Auer, Frank

de Vries, Theo J.A.

Holterman, Jan

English

High-precision machines typically suffer from small but persistent vibrations. As it is difficult to damp these vibrations by passive means, research at the Drebbel Institute is aimed at the development of an active structural element that can be used for vibration control. The active structural element, popularly referred to as ‘Smart Disc’, is based on a piezoelectric position actuator and a piezoelectric force sensor.One of the main problems in active control is to ensure stability. In this respect it is often advantageous to consider the use of so-called collocated actuator-sensor-pairs, as this enables to actively implement a passive control law, which is robustly stable, irrespective of structural modeling errors. Within the context of vibration control for lightly damped structures, collocated actuator-sensor-pairs are known to be well-suited to obtain robust active damping [1, 2]

University of Twente Research Information

21st Benelux MeetingonSystems and ControlMarch 19 – 21, 2002Veldhoven, The NetherlandsBook of AbstractsBram de Jager and Hans Zwart (eds.)Book of Abstracts 21st Benelux Meeting on Systems and ControlTechnische Universiteit Eindhoven, Eindhoven, 2002ISBN 90-386-2893-5Decoupling of collocated actuator-sensor-pairsfor active vibration controlJan Holterman, Theo J.A. de VriesDrebbel Institute for Mechatronics, University of TwenteP.O. Box 217, 7500 AE EnschedeThe NetherlandsEmail: j.holterman@utwente.nl, t.j.a.devries@utwente.nlFrank AuerASM LithographyDe Run 1110, 5503 LA VeldhovenThe NetherlandsEmail: frank.auer@asml.com1 IntroductionHigh-precision machines typically suffer from small but per-sistent vibrations. As it is difficult to damp these vibrationsby passive means, research at the Drebbel Institute is aimedat the development of anactive structural elementthat canbe used for vibration control. The active structural element,popularly referred to as ‘Smart Disc’, is based on a piezo-electric position actuator and a piezoelectric force sensor.One of the main problems in active control is to ensure sta-bility. In this respect it is often advantageous to considerthe use of so-calledcollocatedactuator-sensor-pairs, as thisenables to actively implement a passive control law, whichis robustly stable, irrespective of structural modeling errors.Within the context of vibration control for lightly dampedstructures, collocated actuator-sensor-pairs are known to bewell-suited to obtain robust active damping [1, 2].2 Example: wafer stepper lens vibrationsA wafer stepper, i.e., the advanced microlithography systemthat is at the heart of Integrated Circuit manufacturing, isan excellent example of a high-precision machine the per-formance of which is limited by the lack of damping withinthe machine frame. Badly damped vibrations of the lens ofthe wafer stepper limit the attainable line width of the circuitpatterns.The lens of the wafer stepper is conventionally suspendedby means of three (passive) lens support blocks, consti-tuting a kinematically well-designed interface to the so-called metroframe of the wafer stepper. In order to performSmart Disc experiments, the lens support blocks have beenequipped with two piezoelectric stacks, both comprising aposition actuator and a collocated force sensor. Each of theresulting ‘Piezo Active Lens Mounts’ has two perpendicularactive degrees of freedom.By applying collocated control to the individual piezoelec-tric stacks, all six ‘suspension modes’ of the lens can bedamped. Due to the passivity of the control laws, unmod-eled flexible modes of the lens and the metroframe are alsostabilized.3 Collocated control versus modal analysisControl based on collocated actuator-sensor-pairs is inher-ently in terms oflocal coordinates. Vibration problems how-ever are usually analyzed in terms ofmodal coordinates,corresponding to a limited number of vibration modes, ascaptured in a simplified model of the mechanical structure.In terms of the wafer stepper example: we are primarilyinterested in the six suspension modes of the lens. Froma modal analysis point of view, it is therefore desirable tohave six SISO control problems, each one directly related toa single suspension mode. However, due to the symmetryin the set-up, the frequency response functions from a singleactuator to the collocated sensor are all similar. Tuning ofthe local control laws, such that damping for the individualmodes is optimal, is therefore not straightforward.4 Modal control through decouplingThe above-mentioned problem can be solved by realizingthat decoupling of collocated actuator-sensor-pairs, i.e, thetransformation of the original control problem into modalcoordinates, yields control loops that again enable the im-plementation of a passive control law. Stability of ‘decou-pled collocated control’ does not depend on the accuracy ofthe model that has been used for decoupling.This implies that, for the case of the wafer stepper, a simple‘rigid-body’ model may be used for decoupling of the sixcollocated control loops. Obviously, in contrast to stability,theperformanceof active damping based on ‘decoupled col-located control’doesdepend on the accuracy of the model.References[1] S.M. Joshi, “Control of Large Flexible Space Struc-tures”, Lecture Notes in Control and Information Sciences,Vol.131, Springer-Velag, Berlin, Germany, 1989.[2] A. Preumont, “Vibration Control of Active Structures,An Introduction”, Kluwer Academic Publishers, Dordrecht,The Netherlands, 1997.Book of Abstracts 21st Benelux Meeting on Systems and Control66

Decoupling of collocated actuator-sensor-pairs for active vibration control

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Decoupling of collocated actuator-sensor-pairs for active vibration control

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