Optical Instrumentation Division Stieltjesweg 1 P.O. Box 155 2600 AD DELFT The Netherlands
TNO report DOI-report-030023
APS test bench - control loop
Date
June 16, 2003
Author(s)
N.S. Millet
Copy no No. of copies Number of pages Number of appendices Sponsor Project name Project number
90 VOSTEEN L.L.A. APS - TI-KENNISCENTRUM AP-nulling 008.02528/01.06
All rights reserved. No part of this publication may be reproduced and/or published by print, photoprint, microfilm or any other means without the previous written consent of TNO. In case this report was drafted on instructions, the rights and obligations of contracting parties are subject to either the Standard Conditions for Research Instructions given to TNO, or the relevant agreement concluded between the contracting parties. Submitting the report for inspection to parties who have a direct interest is permitted. © 2003 TNO
www.tno.nl T +31 15 269 2000 F +31 15 269 2111
TNO report | DOI-report-030023 | 1.0 | APS test bench - control loop
Summary Introduction of a control loop in the APS breadboard to enhance the stability of the OPD between the two branches of the nulling interferometer. The real APS and Star simulator will not be used in this report since it is mainly dedicated to the stability of such a set up. The goal was to obtain an OPD stabilization below 1 nm RMS for hours. This goal has been achieved. Yet no test was performed with the real set up and some adjustment will be necessaries. Further work: - Adjusting better the range for OPD correction - Implementing a method to control around the right position (the control signal is periodic, and thus the control has to be performed on the right period of the signal) - Performing a real null measurement to check the results obtained in this report
2 / 87
TNO report | DOI-report-030023 | 1.0
3 / 87
APS test bench - control loop
Contents 1
Introduction ............................................................................................................. 6
2
Theory....................................................................................................................... 7 Measurement of the OPD ................................................................................................ 7 Choice of a wavelength of the control beam.................................................................... 8 Stability of the interferometer without the control loop................................................. 10 The control loop ............................................................................................................. 10
2.1 2.2 2.3 2.4
2.4.1 2.4.2 2.4.3 2.4.4
2.5
Visibility ........................................................................................................................ 14 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5
2.6
Instability of the Laser's intensity .......................................................................................... 18 Instability of the Laser's wavelength ..................................................................................... 18
3.1 3.2 3.3 3.4 3.5 3.6
Equipment .............................................................................................................. 20 References...................................................................................................................... 20 Detectors and power meter ............................................................................................ 20 Delay lines and piezo controller .................................................................................... 20 Delay line, piezo controller, power meter and detectors. ............................................... 21 The control loop ............................................................................................................. 21 Transmitivity and reflectivity ........................................................................................ 22
4.1 4.2
Complete Set up ..................................................................................................... 24 Set up diagram ............................................................................................................... 24 Controle loop ................................................................................................................. 25
4
4.2.1
4.2.2
4.2.3
5
Amplitude in the delay line branch........................................................................................ 15 Amplitude in the corner cube branch..................................................................................... 15 Interferences – nulling output ................................................................................................ 16 Interference – Constructive output ........................................................................................ 16 Conclusion............................................................................................................................. 17
Stability .......................................................................................................................... 18 2.6.1 2.6.2
3
Criteria for a well tuned controller ........................................................................................ 11 PID Controller ....................................................................................................................... 12 Lead and lag filters ................................................................................................................ 13 Control loop over view .......................................................................................................... 14
Controle loop diagram ........................................................................................................... 25 4.2.1.1
About feedback ....................................................................................................................... 26
4.2.1.2
About open/close loop switch ................................................................................................. 26
4.2.1.3
About control loop Set point ................................................................................................... 26
4.2.1.4
About the PID Controller ........................................................................................................ 27
4.2.1.5
About the memory .................................................................................................................. 28
4.2.1.6
About the direct piezo control ................................................................................................. 28
Tuning the PID ...................................................................................................................... 28 4.2.2.1
Ziegler Nichols method ........................................................................................................... 28
4.2.2.2
Trial and error ......................................................................................................................... 29
4.2.2.3
SISO tools – Control toolbox .................................................................................................. 30
Matlab toolboxes ................................................................................................................... 30 4.2.3.1
System identification toolbox .................................................................................................. 30
4.2.3.2
SISO tools – Control toolbox .................................................................................................. 33
Test of the control loop.......................................................................................... 38
TNO report | DOI-report-030023 | 1.0 APS test bench - control loop
5.1
First measurement series ................................................................................................38 5.1.1
5.1.2
5.2
6.1 6.2 6.3
5.1.1.1
Aliasing and high frequency disturbances ...............................................................................38
5.1.1.2
Small flicks..............................................................................................................................40
5.1.1.3
Sound disturbances ..................................................................................................................43
5.1.1.4
Open loop repeatability............................................................................................................44
5.1.1.5
Effect of sampling rate ............................................................................................................46
5.1.1.6
Other improvements made to the set up and conclusion about OPD disturbances ...................46
Close loop measurements ...................................................................................................... 48 5.1.2.1
Air conditioning and cover influence.......................................................................................48
5.1.2.2
