Planar Motor Research Articles

Performance Optimization with LPV Synthesis for Disturbance Attenuation in Planar Motors

Optimizing the performance of motion control systems with variations in nonlinear parameters is not an easy task. To accomplish this task, it is important to design the controller using the linear system approach. In this study, a linear parameter varying (LPV) control method is proposed in which nonlinearities are treated as parameter variations for planar motors. The proposed control method consists of the force and torque modulation with the commutation scheme and the nonlinear current controller with H∞ state feedback control in the form of LPV synthesis to improve the position-tracking performance. An interpolated gain-scheduling controller based on LPV synthesis is determined by applying H∞ control to a linear matrix inequality technique. An interpolated gain-scheduling controller can attenuate disturbance without disturbance estimation. The effectiveness of the proposed control method is evaluated using simulation results and compared with the conventional proportional–integral–derivative control to verify both improved position-tracking performance and disturbance attenuation.

Electromagnetic Analysis for Axial-Flux Induction Planar Motor Based on Reduced Order Coefficient Matrix

Electromagnetic Analysis for Axial-Flux Induction Planar Motor Based on Reduced Order Coefficient Matrix

Optimization of acceleration and force ripple of planar motor based a chamfered magnet array considering coil end effect

According to the increasing throughput and precision requirements of the wafer stage, this paper proposes a new 2-D magnet array to improve the acceleration and force precision of the planar motor. Firstly, an analytical model of the magnet array with chamfered magnets is established based on the harmonic model, in which the influences of the installation height and the magnetization are included. Then, a modified discrete element model of the runway-type coil is proposed to achieve accurate and efficient force calculation because over half of the force ripple is generated by the coil end, which is neglected in the simplified model. Finally, the influence of chamfered magnet array on the field and force is analyzed. The genetic algorithm is used to optimize the planar motor, which results in a 64% reduction in vertical force tipple and a 1.24 times increase in horizontal acceleration.

A Low-Cost Three-Degree-of-Freedom Position Measurement Method of the Y-type Maglev Planar Motor Based on Hall Sensor

A Low-Cost Three-Degree-of-Freedom Position Measurement Method of the Y-type Maglev Planar Motor Based on Hall Sensor

Nonlinear‐disturbance‐observer‐based predictive control for trajectory tracking of planar motors

AbstractTo improve the trajectory tracking performance of planar motors against disturbances, model predictive position control (MPPC) methods using the non‐linear disturbance observer (NDO) are proposed in this study. Based on the single‐axis dynamic model with disturbances, a single‐axis NDO is designed using an extended state observer approach. The designed NDO is expressed as a third‐order non‐linear state‐space equation in which the position error, velocity error, and lumped disturbance in the single axis are taken as the state variables. Two MPPC methods are developed based on the NDO. In the first MPPC, the disturbance is embedded into the prediction model using the NDO, and a controller is designed to minimise a quadratic cost function, which is established by applying the prediction model with disturbance. The output of the controller is the control action. In the second MPPC, a controller is used to minimise the quadratic cost function, which is built by employing the prediction model without disturbance. The sum of the output of the controller and the compensated disturbance estimated by the NDO is the control action. The comparative experiment is performed on a planar motor system self‐developed in the laboratory. The effectiveness of the proposed methods is verified via the experimental results.

Force and Torque Model of Magnetically Levitated System with 2D Halbach Array and Printed Circuit Board Coils

