H-Infinity Loop-Shaped Model Predictive Control With HVAC Application

We formulate a model predictive control (MPC) for linear time-invariant systems based on H-infinity loop-shaping. The design results in a closed-loop system that includes a state estimator and attains an optimized stability margin. Input and output weights are designed in the frequency domain to satisfy steady-state and transient performance requirements, in lieu of standard MPC plant model augmentations. The H-infinity loop-shaping synthesis results in an observer-based state feedback structure. An inverse optimal control problem is solved to construct the MPC cost function, so that the control input computed by MPC is equal to the H-infinity control input when the constraints are inactive. The MPC inherits the closed-loop performance and stability margin of the loop-shaped design when constraints are inactive. We apply the methodology to a multizone heat pump, and validate the results in simulations and laboratory experiments. The design rejects constant unmeasured disturbances, tracks constant references with zero steady-state error, meets transient performance requirements, provides an excellent stability margin, and enforces input and output constraints.