(345h) MPC of a Heat Pump: Achieving Energy Efficiency through Improved Tuning

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.  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).  Given the known system nonlinearities, a traditional linear MPC framework must be extended to include  an augmented offset-free mechanism if any potential plant-model mismatch is to be captured. Such offset-free MPC structures have been seen to be an effective means at regulating both local HVAC systems (see [1] and [2]) as well as in building-based set-point management [3]. Though each have been shown effective in mitigating disturbances and conserving energy usage within the system,  a general tuning framework for tuning the offset-free MPC structures remain unavailable. In a recent work [1], a sequential tuning approach has been shown to aid in tuning. In [2], the tuning approach involved first tuning the state-estimated and augmented model parameters through open-loop step changes and then moving on to tune the MPC parameters. There is still a significant energy gap that can be bridged by designing and implementing a comprehensive tuning framework.

Motivated by these considerations,  a framework is proposed predicated on the idea of internal model control,  where the `desired' response is specified through appropriate first-order time constants. Preserving the strength of the MPC in handling constraints, limits as to how fast a desired response could be achieved without causing chattering are specified. Subsequently, the tuning of the observer and control parameters are done together within an integrated offset-free MPC framework. The efficacy of the proposed tuning framework is demonstrated on the  experimentally-validated heat pump model coupled with realistic variations to both ambient and internal conditions, as well as measurement noise.

 [1]          M. Wallace, B. Das, P. Mhaskar, J. House, T. Salsbury, Offset-free model predictive control of

                a vapor compression cycle, Journal of Process Control 22 (2012) 1374-1386

[2]           M. Wallace, P. Mhaskar, J. House, T. Salsbury, Offset-free model predictive control of

                a heat pump, Ind. & Eng. Chem. Res. (submitted),

[3]           C. Touretzky, M. Baldea, Nonlinear model reduction and model predictive control of residential

                buildings with energy recovery, in: Journal of Process Control (invited paper for Special Issue

                on Control of Buildings), 2013.