Enhancing Magnetic Levitation Control via Moving Horizon Estimation: A Case Study on the Maggy System

We consider how to improve the control of a magnetic levitation system by means of Moving Horizon Estimation algorithms. We thus derive such an online estimator, and analyse the improvements that it may bring to closed-loop state-feedback control performance. We explicitly consider a Moving Horizon Estimation (MHE) problem that accounts for linearized dynamical and measurement models, as long as actuation constraints, and for the purpose derive an unbounded quadratic programming formulation. Through experiments that involve LQR and Model Predictive Control (MPC) approaches we characterize the trade-offs among control performance and computation time, and characterize the robustness of the stabilization by investigating how estimation and control accuracy degrades under model inaccuracies. We discuss the effects of tuning on the results, how the estimation scheme may be improved, and how it may become advantageous especially for complex control maneuvers, full nonlinear models, and state/input bounds.