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We describe a many-channel experiment control system based on a field-programmable gate array (FPGA). The system has 16 bit resolution on 10 analog 100 megasamples-per-second (MS/s) input channels, 14 analog 100 MS/s output channels, 16 slow analog input and output channels, dozens of digital inputs and outputs, and a touchscreen display for experiment control and monitoring. The system can support ten servo loops with 155 ns latency and MHz bandwidths, in addition to as many as 30 lower bandwidth servos. We demonstrate infinite-impulse-response (IIR) proportional–integral–differential filters with 30 ns latency by using only bit-shifts and additions. These IIR filters allow timing margin at 100 MS/s and use fewer FPGA resources than straightforward multiplier-based filters, facilitating many servos on a single FPGA. We present several specific applications: Hänsch–Couillaud laser locks with automatic lock acquisition and a slow dither correction of lock offsets, variable duty cycle temperature servos, and the generation of multiple synchronized arbitrary waveforms.