Optimal control of indoor environmental spaces is explored. A physical model of the system consisting of a heating system, a distribution system and an environmental zone is considered and a seventh order bilinear system model is developed. From the physical characteristics and open-loop response of the system, it is shown that the overall system consists of a fast subsystem and a slow subsystem. By including the effects of the slow subsystem in the fast subsystem, a reduced order model is developed. An optimal control law is designed based on the reduced order model and it is implemented on the full order nonlinear system. Both local and global linearization techniques are used to design optimal control laws. Results showing the disturbance rejection characteristics of the resulting closed-loop system are presented. The use of optimal tracking control to implement large changes in setpoints, in a prescribed manner, is also examined. A general model to describe environmental zones is proposed and its application to multi-zone spaces is illustrated. A multiple-input optimal tracking control law with output error integrators is designed. The resulting closed-loop system response to step-like disturbances is shown to be good.

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