Embedded Predictive Control on an FPGA using the Fast Gradient Method

Model predictive control (MPC) in resource-constrained embedded platforms requires faster, cheaper and more power-efficient solvers for convex programs than is currently offered by software-based solutions. In this paper we present the first field programmable gate array (FPGA) implementation of a fast gradient solver for linear-quadratic MPC problems with input constraints. We use fixed-point arithmetic to exploit the characteristics of the computing platform and provide analytical guarantees ensuring no overflow errors occur during operation. We further prove that the arithmetic errors due to round-off can lead only to reduced accuracy, but not instability, of the fast gradient method. The results are demonstrated on a model of an industrial atomic force microscope (AFM) where we show that, on a low-end FPGA, satisfactory control performance at a sample rate beyond 1 MHz is achievable, opening up new possibilities for the application of MPC.