# Design of a Compact Planar Magnetic Levitation System with Wrench-Current Decoupling Enhancement
## 1 Introduction
The modular stator of multilayer copper conductors in [21] could be expanded easily while achieving precision motion with microlevel motion error. However, the levitation gap was still small. The long-range translation with a large levitation gap can be realized using disc magnets and a cylindrical coil array. A single disc magnet can be controlled for five-DOF motion only [22] because of its symmetry around the vertical axis. In [23], a two-disc-magnet mover could achieve six-DOF motion with an air gap of 25 mm. Then, the unlimited yaw rotation using six disc magnets mounted on a ball-shaped mover was demonstrated in [24]. Nevertheless, the levitation error was large due to the slow sensing and control frequency. In real-time motion control of the planar maglev system, the cross-coupling effect in this overactuated system is usually decoupled by a wrench-current transformation matrix. The force and torque components in this matrix are based on the Lorentz force law which requires the computations of (1) magnetic flux density and (2) forces and torques from the volume integral. For the magnetic flux density, the magnetic node approach [25] is used for the rectangular magnet but is also applicable for the cylindrical magnet. The magnetic flux density of the Halbach array can be rapidly estimated by the order-reduction harmonic model [26; 27]. Next, the volume integral can be solved by numerical methods. The Gaussian quadrature technique which can transform the integral into the summation was implemented on an FPGA for parallel computing [28] and used for real-time decoupling for the maglev rotary table in [29]. Alternatively, selecting the nearest wrench-current transformation matrix from a lookup table, which stores precomputed transformation matrices in a specific range, was used for disc-magnet mover in [22; 30]. However, the lookup table approach has a problem with its discrete data. The effectiveness of decoupling at the no-data locations deteriorates because the transformation matrix is acquired from the nearest data. Therefore, the decoupling enhancement using estimation techniques for the transformation matrix at the locations without lookup data can improve the levitation performance. The multidimensional linear interpolation was implemented in [23; 24] to improve the accuracy in long-range translation and rotation whereas the performance of the fine motion was not examined. This paper presents a novel design of a compact planar maglev system, which is capable of expanding for large-area omnidirectional levitation while performing a high-precision motion, to be applicable to modern manufacturing systems. The main objectives of this work are described as follows:  
1. _The compact and portable design of a five-DOF repulsive planar maglev prototype using an array of square coils with a single disc magnet mover_: The system is intended to perform as a fine motion stage for a precision machining workstation. Meanwhile, the design is capable of expanding the planar stator as a module for long-range levitation. 2. _Wrench-current decoupling enhancement using multidimensional interpolation for the fine motion_: An implementation of a linear interpolation method can improve the levitation performance at the mover pose without data in the lookup table. This method is feasible to deploy on a control system with limited computational resources. The rest of this paper is organized as follows: Section 2 details the compact planar maglev system design. The implementation of the working principle from Section 3 and the wrench-current decoupling enhancement using a linear multidimensional interpolation for the real-time control system are described in Section 4. The results of levitation experiments are presented in Section 5. The discussions of this work are given in Section 6 and a conclusion is provided in Section 7.