In this paper, we develop an architecture for accelerating a primal-dual quadratic program solver associated with linear model predictive control on a Field Programmable Gate Array (FPGA). The architecture exploits the saddlepoint structure of the quadratic program and allows for transparent introduction of pre-conditioning and relaxation to improve solution robustness and convergence. We demonstrate the efficiency of the architecture using fixed-point arithmetic implementation and taking advantage of the sparsity of the problem data to increase scalability and solution speed.