# Design of a Compact Planar Magnetic Levitation System with Wrench-Current Decoupling Enhancement
## 1 Introduction  
Nowadays, magnetic levitation or maglev technology is applied in various fields from macro- to microlevel applications. Maglev technology utilizes the interaction between magnets and/or electromagnets to levitate a magnetized object without contact. By manipulating the actuator outputs, attractive or repulsive forces are generated on the object to control the motion. With its advantages of low friction and contactless motion, maglev can provide high-speed and dustless motion. One of the well-known applications is high-speed transportation such as maglev trains [1] and hyperloop [2]. Meanwhile, various robotic applications using magley technology can be found in [3]. The magley system can perform delicate tasks in micromanipulation [4; 5; 6] and haptics [7]. Moreover, it can also be applied for modern industrial applications, for example, metal melting [8], magnetic bearing [9] for high-speed electrical machines, and metal additive manufacturing [10]. Another industrial application of maglev is for manufacturing systems. Since the suspended object can be controlled for multiple degree-of-freedom (DOF) motion, the magley system can improve the flexibility of the machining or material handling tasks in the production line. For these tasks, the repulsive-type planar magley system, which has the mover levitated on top of the stator, is more suitable than the attractive-type system because it enables the system to work with other automation systems such as CNC machines and industrial robots. For the planar magley system structure, there are two types of movers, namely, moving coils and moving magnets, which work with magnet stators and electromagnet stators, respectively. Even though some research works use moving coilmover [11; 12]; this type of mover is not popular because it must be equipped with or wired to the power source to energize moving coils. By using several combinations of magnet movers and electromagnet stators, the previous research works mainly aimed to develop maglev systems for high-precision and/or long-range motion. For high-precision motion, the system structures are usually designed with multiple sets of coil stators and moving magnet arrays. The mover is controlled to have a fine motion with micro- or nanolevel precision and relatively small errors. An early high-precision maglev stage was developed for photolithography [13] which had a translation range of 50 mm by 50 mm with a motion step size of 50 nm. Subsequent designs of high-precision maglev stages utilized multiple sets of 1-D Halbach arrays with long rectangular coils [14] with 100 mm motion stroke and 20 nm step motion, or square coil arrays [15] which presented the high-precision steps of 1 \(\upmu\)m and its RMSE of 0.58 \(\upmu\)m. The alternative stage design had multiple single-axis maglev actuators made of a cylindrical magnet and a cylindrical coil for vertical and horizontal motion control [16]. The design of a dual-stage mover for fine motion can be found in [17]. Not only precision linear stages, but the design of a circular Halbach array mover and electromagnet stator arranged in a circle can also achieve high-precision rotary table [18; 19]. From the review, the Halbach array mover is widely used because it has the advantage of focusing a strong magnetic field on one side. Most of the proposed systems were invented for short- or medium-stroke motion with a small levitation gap below 10 mm and small rotation ranges. Moreover, most of the structures were designed as multiactuator stages. It is difficult to extend this structure for long-range motion even though some works have long motion strokes. For long-range motion, the stator is designed to be planar and expandable since the motion range of the mover is limited by the stator area. A topology comparison of four coil arrays in [20] indicated that the rectangular coil array in a herringbone pattern provided low-power dissipation and small force/torque ripples on the 2-D Halbach array mover.