Universal Framework for Linear Motors and Multi-Axis Stages with Magnetic Levitation

This dissertation presents the electromagnetic design and experimental validation of a new framework for linear permanent-magnet (PM) machines with targeted applications in precision motion control. In this framework, a single forcer, which can generate two independent force components in two perpendicular directions, consists of a stationary Halbach magnet array and two Lorentz coils with a phase difference of 90° or 270°. Any number of coil pairs can be attached on the same moving frame to work with a common magnet array or matrix, forming a linear or planar PM motor. Key advantages of this framework are simple force calculation, a linear system model, and a reduced number of coils for force generation and allocation in multi-axis positioners. The proposed framework effectively allows for decoupled dynamics, simplifying the linear controller design and real-time implementation. To experimentally verify the theoretical framework proposed herein, a high-precision 6-axis magnetically levitated (maglev) stage is designed, constructed, and controlled. The development of this 6-axis positioning system is an integrated work, including magnetic-force calculation and analysis, mechanical design, fabrication, assembly, system modeling, system identification, and control system design. The mechanical components of the system include a stationary superimposed Halbach magnet matrix, which was previously built, and a moving platen with a plastic frame, four sets of 2-phase coils, and two precision mirrors. For position measurements, there are three laser interferometers for in-plane position measurements, three laser displacement sensors for out-of-plane position sensing, and two 2-channel Hall-effect sensors for the position feedback to initialize the position and expand the travel ranges of the platen in the XY plane. The positioning resolutions of 10 nm in the xy plane and in the vertical axis are demonstrated. In out-of-plane rotation about the two horizontal axes, experimental results show the unprecedented positioning resolution of 0.1 μrad. The maximum travel range in X and Y with nanoscale positioning resolution is 56 mm × 35 mm, limited by the lengths of the precision mirrors attached to the platen. With the trapezoidal-velocity input shaping, achieved performance specifications include the maximum acceleration and velocity of 0.6 m/s2 and 0.06 m/s, respectively, in translations in the horizontal plane. With the platen supported by the air bearings, the maximum acceleration and speed are 1.5 m/s2 and 0.15 m/s, respectively. A load test is performed with the platen carrying a load of 0.54 kg, which is 72% of its total mass, magnetically levitated in 6- axis closed-loop control. Experimental results show the reduced coupled dynamics between different axes in magnetic levitation. This framework of 2-phase Lorentz coils and linear Halbach arrays is highly applicable in precision-positioning linear motors and multi-axis stages, steppers, scanners, nano-scale manipulation and alignment systems, and vibration isolators

Design and Control of a Compact 6-Degree-of-Freedom Precision Positioner with Linux- Based Real-Time Control

This dissertation presents the design, control, and implementation of a compact highprecision multidimensional positioner. This precision-positioning system consists of a novel concentrated-field magnet matrix and a triangular single-moving part that carries three 3-phase permanent-magnet planar-levitation-motor armatures. Since only a single levitated moving part, namely the platen, generates all required fine and coarse motions, this positioning system is reliable and potentially cost-effective. The three planar levitation motors based on the Lorentz-force law not only produce the vertical force to levitate the triangular platen but also control the platen's position and orientation in the horizontal plane. Three laser distance sensors are used to measure vertical, x-, and yrotation motions. Three 2-axis Hall-effect sensors are used to determine lateral motions and rotation motion about the z-axis by measuring the magnetic flux density generated by the magnet matrix. This positioning system has a total mass of 1.52 kg, which is the minimized mass to produce better dynamic performance. In order to reduce the mass of the moving platen, it is made of Delrin with a mass density of 1.54 g/cm3 by Computer Numerical Controlled (CNC) machining. The platen can be regarded a pure mass, and the spring and damping effects are neglected except for the vertical dynamic. Single-input single-output (SISO) digital lead-lag controllers and a multivariable Linear Quadratic Gaussian (LQG) controller were designed and implemented. Real-time control was performed with the Linux-Ubuntu operating system OS. Real Time Application Interface (RTAI) for Linux works with Comedi and Comedi libraries and enables closed-loop real-time control. One of the key advantages of this positioning stage with Hall-effect sensors is the extended travel range and rotation angle in the horizontal mode. The maximum travel ranges of 220 mm in x and 200 mm in y were achieved experimentally. Since the magnet matrix generates periodical sinusoidal flux densities in the x-y plane, the travel range can be extended by increasing the number of magnet pitches. The rotation angle of 12 degrees was achieved in rotation around z. The angular velocities of 0.2094 rad/s and 4.74 rad/s were produced by a 200-mm-diameter circular motion and a 30-mm-diameter spiral motion, respectively. The maximum velocity of 16.25 mm/s was acquired from over one pitch motion. The maximum velocity of 17.5 mm/s in a 8-mm scanning motion was achieved with the acceleration of 72.4 m/s2. Step responses demonstrated a 10-um resolution and 6-um rms position noise in the translational mode. For the vertical mode, step responses of 5 um in z, 0.001 degrees in roation around x, and 0.001 degrees in rotation around y were achieved. This compact single-moving-part positioner has potential applications for precisionpositioning systems in semiconductor- manufacturing

