The cerebellum plays a central role in motor control and learning. Its neuronal network architecture, firing characteristics of component neurons, and learning rules at their synapses have been well understood in terms of anatomy and physiology. A realistic artificial cerebellum with mimetic network architecture and synaptic plasticity mechanisms may allow us to analyze cerebellar information processing in real world by applying it to adaptive control of actual machines. Several artificial cerebellums have previously been constructed, but they required a high-performance hardware to run in real time for real-world machine control. Presently, we implemented an artificial cerebellum with the size of 104 spiking neuron models on a field-programmable gate array (FPGA) which is compact, lightweight, portable, and low-power-consumption. In the implementation three novel techniques are employed: 1) 16-bit fixed-point operation with randomized rounding, 2) fully connected spike information transmission, 3) alternative memory that uses pseudo-random number generators. We demonstrate that the FPGA artificial cerebellum runs in real time, and its component neuron models behave as those in the corresponding artificial cerebellum configured on a personal computer in Python. We applied the FPGA artificial cerebellum to adaptive control of a machine in real-world and demonstrate that the artificial cerebellum is capable of adaptively reducing control error after sudden load changes. This is the first implementation and demonstration of a spiking artificial cerebellum on an FPGA applicable to real-world adaptive control. The FPGA artificial cerebellum may provide neuroscientific insights into cerebellar information processing in adaptive motor control and may be applied to various neuro-devices to augment and extend human motor control capabilities.