Distributed hardware of acoustic sensor networks bears inconsistency of local sampling frequencies, which is detrimental to signal processing. Fundamentally, sampling rate offset (SRO) nonlinearly relates the discrete-time signals acquired by different sensor nodes. As such, retrieval of SRO from the available signals requires nonlinear estimation, like double-cross-correlation processing (DXCP), and frequently results in biased estimation. SRO compensation by asynchronous sampling rate conversion (ASRC) on the signals then leaves an unacceptable residual. As a remedy to this problem, multi-stage procedures have been devised to diminish the SRO residual with multiple iterations of SRO estimation and ASRC over the entire signal. This paper converts the mechanism of offline multi-stage processing into a continuous feedback-control loop comprising a controlled ASRC unit followed by an online implementation of DXCP-based SRO estimation. To support the design of an optimum internal model control unit for this closed-loop system, the paper deploys an analytical dynamical model of the proposed online DXCP. The resulting control architecture then merely applies a single treatment of each signal frame, while efficiently diminishing SRO bias with time. Evaluations with both speech and Gaussian input demonstrate that the high accuracy of multi-stage processing is maintained at the low complexity of single-stage (open-loop) processing.