Selecting Building Predictive Control Based on Model Uncertainty

Selecting Building Predictive Control Based on Model Uncertainty Mehdi Maasoumy 1 , Meysam Razmara 2 , Mahdi Shahbakhti 2 , and Alberto Sangiovanni Vincentelli 3 Abstract— Model uncertainty limits the utilization of Model Predictive Controllers (MPC) to minimize building energy consumption. We propose a new Robust Model Predictive Control (RMPC) structure to make a building controller robust to model uncertainty. The results from RMPC are compared with those from a nominal MPC and a common building Rule Based Control (RBC). The results are then used to develop a methodology for selecting a controller type (i.e. RMPC, MPC, and RBC) as a function of building model uncertainty. RMPC is found to be the desirable controller for the cases with an intermediate level (30%-67%) of model uncertainty, while MPC is preferred for the cases with a low level (0-30%) of model uncertainty. A common RBC is found to outperform MPC or RMPC if the model uncertainty goes beyond a certain threshold (e.g. 67%). I. INTRODUCTION Total primary energy consumption in the United States increased from 78.3 quads in 1980 to 97.8 quads in 2010, of which the building sector accounts for 41% [1]. The building sector is also responsible for about 40% of green- house gas emissions and 70% of electricity use in the United States. 41.4% of energy consumption in buildings is directly related to the space heating, ventilation and air conditioning (HVAC) [1]. Therefore, reducing the energy consumption of buildings by designing smart control systems to operate the HVAC system in a more efficient way is critically important to address energy and environmental concerns. Design and validation practices in the building industry show the importance of a model-based design flow for building controls. To attain energy efficiency, control algo- rithms need to be tailored to the physical properties of the building at hand rather than being an adaptation of a standard sequence designed for a typical building. MPC provides a potential building energy saving of 16%- 41% compared to the commonly used rule-based HVAC con- trollers in the market as shown in [2]–[6]. At each iteration of MPC, a prediction of future states is obtained through forward evolution of the system dynamics. The predictive cost is then calculated and constraints on future states and inputs are applied, leading to a large optimization problem, which is solved to obtain the optimal control action. MPC for building HVAC systems has desirable characteristics such as 1 Mehdi Maasoumy is with Mechanical Engineering Department of Uni- versity of California, Berkeley mehdi@me.berkeley.edu 2 Meysam Razmara and Mahdi Shahbakhti are with Mechanical Engi- neering Department of Michigan Technological University {mrazmara, mahdish}@mtu.edu 3 Alberto Sangiovanni Vincentelli is with the Department of Electrical Engineering and Computer Science, University of California, Berkeley alberto@eecs.berkeley.edu robustness, tunability, and flexibility [4]. Application of MPC for building energy control has been reported in [4]–[13]. Different variations of nominal MPC such as distributed [12], [13], robust [9], [14] and stochastic [8], [15] model predictive control strategies have been also reported. All these MPC techniques rely on accurate building models to achieve optimal performance of HVAC system and provide sufficient comfort level. Hence, reducing model uncertainty is crucial for success- ful realization of building model-based controllers. However, uncertainty is an inevitable attribute of every model. For building models, model uncertainty is even more remarkable due to the substantial contribution of outside and inside thermal heats (realized as disturbance in our model) in the climate of the building, and unpredictability of the environment conditions such as wind speed and direction, ambient temperature, solar radiation and cloudiness of sky, and to some extent indoor factors such as human behavior. In this paper we provide a systematic approach to: • Design model-based building controllers which are ro- bust to model uncertainties; • Assess the overall performance of different control type over a range of model uncertainty in terms of both energy consumption and provided comfort level and • Propose a guideline to pick the right type of controller based on the level of model uncertainty. This paper builds on top of our previous work on de- veloping a parameter adaptive building (PAB) model pre- sented in [16] and centers on designing and analyzing the performance of three types of controllers: 1) a controller which is insensitive to model uncertainty (i.e. a typical on- off control), 2) a controller which is somewhat sensitive to model uncertainty (i.e. nominal MPC) and 3) a controller which is robust against model uncertainty (i.e. Robust MPC) for building HVAC system. II. P ARAMETER -A DAPTIVE B UILDING M ODEL A. System Dynamics 1) Heat Transfer: A building is modeled as a graph in which there are two types of nodes: walls and rooms. n is the total number of nodes, m of which represent rooms and the remaining n − m nodes represent walls. We denote the temperature of room r i with T r i . The wall node and temperature of the wall between room i and j are denoted by (i, j) and T w i,j , respectively, and is governed by the following equation: w C i,j dT w i,j dt k∈N wi,j T r k − T w i,j + r i,j α i,j A w i,j Q rad i,j R i,j k