Huzefa Shakir

Multi-axis maglev nanopositioner for precision manufacturing and manipulation applications

We present a six-axis magnetic-levitation (maglev) stage capable of precision positioning down to several nanometers. This stage has a simple and compact mechanical structure advantageous to meet the performance requirements in the next-generation nanomanufacturing. It uses the minimum number of linear actuators required to generate all six axis motions. In this paper, we describe the electromechanical design, modeling, and control, and the electronic instrumentation to control this maglev system. The stage has a light moving-part mass of 0.2126 kg. It is capable of generating translation of 300 /spl mu/m in the x, y, and z axes, and rotation of 3 mrad about the three orthogonal axes. The stage demonstrates position resolution better than 5 nm rms and position noise less than 2 nm rms. Experimental results presented in this paper show that the stage can carry, orient, and precisely position a payload as heavy as 0.4 kg. The pull-out force was found to be 8.08 N in the vertical direction. Furthermore, under a load variation of 0.14 N, the nanopositioner recovers its regulated position within 0.6 s. All these experimental results match quite closely with the calculated values because of the accurate plant model and robust controller design. This device can be used as a positioning stage for numerous applications, including photolithography for semiconductor manufacturing, microscopic scanning, fabrication and assembly of nanostructures, and microscale rapid prototyping.

Novel electromagnetic actuation scheme for multiaxis nanopositioning

In this paper, we present a novel electromagnetic actuation scheme for nanoscale positioning with a six-axis magnetic-levitation (Maglev) stage, whose position resolution is 3 nm over an extended travel range of 5x5 mm in the x-y plane. We describe the conceptualization of the actuation scheme, calculation of forces, and their experimental verification in detail. This actuation scheme enables the application of forces in two perpendicular directions on a moving permanent magnet using two stationary current-carrying coils. The magnetic flux generated by the magnet is shared by the two coils, one right below and another on one side of the magnet. The magnitudes and directions of the currents in the coils govern the forces acting on the magnet, following the Lorentz-force law. We analyzed and calculated the electromagnetic forces on the moving magnet over a large travel range. We used feedback linearization to eliminate the force-gap nonlinearity in actuation. The new actuation scheme makes the Maglev stage very simple to manufacture and assemble. Also, there is no mechanical constraint on the single moving platen to remove it from the assembly. There are only three NdFeB magnets used to generate the actuation forces in all six axes. This reduces the moving-part mass significantly, which leads to less power consumption and heat generation in the entire Maglev stage. We present experimental results to demonstrate the payload and precision-positioning capabilities of the Maglev nanopositioner under abruptly and continuously varying loads. The potential applications of this Maglev nanopositioner include microfabrication and assembly, semiconductor manufacturing, nanoscale profiling, and nanoindentation.

Nanoscale Path Planning and Motion Control with Maglev Positioners

This paper addresses nanoscale path planning and motion control, which is essential in nanomanufacturing applications such as microstereolithography (muSTL), dip-pen-nanolithography (DPN), and scanning applications for imaging and manipulation of nanoscale surface phenomena, with the magnetic levitation (maglev) technology. We identified the motion trajectories commonly used in industrial applications along with the challenges in optimal path planning to meet the nanoscale motion-control objectives and achieve precise positioning and maximum throughput simultaneously. The key control parameters in path planning are determined, and control design methodologies, including a well-damped lead-lag controller and an optimal linear quadratic regulator are proposed to satisfy the positioning requirements. The proposed methodologies were implemented individually and collectively. The experimental results are presented in this paper to illustrate their effectiveness in planning optimal trajectories. The damped lead-lag controller exhibited the command overshoot values of as small as 0.37%, and the multivariable LQ controller reduced the dynamic coupling among the axes by 97.1% as compared with the decoupled single-input-single-output (SISO) lead-lag controllers. The position resolution of 5 nm was achieved in x and y with the errors in command tracking as small as 4.5 nm. The maglev stage demonstrated excellent performances for the chosen nanomanufacturing applications in terms of position resolution and accuracy, and speed

Multiscale Control for Nanoprecision Positioning Systems With Large Throughput

A problem of continuing interest in feedback control is handling conflicting time-domain performance specifications. Semiconductor manufacturing is one of the applications of particular interest in this context with the demanding feature sizes (on the order of a few tens of nanometers) to be produced on a wafer while still requiring high throughput (greater than 100 wafers per hour). In this brief, we propose a multiscale control design method based on a reduced-order model-following scheme for the dynamic systems with such conflicting time-domain performance requirements. This method uses a dynamic reference model to make the plant output track the model output as closely as possible without increasing the overall order of the control system. Optimal proportional-integral (PI) control is used, which is essentially a modification of the conventional optimal control. A detailed analytical proof is given to show that this control scheme effectively overcomes the limitations of the conventional optimal control techniques and provides consistent performances at nano- as well as macroscale positioning with fast rise and settling times. Benefits and limitations of the proposed control scheme are described and stability and performance analyses are discussed. A six-degree-of-freedom (6-DOF) extended-range magnetically levitated (maglev) nanopositioning stage, which is open-loop unstable, is used as a test bed to demonstrate the developed control strategy. Step responses under a variety of conditions are obtained to verify the effectiveness of the proposed method. This method exhibits significantly better and robust performances in terms of transient as well as steady-state behavior compared with conventional optimal-control schemes. Furthermore, it can be applied to a general class of higher-order linear time-invariant (LTI) systems with or without open-loop instability.

