A series of four automatic tuning machines for 9-cell TESLA-type cavities are being developed and fabricated in a collaborative effort among DESY, FNAL, and KEK. These machines are intended to support high-throughput cavity fabrication for construction of large SRF-based accelerator projects. Two of these machines will be delivered to cavity vendors for the tuning of XFEL cavities. The control system for these machines must support a high level of automation adequate for industrial use by non-experts operators. This paper describes the control system hardware and software design for these machines.