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This report focuses on modeling the thermal behavior of buildings and designing an optimal control algorithm for their HVAC systems. The problem of developing a good model to capture the heat storage and heat transmission properties of building thermal elements such as rooms and walls is addressed by using the lumped capacitance method. The equations governing the system dynamics are derived using the thermal circuit approach, and by denullning equivalent thermal masses, thermal resistors and thermal capacitors. In the control design part, we have introduced a new hierarchical control algorithm which is composed of lower level PID controllers and a higher level LQR controller. The optimal tracking problem is solved in the higher level controller where the interconnection of all the rooms and the walls are taken into consideration. The LQR controller minimizes a quadratic cost function which has two quadratic terms. One takes into account the comfort level and the other represents the control enullort, i.e. the energy consumed to operate the HVAC system. There are two tuning parameters as the weight matrices for each of these two terms by which the performance of the controller can be tuned in different operating conditions. Simulation results show how much energy can be saved using this algorithm.

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