Abstract:

Modern heat pumps are strongly interactive multivariable systems, requiring rigorous application of multi- variable control theory. Important factors to consider are robustness with respect to plant uncertainty, and enforcement of process constraints. This paper summarizes the design of two Model Predictive Control (MPC) architectures for a heat pump application, and compares their design methodologies and performance to a conventional selector-based multi-loop PID architecture. One MPC architecture is an H-infinity loop- shaped MPC that uses inverse optimal control to realize the ro- bustifying compensator as a constrained optimization to enforce constraints. The second is an offset-free MPC architecture that preserves output tracking despite plant-model mismatch and unmeasured disturbances and can be tuned using operational data. We compare the two MPCs and the PID on a constrained heat pump model, assessing closed-loop transients, robustness margins, and tuning complexity. In simulation, all controllers track setpoints with similar performance. During a sensible- heat disturbance, a temperature limit prevents full rejection; even so, both MPC designs counterintuitively reduce the out- door fan speed – which, through coupled system interactions, increases net heat removal and yields improved disturbance rejection without violating constraints. As for robustness, all three designs meet disk-margin targets. For tuning complexity, offset-free MPC > H-infinity loop-shaped MPC > PID. Overall, on this plant, robustness is a tie; offset-free MPC delivers the strongest constrained disturbance handling but requires the most tuning, H-infinity loop-shaped MPC is the middle ground, and PID is simplest.