Comparison of Three Modeling Approaches for a Thermodynamic Cooling System With Time-Varying Delay

In this paper, the modeling of a thermodynamic cooling system is considered, with the emphasis on dealing with the time-varying delay. A detailed characterization of the system output is performed first in the frequency domain, which successfully yields information relating to the location in the physical structure, which causes the time-varying delay. Three approaches are compared for modeling this delay: 1) using an adaptive fractional delay; 2) using an adaptive tapped delay line; and 3) using a polynomial delay. In addition, it is shown that the use of a carefully designed perturbation signal with harmonic suppression is advantageous in this case, as the percentage output power contained in the nonexcited harmonics can serve as a measure of the relative variance of the delay since the system is found to be largely linear.