Control and Optimization of a Compact 6-Degree-of-Freedom Precision Positioner Using Combined Digital Filtering Techniques

This thesis presents the multivariable controller design and implementation for a high-precision 6-degree-of-freedom (6-DOF) magnetically levitated (maglev) positioner. The positioner is a triangular single-moving part that carries three 3-phase permanent-magnet linear-levitation-motor armatures. The three planar levitation motors not only generate the vertical force to levitate the triangular platen but control the platen's position in the horizontal plane. All 6-DOF motions are controlled by magnetic forces only. The positioner moves over a Halbach magnet matrix using three sets of two-axis Hall-effect sensors to measure the planar motion and three Nanogage laser distance sensors for the vertical motion. However, the Hall-effect sensors and the Nanogage laser distance sensors can only provide measurements of the displacement of all 6-axis. Since we do not have full-state feedback, I designed two Linear Quadratic Gaussian (LQG) multivariable controllers using a recursive discrete-time observer. A discrete hybrid H2/H(infinity) filter is implemented to obtain optimal estimates of position and orientation, as well as additional estimates of velocity and angular velocity for all 6 axes. In addition, an analysis was done on the signals measured by the Hall-effect sensors, and from there several digital filters were tested to optimize the readings of the sensors and obtain the best estimates possible. One of the multivariable controllers was designed to close the control loop for the three-planar-DOF motion, and the other to close the loop for the vertical motion, all at a sampling frequency of 800 Hz. Experimental results show a position resolution of 1.5 micrometers with position noise of 0.545 micrometers rms in the x-and y-directions and a resolution of less than 110 nm with position noise of 49.3 nm rms in z

Hochpräziser Mehrkoordinatenantrieb mit repulsiver Magnetführung

Viele moderne Applikationen, z.B. aus der Biotechnologie oder der Halbleiterindustrie, benötigen Mehrkoordinatenantriebe, die Positioniergenauigkeiten im Nanometerbereich und große planare Bewegungsbereiche besitzen. Zudem müssen die zum Einsatz kommenden Systeme auch vakuumtauglich sein. Um diese hohen Anforderungen zu erfüllen, werden magnetisch geführte Mehrkoordinatenantriebe untersucht und entwickelt. Das Ziel der vorliegenden Arbeit besteht darin, einen neuartigen magnetisch geführten Mehrkoordinatenantrieb mit einem großen Fahrbereich zu entwickeln. Im Vergleich zu anderen, aus der Literatur bekannten Lösungen zeichnet sich das vorgeschlagene Konzept durch eine wesentlich vereinfachte kompakte Konstruktion, entkoppelte Antriebsund Führungskräfte und einen von oben frei zugänglichen passiven Läufer aus. Ein wesentlicher Schwerpunkt der Arbeit ist die semi-analytische Kraftberechnung der eingesetzten Aktoren. Die Ergebnisse der hergeleiteten Kraftgleichungen werden den numerischen 3D-FEM und den experimentellen Ergebnissen gegenübergestellt. Zwischen den Ergebnissen der hergeleiteten Kraftgleichungen und den numerisch ermittelten Kräften zeigt sich ein maximaler Fehler von 1 %. Zwischen den Berechnungen und den Messungen ergibt sich ein maximaler Fehler von 5 %. Da der Funktionsnachweis des vorgeschlagenen Konzepts im Vordergrund steht, ist ein Funktionsmuster mit einem Bewegungsbereich von 50 × 50 × 2 mm^3 aufgebaut und in Betrieb genommen worden. Für die Regelung des Systems ist ein Zustandsregler mit integrierender Rückführung implementiert. Erste experimentelle Messungen zeigen, dass das System stabilisiert und der Läufer in den sechs Bewegungsfreiheiten positioniert werden kann. Dabei besitzt das Positionsrauschen in den Koordinaten x, y und z eine Standardabweichung von σx = 193 µm, σy = 178 µm und σz = 8.2 µm und liegt damit im Bereich der Messsystemauflösung.Fields, such as biotechnology and the semiconductor industry, require positioning systems that can offer high precision in the nanometer range in combination with long motion regions. Furthermore the positioning systems should also be vacuum compatible. In order to satisfy these demands, magnetically guided multi-coordinate drives have been investigated and developed. This dissertation seeks to develop a new magnetically guided multi-coordinate drive with an extended range of movement. In comparison with other solutions, this system has a significantly simplified and, more compact structure, decoupled levitation and propulsion forces, and free access to the passive rotor from above. This dissertation focuses on the semi-analytical force calculation of the applied actuators. The results from the derived force equations are compared with the numerical 3D-FEM simulation and the experimental results. The results of the force calculation and the numerical 3D-FEM simulation yield a maximum error of 1 %, while between the force calculations and the measured forces the maximum error is 5 %. The objective of this thesis is to demonstrate the functionality of the proposed system. Thus, a prototype with a movement area of 50×50×2 mm^3 has been built and is operational. A state-space controller with integrated feedback is implemented in order to control the system. Initial experimental measurements show that the system can be stabilized and the rotor can be positioned in six degrees-of-freedom. The position noise in the coordinates x, y and z has standard deviations of σx = 193 µm, σy = 178 µm and σz = 8.2 µm and is thus within the resolution range of the measurement device

