Convex Parameterization and Optimization for Robust Tracking of a Magnetically Levitated Planar Positioning System

Magnetic levitation positioning technology has attracted considerable research efforts and dedicated attention due to its extremely attractive features. The technology offers high precision, contactless, dust/lubricant free, multiaxis, and large-stroke positioning. In this article, we focus on the accurate and smooth tracking problem of a multiaxis magnetically levitated (maglev) planar positioning system for a specific S-curve reference trajectory. The floating characteristics and the multiaxis coupling make accurate identification of the system dynamics difficult, which lead to a challenge to design a high performance control system. Here, the tracking task is achieved by a 2-degree-of-freedom (DoF) controller consisting of a feedforward controller and a robust stabilizing feedback controller with a prescribed sparsity pattern. The approach proposed in this article utilizes the basis of an
${H}_\infty$
controller formulation and a suitably established convex inner approximation. Particularly, a subset of robust stabilizable controllers with prescribed structural constraints is characterized in the parameter space, and so thus the reformulated convex optimization problem can be easily solved by several powerful numerical algorithms and solvers. With this approach, the robust stability of the overall system is ensured with a satisfactory system performance despite the presence of parametric uncertainties. Furthermore, experimental results clearly demonstrate the effectiveness of the proposed approach.