This paper addresses the implementation of model predictive control (MPC) at millisecond range, or faster, sampling rates. This is achieved by designing a custom integrated circuit architecture that is specifically targeted to the MPC problem. As opposed to the more usual approach using a generic serial architecture processor, the design here is implemented using a field programmable gate array (FPGA) and employs parallelism, pipelining and specialized numerical formats. The performance of this approach is profiled via the control of a 14th order resonant structure with 12 sample prediction horizon at 200us sampling rate. The results indicate that no more than 30us are required to compute the control action. A feasibility study indicates that the design can also be implemented in 130nm CMOS technology, with a core area of 2.5mm2. These results illustrate the feasibility of MPC for reasonably complex systems, using relatively cheap, small, and low-power computing hardware.