磁悬浮平面定位系统鲁棒跟踪的凸参数化与优化
Convex Parameterization and Optimization for Robust Tracking of a Magnetically Levitated Planar Positioning System
摘要：
磁悬浮定位技术由于其极具吸引力的特性而吸引了大量的研究工作和专门的关注。该技术提供高精度、非接触式、无灰尘/无润滑剂、多轴和大行程定位。在这项工作中，我们专注于多轴磁悬浮（磁悬浮）平面定位系统的精确和平滑的跟踪问题，为特定的S曲线参考轨迹。悬浮特性和多轴耦合使得系统动态特性的精确辨识变得困难，这给高性能控制系统的设计带来了挑战。在这里，跟踪任务是由一个2自由度（DoF）控制器组成的前馈控制器和一个强大的稳定反馈控制器与规定的稀疏模式。本文提出的方法利用H ∞控制器的基础上制定和适当建立凸内近似。特别地，具有规定的结构约束的鲁棒可镇定控制器的子集的特征在于在参数空间中，因此，重新制定的凸优化问题可以很容易地解决了几个强大的数值算法和求解器。通过这种方法，尽管存在参数不确定性，整个系统的鲁棒稳定性仍能保证令人满意的系统性能。此外，实验结果清楚地证明了所提出的方法的有效性。
英文摘要：
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.
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