State Observer for Optimal Control using White-box Building Models

In order to improve the energy efficiency of buildings, optimal control strategies, such as model predictive control (MPC), have proven to be potential techniques for intelligent operation of energy systems in buildings. However, in order to perform well, MPC needs an accurate controller model of the building to make correct predictions of the building thermal needs (feedforward) and the algorithm should ideally use measurement data to update the model to the actual state of the building (feedback). In this paper, a white-box approach is used to develop the controller model for an office building, leading to a model with more than 1000 states. As these states are not directly measurable, a state observer needs to be developed. In this paper, we compare three different state estimation techniques commonly applied to optimal control in buildings by applying them on a simulation model of the office building but fed with real measurement data. The considered observers are stationary Kalman Filter, time-varying Kalman Filter, and Moving Horizon Estimation. Summarizing the results, all estimators can achieve low output estimation error, but, in the case of the Kalman filters, the estimated state values are not physical. In the case of MHE, the model firstly had to be reduced to 200 states in order to evade the non-positive definite quadratic formulation present in the model and converge in tractable computation time.

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