BlackGEM is an array of telescopes, currently under development at the Radboud University Nijmegen and at NOVA (Netherlands Research School for Astronomy). It targets the detection of the optical counterparts of gravitational waves. The first three BlackGEM telescopes are planned to be installed in 2018 at the La Silla observatory (Chile). A single prototype telescope, named MeerLICHT, will already be commissioned early 2017 in Sutherland (South Africa) to provide an optical complement for the MeerKAT radio array. The BlackGEM array consists of, initially, a set of three robotic 65-cm wide-field telescopes. Each telescope is equipped with a single STA1600 CCD detector with 10.5k x 10.5k 9-micron pixels that covers a 2.7 square degrees field of view. The cryostats for housing these detectors are developed and built at the KU Leuven University (Belgium). The operational model of BlackGEM requires long periods of reliable hands-off operation. Therefore, we designed the cryostats for long vacuum hold time and we make use of a closed-cycle cooling system, based on Polycold PCC Joule-Thomson coolers. A single programmable logic controller (PLC) controls the cryogenic systems of several BlackGEM telescopes simultaneously, resulting in a highly reliable, cost-efficient and maintenance-friendly system. PLC-based cryostat control offers some distinct advantages, especially for a robotic facility. Apart of temperature monitoring and control, the PLC also monitors the vacuum quality, the power supply and the status of the PCC coolers (compressor power consumption and temperature, pressure in the gas lines, etc.). Furthermore, it provides an alarming system and safe and reproducible procedures for automatic cool down and warm up. The communication between PLC and higher-level software takes place via the OPC-UA protocol, offering a simple to implement, yet very powerful interface. Finally, a touch-panel display on the PLC provides the operator with a user-friendly and robust technical interface. In this contribution, we present the design of the BlackGEM cryostats and of the PLC-based control system.