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Modern power converters (power supplies) at CERN are controlled by devices known as Function Generator/Controllers (FGCs), which are embedded computer systems providing function generation, current and field regulation, and state control. FGCs were originally conceived for the LHC in the early 2000s, though later generations are now increasingly being deployed in the accelerators in the LHC Injector Chain (Linac4, Booster, Proton Synchrotron and SPS) to replace obsolete equipment. A new generation of FGC known as the FGC3.2 is currently in development, which will provide for the evolving needs of the CERN accelerator complex and additionally be supplied to other HEP laboratories through CERN’s Knowledge and Technology Transfer program. This paper describes the evolution of FGCs, summarizes tests performed to evaluate candidate components for the FGC3.2 and details the final hardware and software architectures which were chosen. The new controller will make use of a multi-core ARM-based system-on-chip (SoC) running an embedded Linux operating system in contrast to earlier generations which combined a microcontroller and DSP with software running on ’bare metal’., Proceedings of the 17th International Conference on Accelerator and Large Experimental Physics Control Systems, ICALEPCS2019, New York, NY, USA