A multi-axis compact positioner is designed and implemented in this thesis. The single-moving-part positioner is designed to move in the magnetic field generated by a superimposed concentrated-field permanent magnet matrix. The compact positioner is primarily for the stepping and scanning applications that require 3-DOF planar motions. In which, the travel ranges in two orthogonal directions are on the order of 100 mm. The moving platen, which has the size of 185.4 mm x 157.9 mm and weighs 0.64 kg, mainly comprises of a plastic frame and six copper coils. It is actuated in the horizontal plane by flowing six independent electric currents into the coils. The platen is supported against gravity by three air bearings. Force calculation is based on the Lorentz force law. With a current-carrying rectangular coil placed in the magnetic field of the supper-imposed Hallbach magnet matrix, the force acting on the coil is calculated by volume integration. The distances between the longer sides and between the shorter sides of the rectangular coil are designed to fit a half pitch and one pitch of the Hallbach magnet array, respectively. Therefore, the volume integration is simplified considerably. The force-current relation for the entire platen with six coils is derived. Three Hall-effect sensors are attached to the moving platen to measure the magnetic flux densities at the center points of the sensors. The position of the moving platen is determined by the field solution of the magnet matrix and the magnetic flux densities sensed by the Hall-effect sensors. A new discrete PID-like controller is proposed and tested. For the step responses with the step sizes within 1000 micrometers, the overshoots and the steady state errors are negligible. The achieved velocity in x is 10.50 cm/s and in y is 16.25 cm/s, respectively. The achieved acceleration in x is 43.75 cm/s^2 and in y is 95.59 cm/s^2, respectively. The achieved travel ranges are 15.24 cm in x, 20.32 cm in y, and 0.21 rad in the rotational motions about the vertical axis. The positioning resolution in x and y is 8 micrometers with the rms positioning error of 6 micrometers. The positioning resolution in rotation about the vertical axis is 130 microrad.
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机译：本文设计并实现了一种多轴紧凑型定位器。单动部分定位器设计用于在由叠加的集中磁场永磁体矩阵产生的磁场中移动。紧凑型定位器主要用于需要3-DOF平面运动的步进和扫描应用。其中，在两个正交方向上的行进范围约为100毫米。活动压板尺寸为185.4毫米x 157.9毫米，重量为0.64千克，主要由一个塑料框架和六个铜线圈组成。通过将六个独立的电流流入线圈，在水平面上将其启动。压板由三个空气轴承支撑以抵抗重力。力计算基于洛伦兹力定律。将载有电流的矩形线圈放置在上施加的Hallbach磁体矩阵的磁场中，通过体积积分计算作用在线圈上的力。矩形线圈的长边之间和短边之间的距离分别设计为适合Hallbach磁体阵列的一半间距和一个间距。因此，大大简化了体积集成。推导出整个带有六个线圈的压板的力-电流关系。三个霍尔效应传感器安装在移动压板上，以测量传感器中心点的磁通密度。活动压板的位置取决于磁体矩阵的磁场解和由霍尔效应传感器感应的磁通量密度。提出并测试了一种新型的离散PID型控制器。对于步长在1000微米以内的步长响应，超调量和稳态误差可以忽略不计。在x中达到的速度为10.50 cm / s，在y中达到的速度为16.25 cm / s。在x中达到的加速度分别为43.75 cm / s ^ 2和在y中达到的95.59 cm / s ^ 2。在绕垂直轴的旋转运动中，达到的行程范围为x的15.24 cm，y的20.32 cm和0.21 rad。 x和y中的定位分辨率为8微米，均方根定位误差为6微米。绕垂直轴旋转的定位分辨率为130微弧度。
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