In electrically driven thermoacoustic refrigerators, the acoustic pressure and actuator displacement are typically monitored while a nominally harmonic drive frequency is adjusted to achieve a given operating point (e.g., maximum electroacoustic conversion efficiency, acoustic resonance, maximum power, etc.) Most often, pressure and displacement are measured directly, using sensors. Using a model of the electrical and mechanical dynamics of a linear electrodynamic machine and resonant assembly, the actuator displacement and pressure at the piston can be accurately estimated via direct measurement of the voltage and current at the machine terminals. This provides a means for sensorless control of the machine. The estimation method and system parameter extraction method will be described, as well as results of comparisons to sensors. Results from tests on a thermoacoustic refrigerator operating at 3-kW acoustic input power using a sensorless control system implemented to maintain an acoustic resonance will be shown, wherein the refrigerator cold temperature was varied over a practical operating range. The control system tracked the acoustic resonance frequency and achieved the desired phase relationship between pressure and displacement to within 3 deg based on the estimation, thus maintaining essentially optimal electroacoustic conversion efficiency during the test. [Work sponsored by ONR.]