System Identification for Model Predictive Control of Building Region Temperature

Model predictive control (MPC) is a promising technology for energy cost optimization of buildings because it provides a natural framework for optimally controlling such systems by computing control actions that minimize the energy cost while meeting constraints. In our previous work, we developed a cascaded MPC framework capable of minimizing the energy cost of building zone temperature control applications. The outer loop MPC computes power set-points to minimize the energy cost while ensuring that the zone temperature is maintained within its comfort constraints. The inner loop MPC receives the power set-points from the outer loop MPC and manipulates the zone temperature set-point to ensure that the zone power consumption tracks the power set-points computed by the outer layer MPC. Since both MPCs require a predictive model, a modeling framework and system identification (SI) methodology must be developed that is capable of accurately predicting the energy usage and zone temperature for a diverse range of building zones. In this work, two grey-box models for the outer and inner loop MPCs are developed and parameterized. The model parameters are fit to input-output data for a particular zone application so that the resulting model accurately predicts the behavior of the zone. State and disturbance estimation, which is required by the MPCs, is performed via a Kalman filter with a steady-state Kalman gain. The model parameters and Kalman gains of each grey-box model are updated in a sequential fashion. The significant disturbances affecting the zone temperature (e.g., outside temperature and occupancy) may typically be considered as a slowly varying disturbance (with respect to the control time-scale). To prevent steady-state offset in the identified model caused by the slowly time-varying disturbance, a high-pass filter is applied to the input-output data to filter out the effect of the disturbance. The model parameters are subsequently computed from the filtered input-output data without the Kalman filter applied. The Kalman gain is also adjusted as the model parameters are updated to ensure stability of the resulting observer and for optimal estimation. After the model parameters are computed, the steady-state Kalman gain matrix is parameterized and the parameters are updated using the prediction error method with the unfiltered input-output data and the updated model parameters. The Kalman gain update methodology is advantageous because it avoids the need to estimate the noise statistics. Stability of the observer is verified after the parameters are updated. If the updated parameters result in an unstable observer, the update is rejected and the previous parameters are retained. Additionally, since a standard quadratic cost function that penalizes the squared prediction error is sensitive to data outliers in the prediction error method, a piecewise defined cost function is employed to reduce its sensitivity to outliers and to improve the robustness of the SI methodology. The cost function penalizes the squared prediction error when the error is within certain thresholds. When the error is outside the thresholds, the cost function evaluates to a constant. The SI algorithm is applied to a building zone to assess the approach