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

TL;DR

This paper presents a convex parameterization and optimization method for robustly tracking a magnetically levitated planar system, ensuring stability and performance despite uncertainties, validated through experiments.

Contribution

It introduces a convex inner approximation for robust controller design with prescribed structure, improving tracking accuracy for a complex maglev system.

Findings

Achieved stable and accurate tracking of S-curve trajectory.

Validated robustness against parametric uncertainties.

Demonstrated effectiveness through experimental results.

Abstract

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, multi-axis, and large-stroke positioning. In this work, we focus on the accurate and smooth tracking problem of a multi-axis magnetically levitated (maglev) planar positioning system for a specific S-curve reference trajectory. The floating characteristics and the multi-axis 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 paper utilizes the basis of an H-infinity 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 re-formulated 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.