Haiyue Zhu

Modeling of a Two Degrees-of-Freedom Moving Magnet Linear Motor for Magnetically Levitated Positioners

This paper presents a novel analytical model that accurately predicts the current-force characteristic of a 2 degrees-of-freedom moving magnet linear motor (MMLM), where its translator is formed by a Halbach permanent magnet (PM) array. Unlike existing theoretical models, the uniqueness of this proposed model is based on a derived magnetic field model that accounts for the magnetic flux leakage at the edges of the Halbach PM array. Hence, it can be used to model an MMLM that employs a low-order Halbach PM array effectively. To implement the proposed model in high sampling rate control system, a model-based approximation approach is proposed to simplify the model. The simplified model minimizes the computation complexity while guarantees the accuracy of the current-force prediction. MMLM prototype with two separate translators, i.e., one with a single magnetic pole Halbach PM array and the other with six magnetic poles Halbach PM array, were developed to evaluate the accuracy of the proposed models.

Design and Modeling of a Six-Degree-of-Freedom Magnetically Levitated Positioner Using Square Coils and 1-D Halbach Arrays

This paper presents a novel design of six-degree-of-freedom (6-DOF) magnetically levitated (maglev) positioner, where its translator and stator are implemented by four groups of 1-D Halbach permanent-magnet (PM) arrays and a set of square coils, respectively. By controlling the eight-phase square coil array underneath the Halbach PM arrays, the translator can achieve 6-DOF motion. The merits of the proposed design are mainly threefold. First, this design is potential to deliver unlimited-stroke planar motion with high power efficiency if additional coil switching system is equipped. Second, multiple translators are allowed to operate simultaneously above the same square coil stator. Third, the proposed maglev system is less complex in regard to the commutation law and the phase number of coils. Furthermore, in this paper, an analytical modeling approach is established to accurately predict the Lorentz force generated by the square coil with the 1-D Halbach PM array by considering the corner region, and the proposed modeling approach can be extended easily to apply on other coil designs such as the circular coil, etc. The proposed force model is evaluated experimentally, and the results show that the approach is accurate in both single- and multiple-coil cases. Finally, a prototype of the proposed maglev positioner is fabricated to demonstrate its 6-DOF motion ability. Experimental results show that the root-mean-square error of the implemented maglev prototype is around 50 nm in planar motion, and its velocity can achieve up to 100 mm/s.

Integrated Servo-Mechanical Design of a Fine Stage for a Coarse/Fine Dual-Stage Positioning System

Traditionally, the coarse and fine mechanical stages within a dual-stage positioning system are designed separately without consideration about their control performance in dual-stage integration. In this paper, a flexure-based Lorentz motor fine stage is designed concurrently with a simple PID controller to perform the dual-stage positioning, based on the existing coarse stage. The design of fine stage is carried out using a proposed integrated servo-mechanical design approach, where various specifications are considered and formulated as constraints in an optimization problem. Through the approach, both the plant modal parameters and controller parameters of fine stage are concurrently solved. It demonstrates that through suitable mechanical plant design, the fine stage can fulfill various control specifications by only using a simple PID controller, e.g., to compensate sensitivity peak, maintain stability, etc. Meanwhile, the proposed design approach also ensures certain open-loop positioning performance and the decoupling property of coarse/fine stages. The prototype of designed fine stage is fabricated, and experimental investigation indicates that the sensitivity peak is effectively reduced from 14.5 dB of coarse stage to 7.1 dB in the dual-stage system, and the fine stage is able to achieve submicrometer accuracy. The maximal tracking error is also reduced significantly from about 20 μm via the coarse stage to less than 2 μm through dual-stage positioning.

Principle and Modeling of a Novel Moving Coil Linear-Rotary Electromagnetic Actuator

This paper presents a novel electromagnetic actuator that adopts an air-core coil mover to deliver decoupled linear and rotary motions. It uses light-weight moving coil to achieve high speed and dynamic response, and single-phase Lorentz-force driving scheme to realize direct and noncommutation actuation. To overcome the low thrust force of such driving scheme, unique magnetic circuits are used to enhance the thrust force and torque of the proposed actuator. Closed-form analytical solutions for modeling the magnetic field within the coil operating regions of these unique magnetic circuits are presented together with the complete thermal analyses. A prototype was developed and it delivers 10 mm stroke and 90° angular displacement. Using commercially available drivers, it achieved a high throughput of 8000 units/h with 20 μm, and 0.66° tracking accuracy.

