Thermal Responses in Control Loop in Indirect Control of Indoor Environment of Non-Air Conditioned Space with Quasi-Steady-State Model.

Abstract

This work presents the results from the controlling of the thermal environment of an enclosed space using Euler-Lagrange equations in a variable control problem, and compares it with three semi-empirical controller settings. Thermodynamic characteristics of the space of the administrative building equipped with convectors, disseminating heat energy supplied by steam, provided its mathematical model, which is fully commandable and observable. The model of the enclosed space-single-zone room-was reduced to the desired order dimension applied on the model's transfer function. Set in feedback control-loop with a PS controller, the indoor air temperature, heat fluxes as well as heat consumption over screened period were simulated under certain weather conditions and internal thermal loads, thus the thermodynamic responses of the space were obtained. Comparing the outputs with measurements and the results obtained for each simulation case showed energy savings and the optimal variable control method itself as an effective alternative, if Lagrange multipliers in Euler-Lagrange equations could be solved separately apart from model state-form variables. Further, maintaining Hamilton function as time-independent within defined boundaries, proves along with optimal control solution the readiness for its application in control algorithms of current heating systems.