Xtreme motion : control of non-rigid body dynamics of a high
precision positioning stage
Citation for published version (APA):
Hoogendijk, R. (2010). Xtreme motion : control of non-rigid body dynamics of a high precision positioning stage. In H. Stigter, & G. Meinsma (Eds.), Book of abstracts of the 29th Benelux Meeting on Systems and Control, March 30 - April 1, 2010, Heeze, The Netherlands (pp. 156-156). Wageningen University.
Document status and date: Published: 01/01/2010 Document Version:
Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website.
• The final author version and the galley proof are versions of the publication after peer review.
• The final published version features the final layout of the paper including the volume, issue and page numbers.
Link to publication
General rights
Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain
• You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement:
www.tue.nl/taverne
Take down policy
If you believe that this document breaches copyright please contact us at:
openaccess@tue.nl
providing details and we will investigate your claim.
Xtreme Motion: Control of non-rigid body dynamics of a high
precision positioning stage
R. Hoogendijk
Eindhoven University of Technology, Whoog -1.126
r.hoogendijk@tue.nl
Introduction
The trend in the semi-conductor industry is still prescribed by Moore’s law which states that the resolution of chips will increase while the costs per functionality will decrease. To comply with this law, positioning systems of lithography machines need to become faster and more accurate. To make the system faster, higher accelerations are required. New-ton’s Laws prescribe that this can either be done by apply-ing higher forces, or by reducapply-ing the weight of the system. The first option is less favorable, since stronger actuators consume more power and produce more heat, which dete-riorates the performance of the system. An alternative to increase productivity of lithography machines is to increase the standard wafer diameter from the current 300 mm to 450 mm. But, both larger and lighter stages will be more flexi-ble, which can interfere with the accuracy of the positioning system. This motivates research on the control of high pre-cision flexible motion stages. This abstract discusses some of the challenges that will be faced in this research area.
1 Conventional controllers
Currently, most high precision motion systems are con-trolled using geometric decoupling and single-input-single-output (SISO) controllers. Assume that the goal of the con-troller is to achieve good performance at a certain point on the system, denoted by z. The measurement of the position of the system y is typically not performed at the location z, but since it is assumed that the system is rigid, a simple geometric transformation can be used to compute z from y. Moreover, by using geometric decoupling, it is even possi-ble to compute z for all axes in the system separately.
2 Control of flexible motion stages
The approach of the previous section cannot be followed if the system is not rigid, but flexible. In flexible systems the performance z and the measurement y are no longer related via a static, but a dynamic relation. The control problem is visualized clearly by the standard plant formulation, as de-picted in Figure 1. It shows that y= z. The derivation of a control signal to get performance at z using an input u based on a measurement y will be topic of research. Different con-trol strategies such as inferential concon-trol modal concon-trol, H∞ control will be investigated.
P
C
w
u
y
z
Figure 1:Standard plant system representation. The plant P is controlled with controller C, by applying an input u based on a measurement y. Note that the disturbances
w and performance z are different from u and y.
Conventionally, there will be as much actuators in the sys-tem as there are rigid body modes. But the extra dynam-ics in the system will probably require more actuators than rigid body modes to suppress the internal dynamics. In this research, it will be studied, whether extra actuators can be used to improve the performance of the system. When the number of actuators is larger than the number of rigid body modes, the terminology overactuated or non-rigid body con-trol is used.
The term performance has been mentioned a few times now, but presently it is even not clear yet what the performance needs to be for this system. This also depends on the chosen strategy. One approach could be to damp all internal dy-namics. This would give a spatially distributed performance specification. An other approach could be to position the point of interest very accurately while the rest of the sys-tem is allowed to be in motion. This leads to a performance specification at a certain point on the geometry.
3 Conclusion
A few issues regarding the control of flexible high precision motion stages have been discussed. The key feature of these systems is that the control can no longer be done with de-coupling and SISO controllers. The spatial distribution of the system and its internal dynamics have to be taken into account when the system is flexible.
Book of Abstracts 29th Benelux Meeting on Systems and Control
