Multi-Objective Stochastic Design of Robust PI Controllers for Systems with Probabilistic Uncertainty using Genetic Algorithm

N. Nariman-zadeh, A. Hajiloo, and A. Jamali (Iran)


Uncertain systems, robust control, reliability, optimization, and genetic algorithm


A robust approach for the Pareto optimum design of PI controllers for systems with probabilistic uncertainty is presented. In this way, some non-dominated optimum PI controllers in the Pareto sense are found using three non commensurable objective functions both in time and frequency domains based on stochastic behaviour of a system with parametric uncertainties. Such conflicting objective functions are, namely, the probability of instability, the probability of failure to a desired time response and its variance, and the degree of stability from the Nyquist diagram’s percentiles. The first two objective functions have to be minimized whilst the last one to be maximized simultaneously. It is shown that multi objective Pareto optimization of such robust PI controllers using a recently developed diversity preserving mechanism genetic algorithm unveils some very important and informative trade-offs among these objective functions. Consequently, some optimum PI controllers can be compromised and chosen from the Pareto frontiers.

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