Comparison of Model Predictive Control performance using grey-box and white box controller models

Model predictive control (MPC) for building climate control has received increasing attention the last decade. Its large scale implementation is, however, still hampered by the difficulty of obtaining accurate but computationally efficient multi-zone building controller models. This paper compares an existing grey-box approach with a novel white-box approach to obtain a controller model of the building envelope and it compares the performance achieved by using these two approaches. The comparison is made for an existing office building, which is currently controlled using a grey-box MPC [1].  The building envelope and its heating, cooling and air conditioning systems  (HVAC) are modelled using the Modelica building energy simulation library IDEAS. The model is validated using measurement data from the real building. This detailed simulation model is composed of discretised partial differential equations, ordinary differential equations and algebraic equations. The model is therefore too complex to be used as controller model for MPC. Two MPC approaches are compared. On the one hand, the white-box controller model is obtained by linearizing the building envelope part of the simulation model and by pre-computing model inputs such as solar gains through each window [2]. The method generates a linear state space model, which produces very similar temperatures as the original non-linear model. On the other hand, the grey-box identification method that was used to obtain the current controller model, is also applied to the detailed simulation model. Both white-box and grey-box MPC are applied to the detailed simulation model. The dynamics of the HVAC systems are not included in the MPC model but the efficiencies, constraints, cost function and boundary conditions are included. The energy use, the achieved thermal zone comfort and the prediction performance are compared. Finally, a new grey-box model is identified with operation data of the real building and the multi-step ahead prediction performance of the white-box and of both the grey-box models obtained with the simulation data and obtained with the measured data is computed for the real building using the measurement data and the weather forecast, which are used by the current MPC implementation.  [1] Zdenek Vana, Jiri Cigler, Jan Siroky, Eva Zacekova, Lukas Ferkl. Model-based energy efficient control applied to an office building. J. Process Control (2014).  [2] Picard, D., Jorissen, F., and Helsen, L. 2015. Methodology for Obtaining Linear State Space Building Energy Simulation Models. In 11th International Modelica Conference, pages 51–58, Paris.