System Identification and Optimal Control of a 6-DOF Magnetic Levitation Stage With Nanopositioning Capabilities

A systematic procedure for modeling and optimal control of a multivariable 6-DOF (degree-of-freedom) magnetically levitated (maglev) stage has been described in this paper. In our previous publications, we have presented the design, SISO (single-input single-output) control, and testing of the maglev stage with nanometer-precision positioning capability and several-hundred-micrometer travel range. In the present work, we extended the current model to a more rigorous LQR (linear quadratic regulation) controller for the lateral control to reduce the coupling between axes. Independent lead-lag controllers have been used for the vertical control. The system equations have been derived using the Euler angle methodology and linearized about an operating point. The performance of this multivariable control has been analyzed and compared with all the six decoupled SISO controllers. The effect of adding the integrators to eliminate the steady-state error has also been discussed and the performance of the LQR controller with different weight matrices has been compared. In this paper, we also address the issues related to the stochastic modeling of the stage to analyze the coupling between different axes and transfer function identification.Copyright

Nanoscale path planning and motion control

This paper addresses nanoscale path planning and motion control, which is essential in key nanomanufacturing applications such as microstereolithography (/spl mu/STL), dip-pen-nanolithography (DPN), and scanning applications for imaging and manipulation of nanoscale surface phenomena, with the magnetic-levitation (maglev) technology. We identified motion trajectories commonly used in industrial applications along with the challenges in optimal path planning to meet the nanoscale motion-control objectives and achieve precise positioning and maximum throughput simultaneously. Key control parameters in path planning are determined, and control design methodologies including a well-damped lead-lag controller and an optimal linear quadratic regulator are proposed to satisfy the positioning requirements. The proposed methodologies, individually and collectively, were implemented, and experimental results are presented in this paper to illustrate their effectiveness in planning optimal trajectories. The damped lead-lag controller exhibited the command overshoot of as small as 0.37%, and the multivariable LQ controller reduced the dynamic coupling between the axes by 97.1% as compared with the decoupled single-input-single-output (SISO) lead-lag controllers. The position resolution of 5 nm was achieved in x and y with the errors in command tracking as small as 4.5 nm. The maglev stage demonstrated excellent performances for the chosen nanomanufacturing applications in terms of position resolution and accuracy, and speed.

Discrete-Time Closed-Loop Model Identification of Fixed-Structure Unstable Multivariable Systems

This paper presents improved empirical representations of a general class of open-loop unstable systems using closed-loop system identification. A multi-axis magnetic-levitation (maglev) nanopositioning system with an extended translational travel range is used as a test bed to verify the closed-loop system-identification method proposed in this paper. A closed-loop identification technique employing the Box-Jenkins (BJ) method and a known controller structure is developed for model identification and validation. Direct and coupling transfer functions (TFs) are then derived from the experimental input-output time sequences and the knowledge of controller dynamics. A persistently excited signal with a frequency range of [0, 2500] Hz is used as a reference input. An order-reduction algorithm is applied to obtain TFs with predefined orders, which give a close match in the frequency range of interest without missing any significant plant dynamics. The entire analysis is performed in the discrete-time domain in order to avoid any errors due to continuous-to-discrete-time conversion and vice versa. Continuous-time TFs are used only for order-reduction and performance analysis of the identified plant TFs. Experimental results in the time as well as frequency domains verified the accuracy of the plant TFs and demonstrated the effectiveness of the closed-loop identification and order-reduction methods.Copyright

Multiscale Control to Meet the Conflicting Nanoscale Performance Requirements

In this paper, we consider the problem of designing a multiscale control for plants with conflicting time-domain performance requirements. These results follow from the conventional optimal proportional-integral (PI) control. Four different design methods are proposed: (1) a controller-switch technique which makes use of employing two different controllers designed to meet two different performances and are switched during the course of operation, (2) an integral-reset scheme, which resets the integral term in the control law when the new reference point is reached, (3) controller-switch and integral-reset schemes put together to take benefits of both of them, (4) a model-following approach that uses a dynamic reference model without increasing the overall dimension of the system. The objective of the last scheme is to make the output of the plant track the output of the model as closely as possible. Stability analyses and a comparison between the performances of these methods are given. All these methods give better performances as compared with conventional control schemes. Block diagrams are given and step responses are obtained to demonstrate the proposed methods. A six degrees-of-freedom (DOFs) magnetically levitated (maglev) stage with a second-order pure-mass model has been used to demonstrate the capabilities of the aforementioned control strategies. These strategies are not plant-specific and may be generalized to any higher-order plant.Copyright