is obtained for the first-order system having probabilistic uncertainties in its parameters using the probability of failure of those objective functions through a Monte Carlo simulation (MCS) approach. It is shown that multi-objective reliability-based Pareto optimization of the robust PI controllers using multi-objective genetic algorithm with FRS remove the difficulty of selecting suitable crisp values. Besides, the multi-objective Pareto optimization of such robust PI controllers using multi-objective genetic algorithm unveils some very important and informative trade-offs among those objective functions.
