Explicit Model Predictive Control for a Magnetic Levitation System

The paper uses an explicit nonlinear control law constructed upon an approximating solution of a constrained finite-time optimal control (CFTOC) problem. The methodology is based on the piecewise affine approximation of a nonlinear models and the exact explicit solution of a multiparametric optimisation problem associated with a model predictive control (MPC) scheme. The technique is applied to a system with fast dynamics - a magnetic levitation benchmark. The key advantages of this methodology are two-fold: Firstly, having an explicit solution of a CFTOC problem permits the direct implementation of traditionally computational-wise prohibitive control techniques for true real-time applications. Secondly, MPC's systematic fashion to deal with a prediction model eases the design of an optimal control law.