An optimal gas-fired heating system

Utilizing a prescribed system configuration, this paper discusses the mathematical models of the system components used and formulates a method for controlling a domestic heating system in accordance to a prescribed criterion. The optimal problem treated is one of reducing the room temperature deviation from a prescribed reference value to zero, while at the same time minimizing the value of some predetermined performance or cost functional J. The development proceeds in essentially five steps.

1. (a) The development of the mathematical models for each of the elements of the heating system;

2. (b) Combining the mathematical models into a form which is suitable for the application of optimization techniques;

3. (c) Defining an optimization criterion which incorporates the main objective for minimizing room temperature variations with respect to a prescribed reference temperature;

4. (d) Choosing the optimization technique best suited for the problem;

5. (e) Constructing an optimal control system employing the optimization technique developed.

A numerical example compares the performance of the optimal system with a system of the conventional type which can be found in many American homes.