(555a) Offset-Free Model Predictive Control of a Heat Pump

Authors: 
Wallace, M., McMaster University
Mhaskar, P., McMaster University
House, J., Johnson Controls
Salsbury, T., Johnson Controls



The comfort level within the indoor environment of a building is maintained by mechanical and electrical systems classified as heating, ventilating and air-conditioning (HVAC) systems. In many residential and industrial settings this conditioning is provided through the heating and cooling mechanisms of a heat pump. This specific HVAC system is bi-modal in nature, in that it can either absorb/release heat depending on it's mode of operation, enabling any necessary heating/cooling demands to be satisfied through a single unit. The heat pump cooling mechanism is identical to that provided by a Vapor Compression Cycle due to these units sharing the same mechanical components and layout and is the focus of our current work.

The most common realization of a heat pump consists of four components: a compressor, outdoor heat exchanger, expansion valve, and an indoor heat exchanger. In the cooling mode, conditioning performance is tied directly to the tracking performance of the indoor coil's supply air temperature , while safety-related issues center upon the above-zero regulation of the refrigerant superheat temperature at the outlet of the indoor coil. Multiple actuators are available for manipulation to satisfy these control objectives, however one caveat in their operation is the vast range which exists amongst each of their individual energy demands. This includes the most energy intensive actuator, the compressor, drawing electricity to regulate it's motor frequency which directly affects the inlet/outlet refrigerant compression ratio. Less energy intensive in nature are the fan drives which are used in setting the air flow rate over both the indoor and outdoor coils. The final actuator as well as the least energy intensive one, is the expansion valve. Through manipulating the valve flow area, conditioning ability of the indoor coil is directly affected (variation to refrigerant vapor/liquid fraction, refrigerant mass flow rate). On top of the large energy discrepancy amongst actuators, a high level of interaction and subsequent nonlinearities persist within the heat pump dynamics, causing single-input-single-output (SISO) control approaches (classical PI/PID or decoupled versions of it) to be far from superior when one must consider satisfying the interconnected control objectives described previously. A more suitable control approach, in terms of effectively accounting for such system dynamics and control objectives, is that of model predictive control (MPC). Model predictive control is designed to handle these shortfalls in a manner which models system interactions (both known and unknown), uses specific input/output constraints and can incorporate tiered objectives such as tracking and energy use through a single multi-term objective function.

Here, an MPC strategy is developed which manipulates the set-point of an internal heat pump superheat PI controller while also manipulating the ramp height used in adjusting the compressor speed. An optimization problem is formulated within the MPC confines to minimize energy usage while ensuring other tracking and system objectives/constraints are satisfied. A linear supply air temperature model is used for predictions, while an offset-free mechanism in the form of an augmented model and state estimator is also incorporated so as to ensure predictions and plant converge. A detailed internal heat pump interfaced with two additional software clients, one housing the control design and the other providing an accurate medium for a building model, are used for evaluating the performance of this control approach. This will include closed-loop results for a practical test environment which considers realistic variations in both the physical setting as well as in the measuring sensors.