Pareto optimal robust design of fractional-order PID controllers for systems with probabilistic uncertainties

In this paper, a multi-objective optimization approach is used for Pareto optimum design of robust integer-order and fractional-order PID controllers for both integer-order and fractional-order plants with parametric uncertainties. The aim of this paper is to compare the performances of those optimally-designed controllers dealing with parametric uncertainties of both integer-order and fractional-order plants. In this way, four combinations of plants and controllers have been considered in which five conflicting objective functions in both time and frequency domains are used in the Pareto design of both integer-order and fractional-order PID controllers. The results clearly show that effective trade-off design points can be compromisingly explored among the optimal robust integer-order and fractional-order PID controllers obtained using the methodology of this work. Furthermore, the superior robust stability and robust performance of the fractional-order PID controllers will be demonstrated in comparison with those of the integer-order PID controllers.