Precision machining fields often require worktables with different stroke sizes. To address the need for scalability and facilitate manufacturing, this study proposes a novel infinite expansion magnetically levitated planar motor (MLPM) based on PCB stator coils. Different from existing magnetic levitation systems that use PCB coils, the design presented in this paper utilizes smaller coil units, with each coil being independent of one another. The coils are structured in a spiral pattern on a 16-layer PCB, comprising 15 layers of coils, while the last layer is dedicated to wiring and other circuits. Magnetic field modeling is conducted for both the stator coil and the 2D Halbach array structure employed in the system. A simple table lookup method is employed to accurately account for the prevalent end effects observed during system motion. Additionally, the decoupling effect of magnetic force and torque is evaluated by solving for the current vector at different points along a specific trajectory. To verify the accuracy of the proposed system’s modeling, a prototype is developed and tested. Experimental results demonstrate that compared to traditional harmonic model methods, the proposed approach improves the calculation accuracy of magnetic force by 50.31% and torque by 70.65%. This study presents a new MLPM system with vast potential applications in precision manufacturing and robotics. The innovative design and improved performance characteristics make it a promising technology for enhancing the capabilities of worktables in precision machining fields.

Predictor-based model predictive control for maglev planar motor with a 2D Halbach array mover

Magnetic levitated planar motors are widely employed in flexible manufacturing and photolithography due to their characteristics of high precision, high acceleration, and low maintenance. In this paper, a novel predictor-based model predictive control is proposed to improve the tracking performance of a maglev planar motor which consists of a 2D Halbach array mover and stationary square coils. A Kalman filter and finite spectrum assignment based on an augmented system model are employed to forecast mover’s location by compensating for the system delay due to data transmission and processing. The predicted location is fed back to model predictive control for control optimization under the limit of coil currents. Hildreth’s quadratic algorithm is then applied to solve for the optimal control effort within the constraints. Comparative experiments demonstrate the effectiveness of the proposed control strategy, the total tracking error of which is much smaller than the result of a proportional–integral–derivative controller and standard model predictive control in all tests. Additionally, experimental results show that the proposed predictor-based model predictive control can tolerate higher speeds of the mover while retaining mover’s steadiness. The experimental results suggest the proposed predictor-based model predictive control is an effective path-tracking strategy for magnetic levitated planar motors subject to delays.

A Novel Wrench–Current Decoupling Strategy to Extend the Use of Small Lookup Data for a Long-Range Maglev Planar Motor

The maglev planar motor is one of the most promising industrial applications. The planar motor can increase flexibility in modern manufacturing with the multidirectional motion of the mover. In levitation control, the decoupling matrix is used to decouple the strong cross-coupling effect. The Lorentz force-based wrench matrices can be precomputed and stored in the lookup table. However, the motion range is restricted by the data range. This paper presents a wrench–current decoupling strategy to extend the use of small lookup data for long-range planar motion. The horizontal data range is 40 mm by 40 mm, which is determined from the minimally repetitive area of the planar coil array. The quadrant symmetry transformation is used to estimate the data for other areas. The experiment results demonstrated the accomplishment of the developed technique for long-range motion with a maximum motion stroke of 380 mm. The disc-magnet movers can levitate with a large air gap of 30 mm and have a total roll and pitch rotation range of 20 degrees.

Iterative neural network adaptive robust control of a maglev planar motor with uncertainty compensation ability

In this paper, an iterative neural network adaptive robust control (INNARC) strategy is proposed for the maglev planar motor (MLPM) to achieve good tracking performance and uncertainty compensation. The INNARC scheme consists of adaptive robust control (ARC) term and iterative neural network (INN) compensator in a parallel structure. The ARC term founded on the system model realizes the parametric adaptation and promises the closed-loop stability. The INN compensator based on the radial basis function (RBF) neural network is employed to handle the uncertainties resulted from the unmodeled non-linear dynamics in the MLPM. Additionally, the iterative learning update laws are introduced to tune the network parameters and weights of the INN compensator simultaneously, so the approximation accuracy is improved along the system repetition. The stability of the INNARC method is proved via the Lyapunov theory, and the experiments are conducted on an home-made MLPM. The results consistently demonstrate that the INNARC strategy possesses the satisfactory tracking performance and uncertainty compensation, and the proposed INNARC is an effective and systematic intelligent control method for MLPM.

