Mathematical Modelling and Robust Control of the Double Tube Heat Exchanger: the Parametric Approach

 

Dalibor Stević

 

Mathematical modeling of the heat exchangers is a very important part of the designing process in order to define a correct control strategy. Various types of heat exchangers are frequently used as a constructive element in military aircraft and their operation is usually controlled by manipulating inlet fluid temperatures or mass flow rates. In the first part of this paper, a linearized mathematical model of the double tube heat exchanger has been derived taking into account the wall dynamics, which led to its description in a form of a set of partial differential equations. In order to overcome partial differential solutions difficulties, the finite difference method is proposed. Finally, specifying the parameter values of the heat exchanger, under constant initial conditions, the step transient responses have been simulated and presented in a graphic form. In the second part of this paper, the problem of robust control of the double tube heat exchanger based on the parametric approach is considered. The differential-discrete mathematical model of the double tube heat exchanger derived in the first part of this paper containing uncertain parameters is used to determine the largest perturbation in the space of real parameters without destroying closed loop stability. The main idea is to determine the maximally robust controller in sense that it guarantees stability while maximizing the size of perturbation cenetred at nominal values.

Key words: heat exchanger, mathematical modeling, finite difference method, robust controlling, parametric model, controller.