Real-time implementation of an explicit MPC-based reference governor for control of a magnetic levitation system

This paper deals with the design and real-time implementation of an Model Predictive Control (MPC)-based reference governor on an industrial-like microcontroller. The task of the governor is to provide optimal setpoints for an inner Proportional-Summation-Difference (PSD) controller. The MPC-based governor is synthesized off-line as a Piecewise Affine (PWA) function that maps measurements onto optimal references. To achieve a fast and memory-efficient implementation, the PWA function is encoded as a binary search tree. This allows the reference governor to run on a sub-millisecond scale even on a very simple hardware. The proposed concept is experimentally verified on a laboratory device involving a magnetic levitation system. Here, the PSD controller is responsible for controlling the vertical position of the ball in the magnetic field. By using the reference governor, control performance can be significantly improved and input/output constraints enforced in a systematic manner.