H Infinity Loop-Shaped Model Predictive Control with Heat Pump Application

    •  Bortoff, S.A., Schwerdtner, P., Danielson, C., Di Cairano, S., "H Infinity Loop-Shaped Model Predictive Control with Heat Pump Application", European Control Conference (ECC), DOI: 10.23919/​ECC.2019.8796158, June 2019, pp. 2386-2393.
      BibTeX TR2019-052 PDF
      • @inproceedings{Bortoff2019jun,
      • author = {Bortoff, Scott A. and Schwerdtner, Paul and Danielson, Claus and Di Cairano, Stefano},
      • title = {H Infinity Loop-Shaped Model Predictive Control with Heat Pump Application},
      • booktitle = {European Control Conference (ECC)},
      • year = 2019,
      • pages = {2386--2393},
      • month = jun,
      • publisher = {IEEE},
      • doi = {10.23919/ECC.2019.8796158},
      • url = {}
      • }
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In this paper we derive a formulation for Model Predictive Control (MPC) of linear time-invariant systems based on H infinity loop-shaping. The design provides an optimized stability margin for problems that require state estimation. Input and output weights are designed in the frequency domain to satisfy steady-state and transient performance requirements, in lieu of conventional MPC plant model augmentations. The H infinity loop-shaping synthesis results in an observer-based state feedback structure. Using the linear state feedback law, an inverse optimal control problem is solved to design the MPC cost function, and the H infinity state estimator is used to initialize the prediction model at each time step. The MPC inherits the closed-loop performance and stability margin of the loopshaped design when constraints are inactive. We apply the methodology to a multi-zone heat pump system in simulation. The design rejects constant unmeasured disturbances and tracks constant references with zero steady-state error, has good transient performance, provides an excellent stability margin, and enforces input and output constraints.


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