David L. Trumper

Linearizing control of magnetic suspension systems

In many applications, magnetic suspension systems are required to operate over large variations in air gap. As a result, the nonlinearities inherent in most types of suspensions have a significant impact on performance. Specifically, it may be difficult to design a linear controller which gives satisfactory performance, stability, and disturbance rejection over a wide range of operating points. One way to address this problem is through the use of nonlinear control techniques such as feedback linearization. For most common designs of magnetic suspensions the governing equations are in the so-called companion form, lending themselves to feedback linearization. A single degree of freedom magnetic suspension has been designed and constructed in order to compare the performance of linear and nonlinear digital control schemes in a well-controlled experimental environment. We demonstrate the superiority of nonlinear controllers over conventional controllers for systems with large variations in operating point via experiments on our system.

High-precision magnetic levitation stage for photolithography

Abstract In this paper, we present a high-precision magnetic levitation (maglev) stage for photolithography in semiconductor manufacturing. This stage is the world’s first maglev stage that provides fine six-degree-of-freedom motion controls and realizes large (50 mm × 50 mm) planar motions with only a single magnetically levitated moving part. The key element of this stage is a linear motor capable of providing forces in both suspension and translation without contact. The advantage of such a stage is that the mechanical design is far simpler than competing conventional approaches and, thus, promises faster dynamic response and higher mechanical reliability. The stage operates with a positioning noise as low as 5 nm rms in x and y , and acceleration capabilities in excess of 1 g (10 m/s 2 ). We demonstrate the utility of this stage for next-generation photolithography or in other high-precision motion control applications.

Design and analysis framework for linear permanent magnet machines

This paper presents a design and analysis framework for the general class of permanent magnet electric machines. In the analysis, two-dimensional linear or planar motors consisting of permanent magnets and current-carrying coils are treated in a uniform way via the magnetic vector potential. This analysis is developed in order to design novel linear motors for driving precision motion control stages such as those used in wafer steppers. For one such motor structure the authors give analytical formulae for its magnetic field, flux linkage, inductance of the winding, and back electromotive force (EMF). The motor uses a permanent magnet Halbach array in order to improve its power efficiency. By analogy, there also exists an electromagnetic dual of the Halbach array. One such dual utilizes a triangular winding pattern in order to achieve a primarily single-sided magnetic field. The authors also present an efficient magnet matrix for planar surface motors.<<ETX>>

The long-range scanning stage : a novel platform for scanned-probe microscopy

Abstract This paper describes a magnetically suspended six degree-of-freedom precision motion control stage with a horizontal positioning noise of less than 0.6 nm three sigma. The vertical positioning noise is less than 2.2 nm three sigma. The stage utilizes four levitation linear motors to suspend and servo the moving element (platen) throughout its 25 mm × 25 mm × 0.1 mm range of travel. Position feedback is provided by three plane mirror interferometers and three capacitance probes. The suspended platen (12 kg mass) is floated in oil to enhance the stage’s disturbance rejection and to reduce power dissipation in the actuators. The stage has been designed to achieve a positioning accuracy of 10 nm and is used to position samples beneath a scanned probe microscope. The ultimate purpose of this measuring machine is to provide a means of measuring submicron-scale features with nanometer-scale accuracy. The technology can easily be scaled to larger travels, with accuracy limited primarily by the wavelength instability of the HeNe light source. This article gives an overview of the LORS project, emphasizing the system error terms, tolerancing, and experimental results.

Modeling and vector control of a planar magnetic levitator

The authors designed and implemented a magnetically levitated stage with large planar motion capability. This positioning system is the first capable of providing all the motions required for photolithography in semiconductor manufacturing with only a single moving part. This planar magnetic levitator employs four novel permanent-magnet linear motors which generate vertical force for suspension against gravity, and horizontal force for drive. In this paper, the authors discuss electromechanical modeling and real-time vector control of such a permanent-magnet levitator. They describe the dynamics in a DQ frame introduced to decouple the forces acting on the stage. A similar transformation to the Blondel-Park transformation is derived for commutation of the phase currents of the levitator. They provide testing results on step responses of the stage. It shows a 5-nm position noise in x and y, which demonstrates the applicability in the next-generation photolithography.

