Model predictive control (MPC) is a popular advanced model-based control algorithm for controlling systems that must respect a set of system constraints (e.g. actuator force limitations). However, the computing requirements of MPC limits the suitability of deploying its software implementation into embedded controllers requiring high update rates. This paper presents a scalable embedded MPC controller implemented on a field-programmable gate array (FPGA) coupled with an on-chip ARM processor. Our architecture implements an Alternating Direction Method of Multipliers (ADMM) approach for computing MPC controller commands. All computations are performed using floating-point arithmetic. We introduce a software/hardware (SW/HW) co-design methodology, for which the ARM software can configure on-chip Block RAM to allow users to 1) configure the MPC controller for a wide range of plants, and 2) update at runtime the desired trajectory to track. Our hardware architecture has the flexibility to compromise between the amount of hardware resources used (regarding Block RAMs and DSPs) and the controller computing speed. For example, this flexibility gives the ability to control plants modeled by a large number of decision variables (i.e. a plant model using many Block RAMs) with a small number of computing resources (i.e. DSPs) at the cost of increased computing time. The hardware controller is verified using a Plant-on-Chip (PoC), which is configured to emulate a mass-spring system in real-time. A major driving goal of this work is to architect an SW/HW platform that brings FPGAs a step closer to being widely adopted by advanced control algorithm designers for deploying their algorithms into embedded systems.