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Linear quadratic Gaussian control with advanced continuous-time disturbance models for building thermal regulation

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  • Thilker, Christian Ankerstjerne
  • Jørgensen, John Bagterp
  • Madsen, Henrik

Abstract

This paper introduces a linear quadratic control scheme for a continuous-time system with observations taken at discrete times. Particular attention is given to the derivation of the disturbance terms in the model. Control performance may depend critical on accurate disturbance forecasts. This is the case for building climate control, where solar rays pass through e.g. windows and deliver significant amounts of energy and the dynamics can be very fast, fluctuating, and spontaneous. We thus argue that it is critical for control performance to sufficiently describe and include disturbances in the control description to obtain satisfactory control accuracy. We suggest and derive in details a control framework based on continuous-time stochastic differential equations (SDEs) and linear quadratic Gaussian control using an advanced continuous-time disturbance model to supply disturbance forecasts. The numerical simulation results suggest that control with embedded forecasts handles uncertainties well and provides up to 26% performance improvements compared to standard disturbance mitigation techniques. Furthermore, we demonstrate that the quadratic controller has a useful trade-off between variability in the control signal, economic cost, and variability around the reference point.

Suggested Citation

  • Thilker, Christian Ankerstjerne & Jørgensen, John Bagterp & Madsen, Henrik, 2022. "Linear quadratic Gaussian control with advanced continuous-time disturbance models for building thermal regulation," Applied Energy, Elsevier, vol. 327(C).
    • Handle: RePEc:eee:appene:v:327:y:2022:i:c:s0306261922013435
    DOI: 10.1016/j.apenergy.2022.120086
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    References listed on IDEAS

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    1. Junker, Rune Grønborg & Azar, Armin Ghasem & Lopes, Rui Amaral & Lindberg, Karen Byskov & Reynders, Glenn & Relan, Rishi & Madsen, Henrik, 2018. "Characterizing the energy flexibility of buildings and districts," Applied Energy, Elsevier, vol. 225(C), pages 175-182.
    2. Chang-Soon Kang & Jong-Il Park & Mignon Park & Jaeho Baek, 2014. "Novel Modeling and Control Strategies for a HVAC System Including Carbon Dioxide Control," Energies, MDPI, vol. 7(6), pages 1-19, June.
    3. Lago, Jesus & De Ridder, Fjo & De Schutter, Bart, 2018. "Forecasting spot electricity prices: Deep learning approaches and empirical comparison of traditional algorithms," Applied Energy, Elsevier, vol. 221(C), pages 386-405.
    4. Thilker, Christian Ankerstjerne & Madsen, Henrik & Jørgensen, John Bagterp, 2021. "Advanced forecasting and disturbance modelling for model predictive control of smart energy systems," Applied Energy, Elsevier, vol. 292(C).
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