Magnet arrays for synchronous machines

The authors demonstrate that the Halbach array is highly applicable for magnetic excitation in synchronous machines. To this end, they present the geometry of Halbach arrays in Cartesian, polar, and cylindrical coordinates. They also present the design of a Cartesian linear motor which has been optimized for use in conjunction with a class of high-precision magnetic suspension stages for photolithography. They give analytical solutions for this motors fields, forces, commutation structure, and power dissipation. Results for the power-optimum thickness of the stator windings are obtained. It is suggested that an equivalent Halbach geometry electromagnet may find utility in areas such as magnetically levitated trains.<<ETX>>

Ultrafast Tool Servos for Diamond Turning

Abstract This paper presents the design, implementation and control of a new class of fast tool servos, based on a novel ultrafast motor concept. A prototype ultrafast tool servo with a stroke of 30 |im is described. Experimental results demonstrate that the ultrafast tool servo achieves 23 kHz closed-loop bandwidth, as low as 1.7 nm RMS error, 500 G peak acceleration at 10 kHz open-loop operation, and 2.1 nm (0.04%) error in tracking a 3 kHz sinusoid of 16 |im p-v. A 1 kW linear power amplifier and a 1 MHz sampling rate high-speed real-time computer are designed to drive and control this ultrafast tool servo. A digital controller including loop shaping and adaptive feedforward cancellation is designed to control the tool motion.

Design of a rotary fast tool servo for ophthalmic lens fabrication

Abstract We have developed a novel fast tool servo and associated prototype diamond- turning machine for the production of plastic spectacle lenses. Our fast tool servo carries the cutting tool on a rotary arm and, thus, on a circular path, as opposed to straight line paths in conventional designs. The actuator, sensors, and bearings are standard elements that together allow experimentally demonstrated 500 m/s2 instantaneous accelerations at the tool tip over a 3-cm range of cutting depth. We also describe in this paper new approaches we have developed for toolpath generation and calibration. The paper also presents associated control algorithms, because the controller must supply very high dynamic stiffness to the tool servo axis at multiples of the spindle frequency. This stiffness is achieved by means of repetitive control techniques. The new fast tool servo is shown to have great promise for machining asymmetric surfaces with large amplitude asymmetries.

Design, modeling and fabrication of a constant flow pneumatic micropump

This paper characterizes a bi-directional pneumatic diaphragm micropump and presents a model for performance of an integrated fluidic capacitor. The fluidic capacitor is used to convert pulsatile flow into a nearly continuous flow stream. The pump was fabricated in acrylic using a CNC mill. The stroke volume of the pump is ~1 µL. The pump is self-priming, bubble tolerant and insensitive to changes in head pressure and pneumatic pressure within its operating range. The pump achieves a maximum flow rate of 5 mL min−1 against zero head pressure. With pneumatic pressure set to 40 kPa, the pump can provide flow at 2.6 mL min−1 against a head pressure of 25 kPa. A nonlinear model for the capacitor was developed and compared with experimental results. The ratio of the time constant of the capacitor to the cycle time of the pump is shown to be an accurate indicator of capacitor performance and a useful design tool.

Dynamics and Control of the UNCC/MIT Sub-Atomic Measuring Machine

Abstract This paper reports on the design, modeling, implementation, and experimental results for the control of our Sub-Atomic Measuring Machine (SAMM), which has been jointly developed by UNC-Charlotte and MIT. This machine is intended for measuring features on planar substrates with a work volume of 25 mm × 25 mm × 100 μm, with subatomic resolution. The machine uses four linear motors to control motion in six degrees of freedom and provide magnetic suspension. We derive the commutation law for these linear motors based on a least self-heating condition. We also present modeling of the stage motion in six degrees-of-freedom and our controller design using state-space methods. The experimentally-demonstrated RMS stage positioning noise is 0.12 nm in x , 0.082 nm in y , 1.45 nm in z , 22 nrad in θ x , 18 nrad in θ y , and 2.7 nrad in θ z over a 25 second measurement.