Workshop on Optimal Control of Thermal Systems in Buildings using Modelica location:University of Freiburg date:23 - 24 March 2015
MPC involves the knowledge of the complete state vector and the most significant system perturbations in order to determine the best control performance. However, this information may not be directly or completely available through measurement. In building applications often some information is lacking and the number of sensors deployed and their quality is greatly varying. As a consequence the building system models used by MPC contain several unmeasured state variables, e. g. the temperatures of the walls representing thermal inertia of the building. An optimal control sequence should be able to correctly account for the dynamic effects caused by the thermal inertia, which means that these states’ values should be estimated.
Three different state estimation techniques, namely deterministic state optimization (1), moving horizon estimation (2) and unscented Kalman filter (3), are compared. They are implemented in a python framework for data handling and estimate the state vector of a simulation model in Modelica. Python addresses the Modelica models through JModelica.org for optimization (1,2) and through pyfmi for simulation (3).
(1) Deterministic state optimization assumes a perfect, deterministic model used to simulate over a past horizon. The past state vector at the start of the horizon is optimized to fit the model output to the measurement data, which finds the current state vector (at the end of the past horizon).
(2) Moving horizon estimation assumes process noise and measurement noise to simulate over a past horizon. The past state vector at the start of the horizon is assumed to be known and minimized series of process noise is added to find the current state vector.
(3) Unscented Kalman filter can assume a perfect, deterministic model, to simulate over one past timestep. The past state vector at one timestep back is assumed to be known and the current state vector is calculated by the filter.
The three algorithms are compared based both on quantitative goodness of fit (GOF) and qualitative indicators. Also, the computational performances, the ease of use and tool/model requirements are reported. The state estimation algorithms are first evaluated using simulation data and will be tested in a real multi-zone office building in Brussels for which an MPC is implemented. This allows assessing the impact of model mismatch, perturbation, and uncertainties on the ability to correctly estimate the unmeasured state variables.