Model predictive control (MPC) is one of the most effective and well-known methods of advanced control technology, which is being used in more and more areas, such as building automation.
The concept behind it is to predict the future behaviour of a system to be controlled within a defined period of time. A control command is optimised in such a way that it minimises a cost function within certain limits. Accordingly, the control command is calculated by solving an optimisation problem for a finite horizon of the control loop in each sampling interval. The first section of the resulting optimal control command is then applied until the next sampling interval, while the horizon is shifted forwards and the entire process is repeated. [1] This abstract description is well illustrated by a standard scheme for closed-loop MPC control in building control, see Figure 1. White blocks represent actual functions of the MPC controller, grey blocks represent the digital model of the building and external weather forecasts.
Starting from the actual building (‘Building’), the building output vector 𝑦𝑘 (e.g. wall temperatures) is passed on to the ‘Estimator’ at time step 𝑘, taking into account the previous control variable 𝑢𝑘 and the influence of the weather and other disturbance variables 𝑑𝑘, whereby a state estimate 𝑥̂𝑘 of the room temperatures is created. The resulting output forms the starting states for the simulation and is fed into the digital model of the building together with the influence of estimated disturbance variables 𝑑̂𝑘 (in this case the weather forecasts). At this point, final state predictions are simulated for the time step 𝑥𝑘+1 using the digital building model. The ‘optimisation problem’ is then calculated using this status information and taking into account constraints for 𝑥𝑘 and 𝑢𝑘 and their target values. The aim of this is to minimise a cost function. This function relates to the course of the system over a certain time horizon 𝑁-1 and attempts to minimise deviations between the desired and actual behaviour as efficiently as possible. In this case, this would refer to deviations between the desired and simulated room temperatures. Based on this optimisation, the control variable 𝑢𝑘 is output, which can control heat flows, valve openings or pump outputs, for example, in order to ultimately guarantee the desired room temperatures in the building in the most efficient white way. Finally, the cycle starts again for the next time horizon. [2, S. 193]
In short, MPC controllers help to heat buildings as efficiently as possible and thus save energy and costs. As just described, this first requires the actual building, a digital twin of it and algorithms for optimisation. In practice, setting up and validating the digital building model is particularly time-consuming and costly. In addition, each MPC control system is customised to the respective building and is difficult to transfer to others without further ado. This is also one reason why this technology has so far only been used in large buildings such as office complexes and to some extent in industry, as the quantitative energy savings are worthwhile here. Use in private households would therefore be uneconomical due to the effort involved and without a standardised solution. Nevertheless, model predictive control is being intensively researched and further developed in the field of building technology, but also in countless other areas, and will certainly have a firm place in the future of control technology.
[1] Institute for Systems Theory and Automatic Control. “Model Predictive Control.” [Online]
https://www.ist.uni-stuttgart.de/research/group-of-frank-allgoewer/model-predictive-control/
[2] J. Drgoňa et al., “All you need to know about model predictive control for buildings,” Annual Reviews in Control, Jg. 50, S. 190–232, 2020. doi: 10.1016/j.arcontrol.2020.09.001. [Online]
https://www.sciencedirect.com/science/article/pii/S1367578820300584
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