Development of a compensation-aware virtual rehabilitation system for upper extremity rehabilitation in community-dwelling older adults with stroke

BackgroundCompensatory movements are commonly observed in older adults with stroke during upper extremity (UE) motor rehabilitation, which could limit their motor recovery.AimThis study aims to develop a compensation-aware virtual rehabilitation system (VRS) that can detect compensatory movements and improve the outcome of UE rehabilitation in community-dwelling older adults with stroke.MethodsThe VRS development includes three main components: (1) the use of thresholds for determining compensatory movements, (2) the algorithm for processing the kinematic data stream from Kinect to detect compensation in real-time, and (3) the audio-visual feedback to assist older adults with stroke to be aware of the compensation. Two studies were conducted following the VRS development, where Study 1 identified the value of thresholds for determining compensatory movements in two planar motor exercises, and Study 2 provided preliminary validation for the developed VRS by comparing two groups undergoing VR training or conventional training (CT) in a community rehabilitation center.ResultsThe VRS could effectively detect all determined compensatory movements and timely trigger feedback in response to the detected compensatory movements. The VR participants showed significant improvements in Fugl-Meyer Assessment-Upper Extremity (FMA-UE, p = 0.045) and Wolf Motor Function Test (WMFT, p = 0.009). However, the VR and CT groups had no significant differences in outcome measures.ConclusionThe VRS demonstrates the ability to detect compensation and the potential of assisting older adults with stroke to improve motor functions. Suggestions are given for further improvements of the VRS to support the older adult with stroke to reduce compensation.

Integrated optimization of 3D structural topology and 2D Halbach parameters for maglev planar motor

With the increasing demand of mechanical stiffness performance and electromagnetic performance of maglev planar motor, especially the moving-magnet motor with Halbach array, an integrated optimization with 3D structural optimization and magnet parameter optimization is proposed and executed in this paper. The macroscopic electromagnetic performances consisting of thrust-mass ratio and power dissipation are taken as the optimization objective, which improves the performance more directly and comprehensively than traditional optimization methods. A streamlined dual-loop optimization framework is constructed and proved to be able to reduce the computational consumption by tens of times compared to the initial conventional framework, authentically guaranteeing a smooth integrated optimization. At the outer loop of the optimization framework, this paper proposes an oriented strategy for the individuals of Genetic Algorithm (GA) to quickly meet the strict constraints. The integrated optimization method solves the parameter coupling problem between electromagnet and stiffness. Compared to existing optimized structure, the resulting structure improves the thrust-mass ratio by 7.7%, power dissipation by 12.8% and natural frequency by 16.6%, respectively. Mechatronic experimental results in maglev planar motor systems show that the proposed integrated optimization can significantly improve the control bandwidth and reduce the current consumption, laying the foundation for better performance in practical applications.

Design of a trajectory contour controller for a dual‐axis precision motion stage based on improved iterative learning

AbstractTo solve the problem of contour error (CE) arising from the dual‐axis coupling of the X–Y coordinate planar motor stage under reciprocating motion conditions in integrated circuit (IC) manufacturing, the following two perspectives are considered: indirect intervention from a single‐axis servo tracking error (TE) control and direct intervention from a dual‐axis cross‐coupling control (CCC). An improved motion controller is designed using the iterative learning control (ILC) principle in conjunction with the motion characteristics of the dual‐axis mechanism. Specifically, the variable gain iterative learning controller with a variable forgetting factor (VFF‐VGILC) is designed to address the characteristics of single‐axis trajectory repetition and variable velocity planning in dual‐axis coupling. The significance of the VFF‐VGILC is to increase the servo control bandwidth of a single axis. On the other hand, the cross‐coupled iterative learning controller (CCILC) is designed on the dual‐axis cross‐coupling, while a pre‐compensation strategy is introduced in the CCC structure to form the pre‐CCILC. After experimental designing and testing are performed, the X–Y coordinate planar motor stage can effectively reduce the CE under various trajectory movements compared with the traditional controller. The trajectory curves drawn can meet the motion control requirements better and effectively enhance the motion control capability of the mechanism.

