Singular Perturbation Method for Smart Building Temperature Control Using Occupant Feedback

Abstract

In this work we propose a framework for incorporating occupant feedback towards temperature control of multi-occupant spaces, and analyze it using singular perturbation theory. Such a system would typically have to accommodate occupants with different temperature preferences, and incorporate that with thermal correlation among multiple zones to obtain optimal control for minimization of occupant discomfort and energy cost. In current practice, an acceptable temperature set point for the occupancy level of the zone is estimated, and the control law is designed to maintain temperature at the corresponding set point irrespective of the changes in occupancy and the preferences of multiple occupants. Proposed algorithm incorporates active occupant feedback to minimize aggregate user discomfort and total energy cost. Occupant binary feedback in the form of hot/cold or thermal comfort preference input is used by the control algorithm. The control algorithm also takes the energy cost into account, trading it off optimally with the aggregate occupant discomfort. For convergence to the optimal, sufficient separation between the occupant feedback frequency and the temperature dynamics of system is necessary; in absence of which, the occupant feedback provided do not correctly reflect the effect of current control input value on occupant discomfort. Under sufficient time scale separation, using singular perturbation theory, we establish the stability condition of the system and show convergence of the proposed solution to the desired temperature that minimizes energy cost plus occupant discomfort. The occupants are only assumed to be rational in that they choose their own comfort range to minimize individual thermal discomfort. Optimization for a multi-zone building also takes into account the thermal correlation among different zones. Simulation study with parameters based on our test facility, and experimental study conducted in the same building demonstrates performance of the algorithm under different occupancy and ambient conditions.

Literature Review for Sensor Impact Evaluation and Verification Use Cases - Building Controls and Fault Detection and Diagnosis (FDD)

“…Several researchers have addressed the question of co-optimizing thermal comfort among occupants and energy consumption of building HVAC equipment through advanced control algorithms. For example, decentralized consensus-based algorithms (in which the occupant feedback is obtained through wearable sensors or interactive mobile applications) and singular perturbation methods (again, with active occupant feedback) have been proposed to attain this objective [84,85]. The importance of including humans in the automation process by their feedback was also highlighted in a study by Jung and Jazizadeh [30].…”

Tensor Product‐Based Model Transformation and Optimal Controller Design for High Order Nonlinear Singularly Perturbed Systems

“…Note that the presence of the small parameter ε that multiplies describes the nonlinear studied system by the standard singularly perturbed form and allows the separation of the states in two separate time scales when Assumptions 1 to 3 are satisfied .…”