Conceptual design and modeling of a six degrees-of-freedom unlimited stroke magnetically levitated positioner

Magnetic levitation technology is a promising solution to achieve ultra-precision motion. This paper presents a novel conceptual design of a 6 degrees-of-freedom (DOF) magnetically levitated (maglev) planar positioner. The advantages of the proposed maglev positioner includes that, it is able to deliver unlimited planar motion stroke with good power efficiency, allow multi-translators simultaneously above the same stator and also with low system complexity. The proposed design employs four groups of 1D Halbach PM arrays and a set of square coils as the translator and stator, respectively. Furthermore, an analytical modeling approach is proposed to model the Lorenz force of the square coil accurately, which considers the corner area effect of the coil model. By controlling the currents energized in the coils underneath the Halbach PM array, the translator delivers the desired 6-DOF motions. Finally, FEA simulation is conducted to validate the accuracy of the proposed force model, and limited variance is observed.

Motion control of robotic manipulators with disturbance decoupling

A scheme for the decoupling control of robotic manipulators, based on a dynamic model that includes both the mechanical dynamics of the links and the electrical dynamics of the joint motors, is proposed in this paper. The highly nonlinear and strongly cross-coupled electromechanical system is firstly decoupled and linearized into a set of decoupled linear subsystems. Disturbance decoupling is then conducted for disturbance and uncertainty attenuation. The resulting algorithm is so simple that both modelling difficulty and control complexity of the manipulator systems can be reduced significantly.<<ETX>>

Analysis of force harmonics and eddy current damping for 2 DOF moving magnet linear motor

This paper presents the analysis of force harmonics and eddy current damping for 2 DOF moving magnet linear motor (MMLM), which is utilized in magnetically levitated (maglev) positioning systems. A novel current-force model considering higher-order harmonics is proposed for MMLM in this paper, and this model provides an analytical tool to analyze the force ripple effect in MMLM theoretically. A commutation law is derived based on the proposed current-force model, which can ideally eliminate the force ripple in theory. In addition, the eddy current damping effect for a moving Halbach permanent magnet (PM) array on the conductive plate is analytically modeled in this work. By utilizing this model, the damping effect of MMLM can be derived using first principle. Finally, a prototype of MMLM is fabricated and experiment is conducted to implement the proposed commutation law and verify the eddy current damping model.

Modeling and design of a size and mass reduced magnetically levitated planar positioner

Magnetic lévitation technology is a promising solution to achieve ultra-precision motion. This paper presents a design of maglev planar positioner with less size and mass, compared with existing designs. The maglev planar positioner employs four groups of low-order moving magnet linear motors (MMLM) to provide force, and the Halbach PM array in each MMLM contains only one magnetic pole. As a result, the size and mass of the proposed maglev planar positioner is significantly reduced. Due to the inaccuracy of existing force models in predicting such a low-order MMLM, a novel modeling approach is introduced to derive the analytical force model in this paper. Finally, a prototype of this MMLM with one magnetic pole Halbach PM array is developed, and the experiment is conducted to validate the accuracy of the proposed force modeling approach.

Analytical Model-Based Multiphysics Optimization of a Nanopositioning Electromagnetic Actuator

This paper presents the multiphysics optimization of a new class of nanopositioning actuators, termed as flexure-based electromagnetic linear actuator (FELA). The optimization is carried out analytically based on the derived closed-form magnetic field, force, and thermal models, while its objectives include the maximizing of force generation and minimizing of thermal generation, which are both crucial for the nanopositioning actuators. The optimization results show that the new version of FELA achieved 67.3% improvement in force generation for certain current and 46.2% thermal reduction for certain output force, compared to the previous version of FELA with the same size, which was optimized using the numerical methods. The optimization results are also validated by the experiments of the new version FELA prototype, where 56.2% improvement in current–force sensitivity and 43% above reduction in thermal power are demonstrated experimentally. Furthermore, by utilizing the established modeling framework, several fundamental questions on the design of FELA are answered theoretically in this paper, such as the effect about the uniform and radial magnetization of the permanent magnet and the performance tradeoff between the different number of magnet segments.

Robust Control of Robotic Manipulators with Model-Based Precompensation and SMC Postcompensation

Robust and reliable control of robotic manipulators is studied. A model-based precompensation configuration is first used to decouple and linearize the highly complicated electromechanical dynamics of robotic manipulators. Then a linear state-feedback control law is used for closed-loop control. Finally, simplified SMC is adopted to postcompensate for the resulting error dynamics of the closed-loop control system. It is shown that the intentionally introduced control redundancy will not only ensure global high performance for the resulting system, but will also provide the system with built-in high reliability.