Generation Mechanism and Decoupling Strategy of Coupling Effect in Maglev Planar Motor

Magnetically levitated (maglev) planar motor is a promising precision motion system in industry. In order to address the issue of coupling effect in maglev planar motor and achieve satisfying precision motion performance, a novel decoupling strategy based on generation mechanism of coupling effect is proposed in this article. Detailed modeling process is first provided including wrench modeling, coordinates transformation, and control allocation. Further theoretical analysis proves that coupling effect caused by certain factors can be observed by specific phenomena which can be utilized as a criterion for calibration. An effective synthesized decoupling strategy is then proposed. In comparative experimental investigation, the practical phenomena are consistent with the prediction by the proposed theoretical analysis. After applying the proposed decoupling strategy, the tracking errors in the affected axes are enormously reduced and the coupling effect is eliminated to a great extent. Achieved by simply observing specific phenomena, the proposed decoupling method for maglev planar motor is actually a meaningful supplement to existing baseline to further calibrate certain factors that are not considered in previous methods.

Cascaded iterative learning motion control of precision maglev planar motor with experimental investigation

Cascaded iterative learning control (CILC) is explored for a magnetically levitated (maglev) planar motor to achieve excellent tracking motion performance in this paper. The CILC control method is based on traditional iterative learning control (ILC) with deeper iterations. CILC solves the difficulty of ILC in constructing perfect learning filter and low-pass filter to obtain excellent accuracy. Specifically, in CILC, the traditional ILC strategy is implemented several times by the operation of feedforward signal registering and clearing in a cascaded structure, which makes the motion error reach an accuracy level superior to traditional ILC even though the filters are imperfect. The fundamental principle, convergence and stability of CILC strategy are explicitly presented and analyzed. Through the structure of CILC, the repetitive component of the convergence error can be completely eliminated in theory, while the non-repetitive component is accumulated but the sum is bounded. Simulation investigation and comparative experimental investigation on maglev planar motor are both conducted. The results consistently show that the CILC strategy is not only superior to PID and model-based feedforward control, but also obviously outperforms traditional ILC. The CILC investigations on maglev planar motor also provide a clue that CILC has appreciable application prospect for precision/ultra-precision systems requiring extreme motion accuracy.

Design of a Compact Planar Magnetic Levitation System with Wrench–Current Decoupling Enhancement

Magnetic levitation technology has promising applications in modern manufacturing, especially for fine-motion stage and long-range omnidirectional planar motors. This paper presents the development of a compact planar maglev prototype with the potential to achieve both applications to increase flexibility for the manufacturing system. The planar stator is designed by using optimized square coils arranged in the zigzag configuration, which provides a better uniform magnetic flux density compared with another configuration. The stator is a compact and portable module with built-in current amplifier units. The single-disc magnet mover is deployed with five controllable degrees of freedom. The cross-coupling effect is decoupled by a precomputed Lorentz force based wrench—current transformation matrix stored in the lookup table. A 2-D linear interpolation is implemented to enhance decoupling effectiveness which is offered via discrete lookup data. Experiments with motion-tracking cameras and a basic controller demonstrate the results of fine step motion of 10 and 20 µm and rotation steps of 0.5 and 1.0 mrad. The potential for multidirectional material handling is represented by a total horizontal translation range of 20 mm by 20 mm with a maximum air gap of 26 mm and a total rotation range of 20 degrees for both roll and pitch.

Modeling and Control of a Magnetic Levitation Platform

We present two models for a specific class of magnetic levitation system, a type of planar magnetic motor, designed for magnetic levitation of a single permanent magnet using a combination of permanent magnets and electromagnets. The first model is based on established semi-analytical solutions for magnetic fields generated by ideal solenoids, while the second model employs a novel discretization that is well suited for real-time control. Simulations show that the models have comparable accuracy to a standard filament model, but with a reduction in computational time of up to 98 %, for the discretized model. A simulation study demonstrates the models’ applicability for advanced control, using a linear-quadratic regulator (LQR) for stable levitation, and a nonlinear model predictive controller (NMPC) to showcase novel control behavior.

