Extremum Seeking Control, Experimental Evaluation, Air Conditioning System, Statistical Analysis, Input-output Correlation
Extremum Seeking Control (ESC) has emerged as a model-free real-time optimization framework, typically based on dither-demodulation driven gradient estimation. However, such conventional ESC suffers from slow convergence. Salsbury et al. have recently proposed an input-output correlation based ESC (IOC-ESC) strategy anchored on a statistical analysis. The IOC-ESC algorithm is less sensitive to changes in its internal parameters because of the use of a normalized correlation coefficient in the feedback loop. The design goal of the algorithm is to have only two tunable parameters: (1) a time scale parameter that relates to the time open loop time constant of the system; and (2) the amplitude of the dither signal. A suitable set of generic internal parameters is still in the process of being identified as more test data become available from different system types. For the work reported here, the feedback gain (referred to as the tuning factor) with the IOC-ESC was also tuned for optimal performance. This study aims to conduct an experimental evaluation for the IOC-ESC strategy with a ductless mini-split air conditioning system, compared with conventional ESC (CON-ESC). The system features variable-capacity compressor operation and variable-speed operation for the evaporator and condenser fans. In this study, both single-input and two-input ESC scenarios are tested. The manipulated inputs include the evaporator and condenser fan speeds, while the total power consumption is used as feedback for all cases. The experimental setup is developed with a 9000 BTU variable-speed mini-split AC system serving a 4’x8’x6’ insulated chamber, and an electrical fan heater is used to provide an artificial heat load. The data acquisition and control algorithms are implemented on a National Instruments CompactRIO platform. Both IOC-ESC and CON-ESC are tested with the same setup. For single-input scenario, the manipulated input is the condenser fan speed. The testing results of five trials of IOC-ESC are used to evaluate the impact of the two tuning parameters, i.e. dither frequency and tuning factor, on the ESC performance. IOC-ESC#1, IOC-ESC#4 and IOC-ESC#5 have the same dither frequency but different tuning factors, while IOC-ESC#1, IOC-ESC#2 and IOC-ESC#3 have the same tuning factor but different dither frequencies. The testing results of two trials of CON-ESC are then compared with the IOC-ESC results. Both CON-ESC and IOC-ESC can effectively reduce the power consumption of the mini-split system without sacrificing zone temperature regulation. Moreover, the settling time of IOC-ESC ranges from 300 to 600 seconds, while the settling time of CON-ESC ranges from 900 to 1200 seconds. Overall, the IOC-ESC converges faster than the CON-ESC. For two-input scenario, the manipulated inputs are condenser fan speed and evaporator fan speed. The testing results of the two-input IOC-ESC are compared with the result of a two-input CON-ESC trial by Yan et al. with the same system. The settling times for CON-ESC and IOC-ESC are about 1800 and 1200 seconds, respectively. In summary, both CON-ESC and IOC-ESC can optimize the condenser fan speed and evaporator fan speed for energy efficient operation, while the IOC-ESC converges faster and has fewer tuning parameters.