Design and Analysis of Long-Stroke Planar Switched Reluctance Motor for Positioning Applications

This paper presents the design, control, and experimental performance evaluation of a long-stroke planar switched reluctance motor (PSRM) for positioning applications. Based on comprehensive consideration of the electromagnetic and mechanical characteristics of the PSRM, a motor design is first developed to reduce the force ripple and deformation. A control scheme with LuGre friction compensation is then proposed to improve the positioning accuracy of the PSRM. Furthermore, this control scheme is proven to ensure the stable motion of the PSRM system. Additionally, the response speed and steady-state error of the PSRM system with this control scheme are theoretically analyzed. Finally, the experimental results are presented and analyzed. The effectiveness of the precision long-stroke motion of the PSRM and its promise for use in precision positioning applications are verified experimentally

Cooperative Manipulation using a Magnetically Navigated Microrobot and a Micromanipulator

The cooperative manipulation of a common object using two or more manipulators is a popular research field in both industry and institutions. Different types of manipulators are used in cooperative manipulation for carrying heavy loads and delicate operations. Their applications range from macro to micro. In this thesis, we are interested in the development of a novel cooperative manipulator for manipulation tasks in a small workspace. The resultant cooperative manipulation system consists of a magnetically navigated microrobot (MNM) and a motorized micromanipulator (MM). The MNM is a small cylinder permanent magnet with 10mm diameter and 10mm height. The MM model is MP-285 which is a commercialized product. Here, the MNM is remotely controlled by an external magnetic field. The property of non-contact manipulation makes it a suitable choice for manipulation in a confined space. The cooperative manipulation system in this thesis used a master/slave mechanism as the central control strategy. The MM is the master side. The MNM is the slave side. During the manipulation process, the master manipulator MM is always position controlled, and it leads the object translation according to the kinematic constraints of the cooperative manipulation task. The MNM is position controlled at the beginning of the manipulation. In the translation stage, the MNM is switched to force control to maintain a successful holding of the object, and at the same time to prevent damaging the object by large holding force. Under the force control mode, the motion command to the MNM is calculated from a position-based impedance controller that enforces a relationship between the position of the MNM and the force. In this research, the accurate motion control of both manipulators are firstly studied before the cooperative manipulation is conducted. For the magnetic navigation system, the magnetic field in its workspace is modeled using an experimental measurement data-driven technique. The developed model is then used to develop a motion controller for navigating of a small cylindrical permanent magnet. The accuracy of motion control is reached at 20 µm in three degrees of freedom. For the motorized micromanipulator, a standard PID controller is designed to control its motion stage. The accuracy of the MM navigation is 0.8 µm. Since the MNM is remotely manipulated by an external magnetic field in a small space, it is challenging to install an on-board force sensor to measure the contact force between the MNM and the object. Therefore, a dual-axial o_-board force determination mechanism is proposed. The force is determined according to the linear relation between the minimum magnetic potential energy point and the real position of the MNM in the workspace. For convenience, the minimum magnetic potential energy point is defined as the Bmax in the literature. In this thesis, the dual-axial Bmax position is determined by measuring the magnetic ux density passing through the workspace using four Hall-effect sensors installed at the bottom of an iron pole-piece. The force model is experimentally validated in a horizontal plane with an accuracy of 2 µN in the x- and y- direction of horizontal planes. The proposed cooperative manipulator is then used to translate a hard-shell small object in two directions of a vertical plane, while one direction is constrained with a desired holding force. During the manipulation process, a digital camera is used to capture the real-time position of the MNM, the MM end-effector, and the manipulated object. To improve the performance of force control on the MNM, the proposed dual-axial force model is used to examine the compliant force control of the MNM while it is navigated to contact with uncertain environments. Here, uncertain refers to unknown environmental stiffness. An adaptive position-based impedance controller is implemented to estimate the stiffness of the environment and the contact force. The controller is examined by navigating the MNM to push a thin aluminum beam whose stiffness is unknown. The studied cooperative manipulation system has potential applications in biomedical microsurgery and microinjection. It should be clarified that the current system setup with 10mm ×10 mm MNM is not proper for this micromanipulation. In order to conduct research on microinjection, the size of the MNM and the end-effector of the MNM should be down-scaled to micrometers. In addition, the navigation accuracy of the MNM should also be improved to adopt the micromanipulation tasks