On Improved Commutation for Moving-Magnet Planar Actuators

The demand for high-precision and high-throughput motion control systems has increased significantly in recent years. The use of moving-magnet planar actuators (MMPAs) is gaining popularity due to their advantageous characteristics, such as complete environmental decoupling and reduction of stage mass. Nonetheless, model-based commutation techniques for MMPAs are compromised by misalignment between the mover and coil array and mismatch between the ideal electromagnetic model and the physical system, often leading to decreased system performance. To address this issue, a novel improved commutation approach is proposed in this paper, which is applicable for general planar motor applications, by means of dynamic regulation of the position dependence of the ideal model-based commutation algorithm, which allows for attenuation of magnetic misalignment, manufacturing inaccuracies and other unmodelled phenomena. The effectiveness of the proposed approach is validated through experiments using a state-of-the-art moving-magnet planar actuator prototype.

Robust Precision Position Tracking of Planar Motors Using Min-Max Model Predictive Control

In this article, a min-max model predictive control (MPC) method of planar motors is proposed for the first time to achieve robust precision position tracking, which has a low computational burden and strong capability to deal with the problems of stability, robustness, optimization, and input constraints. A state-space model with a homogeneous state equation is built to describe the dynamics of the time-varying reference trajectory. Combining the state-space model of the reference trajectory and that of the planar motor, an augmented state-space model is established to obtain an error state formulation. Then, using the error state formulation, a min-max optimal control problem subject to the constraints on bounded uncertainty, stability, and control input is developed. Moreover, applying the theory of asymptotically stable invariant ellipsoids and employing the nested invariant ellipsoids, the explicitly linear state-feedback control laws are obtained using a linear-matrix-inequalities based offline control algorithm. Finally, the min-max MPC is applied to a planar motor system developed in the laboratory for an experimentally comparative study. The results demonstrate the effectiveness of the proposed min-max MPC of planar motor for robust precision position tracking applications.

Real-Time Data-Driven Force and Torque Modeling on a 2-D Halbach Array by a Symmetric Coil Considering End Effect

Halbach arrays have been widely implemented in magnetic levitation systems. They concentrate the magnetic field over one side, and their magnetic flux density in the central region can be modeled. This article proposes a novel lookup table-free data-driven method to model the force and torque on a 2-D Halbach array when the magnet array is above a stationary coil. One critical contribution of this article is the rapid and accurate force and torque modeling when the coil is located near the edge of the 2-D magnet array. First, the area under the 2-D Halbach array is divided into a central region, edge regions, and corner regions. Then, nonlinear force and torque components are identified and modeled with a modified third-order Fourier series for force and torque modeling. The proposed model is implemented on an industrial server, and the average computation time is measured to be <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.3 ~\mu \text{s}$ </tex-math></inline-formula> . This model is universal for symmetric coils, verified through experimental measurements with circular and square coils of different sizes. The measurement result agrees well with the proposed modeling method, showing that the proposed method is suitable for real-time control of the ironless planar motor.

Lyapunov-Based Controller Using Nonlinear Observer for Planar Motors

In general, it is not easy work to design controllers and observers for high-order nonlinear systems. Planar motors that are applied to semiconductor wafer-stage processes have 14th-order nonlinear dynamics and require high resolution for position tracking. Thus, many sensors are required to achieve enhanced tracking performance because there are many state variables. To handle these problems, we developed a Lyapunov-based controller to improve the position tracking performance. Consequently, a nonlinear observer (NOB) was also developed to estimate all of the state variables including the position, the velocity, and the phase current using only position feedback. The closed-loop stability is proved through Lyapunov theory and the input-to-state stability (ISS) property. The proposed method was evaluated based on the simulation results and compared with the conventional proportional–integral–derivative (PID) control method to show the improvement in the position tracking performance.