Abstract:

Two alternative realtime gradient descent algorithms for energy-optimizing control of a multi-zone heat pump system are considered. In the first approach, a model of the compressor and outdoor fan power consumption is used to obtain the gradient of power with respect to high- and low-side pressures and actuator settings. From this relationship, a gradient descent controller is obtained to drive the outdoor fan speed to a value that is predicted to minimize the power consumption.
In the second approach, a time-varying extremum seeking controller is derived. Extremum seeking controllers estimate the gradient of the mapping between the system input and a measurement, and steers the input to a value that minimizes the measurement. Determination of the gradient information is model-free so that estimation and control are simultaneously performed on the system. As with the prior approach, the outdoor fan is controlled to a value that minimizes power.
A multi-physical model of the heat pump is used to compare the controllers performance. The convergence rate is compared from an initial condition response where the outdoor fan is initialized to a suboptimal starting speed. The sensitivity to modeling error is judged by considering operating points distinct from the conditions at which linearization in the model-based approach is calculated. We show that because the model-based optimizer benefits from problem-specific information, convergence to a final value is faster than extremum seeking and that this final value is near the true optimizer, but not guaranteed to reach the true optimum in the presence of modeling errors. Conversely, we show that the extremum seeking converges more slowly that the model-based approach, but because ESC actively experiments with the plant online, the true optimizer is reached.