Design and control of a 6-Degree-of-Freedom levitated positioner with high precision

This dissertation presents a high-precision positioner with a novel superimposed concentrated-field permanent-magnet matrix. This extended-range multi-axis positioner can generate all 6-DOF (degree-of-freedom) motions with only a single moving part. It is actuated by three planar levitation motors, which are attached on the bottom of the moving part. Three aerostatic bearings are used to provide the suspension force against the gravity for the system. The dynamic model of the system is developed and analyzed. And several control techniques including SISO (single input and single output) and MIMO (multi inputs and multi outputs) controls are discussed in the dissertation. The positioner demonstrates a position resolution of 20 nm and position noise of 10 nm rms in x and y and 15 nm rms in z. The angular resolution around the x-, y-, and z-axes is in sub-microradian order. The planar travel range is 160 mm ?? 160 mm, and the maximum velocity achieved is 0.5 m/s at a 5-m/s2 acceleration, which can enhance the throughput in precision manufacturing. Various experimental results are presented in this dissertation to demonstrate the positioner??s capability of accurately tracking any planar trajectories. Those experimental results verified the potential utility of this 6-DOF high-precision positioner in precision manufacturing and factory automation

Positioning Control System for a Large Range 2D Platform with Submicrometre Accuracy for Metrological and Manufacturing Applications

The importance of nanotechnology in the world of Science and Technology has rapidly increased over recent decades, demanding positioning systems capable of providing accurate positioning in large working ranges. In this line of research, a nanopositioning platform, the NanoPla, has been developed at the University of Zaragoza. The NanoPla has a large working range of 50 mm × 50 mm and submicrometre accuracy. The NanoPla actuators are four Halbach linear motors and it implements planar motion. In addition, a 2D plane mirror laser interferometer system works as positioning sensor. One of the targets of the NanoPla is to implement commercial devices when possible. Therefore, a commercial control hardware designed for generic three phase motors has been selected to control and drive the Halbach linear motors.This thesis develops 2D positioning control strategy for large range accurate positioning systems and implements it in the NanoPla. The developed control system coordinates the performance of the four Halbach linear motors and integrates the 2D laser system positioning feedback. In order to improve the positioning accuracy, a self calibration procedure for the characterisation of the geometrical errors of the 2D laser system is proposed. The contributors to the final NanoPla positioning errors are analysed and the final positioning uncertainty (k=2) of the 2D control system is calculated to be ±0.5 µm. The resultant uncertainty is much lower than the NanoPla required positioning accuracy, broadening its applicability scope.<br /

Multi-DOF precision positioning methodology using two-axis Hall-effect sensors

A novel sensing methodology using two-axis Hall-effect sensors is proposed, where the absolute positioning of a device atop any magnet matrix is possible. This methodology has the capability of micrometer-order positioning resolution as well as unrestricted translational and rotational range in planar 3-DOF (degree-of-freedom) motions, with potential capability of measuring all 6-DOF motions. This research presents the methodology and preliminary experimental results of 3-DOF planar motion measurements atop a Halbach magnet matrix using two sets of two-axis Hall-effect sensors. Analysis of the Halbach magnet matrix is presented to understand the generated magnetic field. The algorithm uses the Gaussian least squares differential correction (GLSDC) algorithm to estimate the relative position and orientation from the Hall-effect sensor measurements. A recursive discrete-time Kalman filter (DKF) is used in combination with the GLSDC to obtain optimal estimates of position and orientation, as well as additional estimates of velocity and angular velocity, which we can use to design a multivariable controller. The sensor and its algorithm is implemented to a magnetic levitation (maglev) stage positioned atop a Halbach magnet matrix. Preliminary experimental results show its position resolution capability of less than 10 µm and capable of sensing large rotations. Controllers were designed to close the control loop for the three planar degrees of freedom motion using the GLSDC outputs at a sampling frequency of 800 Hz on a Pentek 4284 digital signal processor (DSP). Calibration was done by comparing the laser interferometers and the GLSDCÂs outputs to improve the positioning accuracy