Optimal linear PI fuzzy controller design of a heat exchanger

This study aims at improving the control of a heat exchanger, described by a partial differential equation, by optimizing a linear proportional–integral fuzzy controller. The design of the controller is based on the use of a finite-dimensional approximate model, of high order, derived by spatially lumping the infinite-dimensional model of the heat exchanger. The design procedure consists to optimize the scaling factors of the linear fuzzy controller, by solving an unconstrained optimization problem issued from the simplification of a formulated constrained optimization where the objective function is an integral error measure, and the constraints are the relationships between fuzzy and conventional PID gains. The formulated unconstrained optimization problem is then solved using jointly the Matlab Optimization Toolbox and Simulink. Through simulation, the performances of the heat exchanger are evaluated, and the obtained results show that the fuzzy controller produces improved control performance with respect to the conventional controller.