Huzefa Shakir

Doctoral Candidate

Precision Mechatronics and Nanotechnology Lab

Mechanical Engineering Department

Texas A&M University

IEEE Transactions on Control System Design

Abstract —A problem of continuing interest in feedback control is handling the conflicting time-domain performance specifications. Semiconductor manufacturing is one of the applications of particular interest in this context with the demanding feature sizes to be produced on the wafer (on the order of few tens of nanometers) while still requiring high throughput (greater than 100 wafers per hour). In this paper, we propose a multiscale-control design method based on 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. A proportional-integral control is used, which is essentially a modification of the conventional optimal control. A detailed analytical proof of given to show that this control scheme effectively overcomes the limitations of the conventional optimal control techniques and provide consistent performances at nano- as well as macro-scale 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 developed the control strategy. Step responses under a variety of conditions are obtained to verify the effectiveness of the proposed method. This method exhibited 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 and is not just limited to a specific positioning system.

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IEEE/ASME Trans on Mechatronics

Abstract — This paper addresses nanoscale path planning and motion control, which is essential in nanomanufacturing applications such as microstereolithography (μSTL), 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.

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Precision Engineering

Abstract — This paper presents two novel 6-axis magnetic-levitation (maglev) stages capable of nanoscale positioning. These stages have very simple and compact structures, which is advantageous to meet the demanding positioning requirements of the next-generation nano-manipulation and nano-manufacturing. Six-axis motion generation is accomplished by the minimum number of actuators and sensors. The first-generation maglev stage, namely the D -stage, is capable of generating translation of 300 m m and demonstrates position resolution better than 2 nm rms (root-mean-square). The second-generation maglev stage, namely the Y-stage, is capable of positioning at a resolution better than 3 nm rms over a planar travel range of 5 × 5 mm. A novel actuation scheme was developed for the compact structure of this stage that enables 6-axis force generation with just 3 permanent-magnet pieces. This paper focuses on the design and precision construction of the actuator units, the moving platens, and the stationary base plates. The performance of the two precision positioners is compared in terms of their positioning and load-carrying capabilities and ease of manufacture. The superiority of the developed instruments is also demonstrated over other prevailing precision positioning systems in terms of the travel range, resolution, and dynamic range. The potential applications of the maglev positioners include semiconductor manufacturing, micro-fabrication and assembly, nanoscale profiling, and nano-indentation. 

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IEEE Transactions on Magnetics

Abstract — In this paper we present a novel electromagnetic actuation scheme developed for nanoscale positioning with a 6-axis magnetic-levitation (maglev) stage, whose position resolution is 3 nm over an extended travel range of 5 × 5 mm in the x-y plane. The conceptualization of the actuation scheme, calculation of forces, and their experimental verification are described in detail. This actuation scheme presented herein 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. Feedback linearization is applied to eliminate the force-gap nonlinearity in actuation. This new actuation scheme makes the mechanical design of 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 3 NdFeB magnets used to generate the actuation forces in all 6 axes. This reduces the moving-part mass significantly, which leads to less power consumption and heat generation in the entire maglev stage. Several experimental results are presented 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 nano-indentation.

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IEEE Industry Application Society

Abstract — We present a 6-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 6-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 0.212 kg. It is capable of generating translation of 300 μm 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 nano-structures, and microscale rapid prototyping.

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ASME International Mechanical Engineering Congress and Exposition 2005 [1]

Abstract — 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.

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ASME International Mechanical Engineering Congress and Exposition 2005 [2]

Abstract — This paper presents a novel multi-axis positioner that operates on the magnetic-levitation (maglev) principle. This maglev stage is capable of positioning at the resolution of a few nanometers over a planar travel range of several millimeters. A novel actuation scheme was developed for the compact design of this stage that enables 6-axis force generation with just 3 permanent magnets. We calculated the forces with electromagnetic analysis over the whole travel range and experimentally verified them with a unit actuator. The single moving part, namely the platen, is modeled as a pure mass due to the negligible effect of magnetic spring and damping. There are 3 laser interferometers and 3 capacitance sensors to sense the 6-axis position/rotation of the platen. A lead-lag compensator was designed and implemented to control each axis. A nonlinear model of the force was developed by electromagnetic analysis, and feedback linearization was applied to cancel the nonlinearity of the actuators over the large travel range. Various experiments were conducted to test positioning, loading, and vibration-isolation capabilities. This maglev stage has a moving mass of 0.267 kg. Its position resolution is 4 nm over a travel range of 5 × 5 mm in the x-y plane. It can carry and precisely position an additional payload of 2 kg. Its potential applications include semiconductor manufacturing, micro-fabrication and assembly, nanoscale profiling, and nano-indentation.

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American Control Conference 2005

Abstract — This paper addresses nanoscale path planning and motion control, which is essential in key nanomanufacturing applications such as microstereolithography (μSTL), 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.

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ASME International Mechanical Engineering Congress and Exposition 2004

Abstract — 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.

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IEEE Industry Application Society 39th Annual Meeting 2004

Abstract — We present a 6-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 6-axis motions. Three vertical actuators are used to levitate the moving part, namely the platen, and maintain its vertical position. Other three horizontal actuators control its position and rotation in the horizontal plane. In this paper, we describe the electromechanical design, modeling and control, and the electronic instrumentation to control this maglev system. We modeled the platen as a pure mass due to negligible spring and damping forces while it is levitated without contact. The stage has a light moving-part mass of 0.2126 kg. It is capable of generating translation of 300 μm 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. The total power consumption by all the actuators is only a fraction of a watt. Experimental results presented in this paper show that the stage can carry, orient, and precisely position a payload as heavy as 0.3 kg. The pull-out force was found to be 8.08 N in the vertical direction. Furthermore, under the effect of a load variation of 0.14 N, the plant 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 of delicate instruments, fabrication and assembly of nano-structures, and microscale rapid prototyping.

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TEX-MEMS VI Meeting 2004

Abstract — We developed a compact 6-DOF (degree of freedom) maglev stage that levitates a platen of 0.212 kg and has nanopositioning capability over the linear travel range of 300 mm. A controller was designed and implemented to stabilize the platen. The decoupling between the vertical and horizontal actuation forces was considered and taken care into controller. Various kinds of experiments were carried out to test the capabilities of the system. The experimental results show that the maglev device has a position resolution of better than 2 nm with a maximum velocity of 1 m/s and an acceleration of 30 m/s2. This positioner can carry an additional payload of 400 g to orient and position the object under nanopositioning precisely. The nominal power consumption is only 15 mW by each horizontal actuator, and 320 mW by each vertical actuator. The potential applications of this maglev device include fabrication of nanoparts and their assembly, vibration isolation for delicate instrumentation, and microscale stereolithography.

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