Robust multi-objective optimization of state feedback controllers for heat exchanger system with probabilistic uncertainty

Abstract

The performance of thermal control systems has, in recent years, improved in numerous ways due to developments in control theory and information technology. The shell-and-tube heat exchanger (STHX) is a medium where heat transfer process occurred. The accuracy of the heat exchanger depends on the performance of both elements. Therefore, both components need to be controlled in order to achieve a substantial result in the process. For this purpose, the actual dynamics of both shell and tube of the heat exchanger is crucial. In this paper, optimal reliability-based multi-objective Pareto design of robust state feedback controllers for a STHX having parameters with probabilistic uncertainties. Accordingly, the probabilities of failure of those objective functions are also considered in the reliability-based design optimization (RBDO) approach. A new multi-objective uniform-diversity genetic algorithm (MUGA) is presented and used for Pareto optimum design of linear state feedback controllers for STHX problem. In this way, Pareto front of optimum controllers is first obtained for the nominal deterministic STHX using the conflicting objective functions in time domain. Such Pareto front is then obtained for STHX having probabilistic uncertainties in its parameters using the statistical moments of those objective functions through a Hammersley Sequence Sampling (HSS) approach. It is shown that multi-objective reliability-based Pareto optimization of the robust state feedback controllers using MUGA includes those that may be obtained by various crisp threshold values of probability of failures and, thus, remove the difficulty of selecting suitable crisp values. Besides, the multi-objective Pareto optimization of such robust feedback controllers using MUGA unveils some very important and informative trade-offs among those objective functions. Consequently, some optimum robust state feedback controllers can be compromisingly chosen from the Pareto frontiers.