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

Abstract

Magnetic levitation positioning technology has attracted considerable research efforts and dedicated attention due to its extremely attractive features. The technology offers highprecision, contactless, dust/lubricant-free, multi-axis, and largestroke 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∞ 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.

Global Iterative Sliding Mode Control of an Industrial Biaxial Gantry System for Contouring Motion Tasks

“…where r ∈ R 3 is the reference signal vector of the three axes, w i ∈ R 3 is the iterative variable vector during the consecutive iterations. ( 15) and (16) show that the iterative learning control input will be added to the reference signal. Generally, a lowpass filter will be used in the iterative learning law, and thus the original reference signal is not allowed to be changed by the filter.…”

“…As alternatives in the literature, the multi-axis coupling can also be modeled with certain assumptions and then a decentralized control scheme is developed for the gantry system [13], [14]. However, the system identification for such multi-axis systems is inevitably inaccurate [15], [16]. With regards to the issues of multi-axis cooperation, the methodology of coordinated frames is also further proposed in the literature; such as the global task coordinate frame (GTCF) [17], [18] and the Newton-ILC contouring control method [19].…”

Adaptive Fractional-Order Sliding Mode Controller with Neural Network Compensator for an Ultrasonic Motor

“…However, because there exists the presence of unmodeled dynamics, disturbances, and uncertainties in the system, a highfrequency phenomenon called chattering is always arisen in implementing SMC [15]. The chattering effect could reduce the accuracy or damage the actuators, as pointed out in several works [16]- [18]. Significatnly, the chattering is relevant to the disturbance [19].…”

Iterative Super-Twisting Sliding Mode Control: A Case Study on Tray Indexing

“…Mechatronic systems have been widely used in manufacturing industry, such as inspection process, transmission task, stepping and scanning device. As a popular application, timing-belt driven tray indexing is applied for industrial transmission tasks in such areas due to its strong transmission force and low cost [1], [2]. Nevertheless here, there are actually some high-order modes and other unmodeled dynamics which exert inevitable affects on the system performance [3]- [5].…”

“…Meanwhile, the motion accuracy could be ensured at a high level versus the uncertainties. (2). The architecture combines the merits of each term organically.…”