The optimal control problem for a representative heating, ventilating, and air conditioning system is developed and solved. The approach to the solution involves discretising the problem in time and determining optimal values of the control variables at discrete times. The governing equations are formulated to account for transient effects in a heat exchanger that conditions the air and the thermal space. Variable air flow through the system as well as variable recirculation capabilities are included. The cost function includes energy costs and penalties associated with system operation. Optimal temporal responses for heat exchanger and fan flow rate are solved using a nonlinear optimisation technique. The results are in good agreement with those obtained using the calculus of variations method. The discrete optimal control solution is compared to the traditional bang-bang control approach. Results for optimal system responses and total costs are presented for several cases designed to demonstrate the capabilities of the method, the advantages of optimal control, and the benefits of continuous variation of the control variables.

KEYWORDS: optimisation, controls, heating, ventilation, air conditioning, heat exchangers, air flow rate, recirculating, costs, energy consumption, operations, fans, calculating, comparing, case studies