Model predictive control (MPC) is an optimisation-based scheme that imposes a real-time constraint on computing the solution of a quadratic programming (QP) problem. The implementation of MPC in fast embedded systems presents new technological challenges. In this paper we present a parameterised field-programmable gate array implementation of a customised QP solver for optimal control of linear processes with constraints, which can achieve substantial acceleration over a general purpose microprocessor, especially as the size of the optimisation problem grows. The focus is on exploiting the structure and accelerating the computational bottleneck in a primal-dual interior-point method. We then introduce a new MPC formulation that can take advantage of the novel computational opportunities, in the form of parallel computational channels, offered by the proposed pipelined architecture to improve performance even further. This highlights the importance of the interaction between the control theory and digital system design communities for the success of MPC in fast embedded systems.