Development of a Quick Performance Assessment Method for Active Vibration Isolation Systems

130 Pages·2015·5.03 MB·English

by  Alper Nizamoglu

Development of a Quick Perfor-
mance Assessment Method for
Active Vibration Isolation Sys-
tems
Focusing on Photo-lithography Applications
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Delft Center for Systems and Control

Development of a Quick Performance
Assessment Method for Active
Vibration Isolation Systems
Focusing on Photo-lithography Applications
Master of Science Thesis
For the degree of Master of Science in Mechanical Engineering at Delft
University of Technology
Alper Nizamoglu
August 17, 2015
Faculty of Mechanical, Maritime and Materials Engineering (3mE) · Delft University of
Technology
The work in this thesis was supported by Carl Zeiss Semi-Manufacturing Technology (SMT)
Gesellschaft mit beschränkter Haftung (GmbH). Their cooperation is hereby gratefully ac-
knowledged.
Copyright (cid:13)c Delft Center for Systems and Control (DCSC)
All rights reserved.
Delft University of Technology
Department of
Delft Center for Systems and Control (DCSC)
The undersigned hereby certify that they have read and recommend to the Faculty of
Mechanical, Maritime and Materials Engineering (3mE) for acceptance a thesis
entitled
Development of a Quick Performance Assessment Method for Active
Vibration Isolation Systems
by
Alper Nizamoglu
in partial fulfillment of the requirements for the degree of
Master of Science Mechanical Engineering
Dated: August 17, 2015
Supervisor(s):
dr.ir. J.W. van Wingerden
dr.ir. S. Dietz
Reader(s):
prof.dr.ir. M. Verhaegen
ir. E. van Solingen

Abstract
The performance of high precision applications highly depend on the ability to reject me-
chanical disturbances. Extreme accuracies can only be achieved if the object can be isolated
from its environment. Vibration isolation is the process of isolating an object from the source
of vibration. In active vibration isolation, an entire instrument of sensors, controllers and
actuators are used to achieve a better performance. Future systems like Extreme Ultra-
Violet (EUV) Lithography are expected to rely more and more on active isolation systems,
which puts new requirements on analysis and simulation methods.
In high precision applications of complex systems high degree of vibration isolation is needed.
In these cases it is required to have a more detailed model of the system, which is usually
done with state of the art Finite Element Modelling (FEM) techniques. However, FEM is
not appropriate when for example the details of the geometry, location of the isolators or
components of the system are not yet known. This typical challenge is to be faced in the
concept design phase of the complex systems like EUV-lithography.
In this thesis, we discuss how to develop a methodology with low fidelity models, where we
can better understand the system and perform quick system assessment techniques to easily
compare various design options. As particular case we derive the 3-Dimensional lumped
elements model of the Active Vibration Isolation System (AVIS), defining the disturbance
inputs in terms of their spectra and quantitatively measuring the performance of the system
by using Cumulative Power Spectrum (CPS) and H norm. Simulation experiments are done
2
to evaluate the performance for different configurations of the system.
Master of Science Thesis Alper Nizamoglu
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Alper Nizamoglu Master of Science Thesis
Table of Contents
Acknowledgements xi
1 Introduction 1
1-1 Photo-lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1-1-1 Developments in Photo-lithography. . . . . . . . . . . . . . . . . . . . . 2
1-2 Vibration Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1-2-1 Passive Vibration Isolation . . . . . . . . . . . . . . . . . . . . . . . . . 5
1-2-2 Active Vibration Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1-3 Motivation and the Goal of the Thesis . . . . . . . . . . . . . . . . . . . . . . . 9
1-4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Effects of Physical Parameters in 2D Isolation Systems 11
2-1 Point Mass Supported by 2 Springs . . . . . . . . . . . . . . . . . . . . . . . . . 12
2-2 2 Dimensional Body Supported by 4 Springs . . . . . . . . . . . . . . . . . . . . 16
2-2-1 Description of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2-2-2 Finding Pre-stress Forces . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2-2-3 Deriving the Stiffness Matrix . . . . . . . . . . . . . . . . . . . . . . . . 19
2-2-4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2-3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3 3D Modeling of the Active Vibration Isolation System 23
3-1 Configuration of the Isolators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3-1-1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3-2 Matrix Equations for Vibration Isolation System . . . . . . . . . . . . . . . . . . 27
3-2-1 Obtaining the State Space Model . . . . . . . . . . . . . . . . . . . . . 29
3-2-2 Effect of Gravity on the Natural Frequencies . . . . . . . . . . . . . . . . 30
3-2-3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Master of Science Thesis Alper Nizamoglu
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3-3 Transmissibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3-4 Active Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3-4-1 Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3-4-2 Sensors and Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3-5 AVIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3-5-1 Controller K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
v
3-5-2 Generalized Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3-5-3 General Control Problem for Analysis of Disturbances . . . . . . . . . . . 44
3-5-4 Illustrative Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3-5-5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3-6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4 Disturbance Modeling 49
4-1 Floor Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4-1-1 Vibration Criteria Curves . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4-1-2 Data Representation in VC Curves . . . . . . . . . . . . . . . . . . . . . 52
4-1-3 Discussion on Modeling Floor Vibration . . . . . . . . . . . . . . . . . . 54
4-2 Sensor Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4-2-1 Testing the Robustness of the Method . . . . . . . . . . . . . . . . . . . 56
4-2-2 Conducting the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . 57
4-2-3 Discussion on Modelling the Sensor Noise . . . . . . . . . . . . . . . . . 58
5 Performance Assessment 61
5-1 Power Spectral Density and Cumulative Power Spectrum . . . . . . . . . . . . . 62
5-1-1 Obtaining PSD of the Output . . . . . . . . . . . . . . . . . . . . . . . 62
5-1-2 Calculating Cumulative Power Spectrum . . . . . . . . . . . . . . . . . . 64
5-1-3 Illustrative Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5-2 H Norm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
2
5-2-1 Stochastic Interpretation of H Norm . . . . . . . . . . . . . . . . . . . 67
2
5-2-2 Illustrative Example 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5-2-3 Illustrative Example 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5-2-4 Spectral Decomposition and PSSSID . . . . . . . . . . . . . . . . . . . . 72
5-3 Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5-4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6 Conclusion 81
6-1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6-2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 82
A A1 85
A-1 Deriving the Equations of Motion for 3D Rigid Body . . . . . . . . . . . . . . . 85
Alper Nizamoglu Master of Science Thesis