Typical results with different compensators ............................................................................49
Later measurement series ...............................................................................................53 5.2.1 5.2.2 5.2.3 5.2.4
6
Open loop measurements ...................................................................................................... 38
Changing the laser source – Identifying the 5kHz peak ........................................................ 53 Introducing the phase shifter in the set up ............................................................................. 54 New open loop response of the extended set up .................................................................... 55 Stability of controlled systems .............................................................................................. 56
Double loop set up ................................................................................................. 57 The new set-up ...............................................................................................................57 Results ............................................................................................................................60 Improving performance ..................................................................................................62 6.3.1 6.3.2
Measurement over night ........................................................................................................ 62 Different test.......................................................................................................................... 64 6.3.2.1
Air conditioning ......................................................................................................................64
6.3.2.2
Some one in the room ..............................................................................................................66
6.3.2.3 6.3.2.4
6.4
7
During the day ......................................................................................................................67 Measurement over one week-end ............................................................................................68
Explanations about the fluctuations of low resolution output ........................................69
Conclusion .............................................................................................................. 71
8 8.1
Appendix ................................................................................................................ 72 Setting windows, Simulink and Matlab to use the I/O card ...........................................72 8.1.1 8.1.2
8.1.3 8.1.4 8.1.5
8.2 8.3
8.1.2.1
Creating a new model ..............................................................................................................73
8.1.2.2
Solver ......................................................................................................................................74
8.1.2.3
Target Configuration ...............................................................................................................74
8.1.2.4
RTLinux v3.1 code generation options ....................................................................................75
8.1.2.5
TLC Debugging .......................................................................................................................75
8.1.2.6
General Code Generation Options ...........................................................................................76
8.1.2.7
External Mode .........................................................................................................................76
Command overview .............................................................................................................. 77 Generating code, compiling code and running the model...................................................... 77 Running the model automatically .......................................................................................... 78
Derivative – From Simulink Help ..................................................................................78 Function used under Matlab for analyze ........................................................................78 8.3.1 8.3.2
8.4
Installation of the Windows System ...................................................................................... 72 Using the code generation environment. ............................................................................... 73
Calculating a density spectrum power (DSP) without the signal processing toolbox ............ 78 Calculating RMS, maximum and mean value of OPD drift .................................................. 79
Mechanical vibration of aluminium plates .....................................................................80
4 / 87
TNO report | DOI-report-030023 | 1.0
5 / 87
APS test bench - control loop
8.4.1 8.4.2
8.5
How to make it run again & data stored ........................................................................ 82 8.5.1 8.5.2 8.5.3
8.6
9
Big plate frequency ............................................................................................................... 81 Mach Zender's mirrors........................................................................................................... 81 Software requirements ........................................................................................................... 82 Model locations ..................................................................................................................... 82 Tips for Simulink .................................................................................................................. 83 8.5.3.1
To change the sampling rate.................................................................................................... 83
8.5.3.2
To store data............................................................................................................................ 83
Last added graph ............................................................................................................ 84
References .............................................................................................................. 90
TNO report | DOI-report-030023 | 1.0
6 / 87
APS test bench - control loop
1
Introduction Nulling interferometry is dedicated to the detection of Earth-like planets. Theoretically, detecting such planets is possible via spectrometry in the wavelength band of λ∈[4, 20]µm. The main problem is that those planets are next to their stars, which are 106 times more powerful. In order to detect the signal coming from the planet, the signal coming from the star has to be decreased by 106 times. Obtaining such a null ratio requires a good design of the set up, and more precisely a good design of the Achromatic Phase Shifter (APS) used to introduce a phase difference of π between the two branches of a Mach Zeinder-like interferometer. However, no matter how good the design is, there is still a drift of the OPD in the interferometer mainly due to temperature effect and vibrations. Since the drift decreases the nulling interferometer's capacities, it has to be corrected, and thus we have to implement a control loop to correct any OPD shift. This report is mainly dedicated to the making of the control loop that should be implemented on the APS breadboard. Since we only want to know to what extend the system can be stable, we won't introduce the APS or the star simulator. The layout of the all system used here is the following:
Blue beams are at a higher level
Figure 1.2.1.a – Simplified layout – set up used to test the control loop
Note: The two delay lines usually used on this set up were not available during all the testing of the control loop. Thus the symmetry between the two branches of the interferometer is lost, and we can't expect a 106 null ratio in our measurement. Note: Please refer to the reference document [1] for a more detailed description of the set up.
TNO report | DOI-report-030023 | 1.0
7 / 87
APS test bench - control loop
2
Theory
2.1
Measurement of the OPD To correct the OPD shift, we have to get a reliable measurement of this OPD. This may be achieved by using both destructive and constructive interferences. For testing, we use a control laser to get a powerful coherent beam, but for the final set up, the control beam should be extracted from the starlight. Control source (laser)
Each beam splitter introduce a π/2 difference of phase between the transmitted and the reflected beams
Delay line Constructive interference
Fixed reflecting corner cube Destructive interference
Figure 2.1.a – How to get constructive and destructive control signal
Destructive intensity is given by
ID =
I0 .(1 + cos ϕ ) 2
IC =
I0 .(1 − cos ϕ ) 2
Constructive intensity is given by
Where ϕ is the phase-difference introduced between the two branches of the nulling interferometer. Assuming that ϕ is located in the linear area of cosϕ (fig.4.2.1.1.c),
π cos ϕ = cos + δϕ = sin δϕ ≈ δϕ 2
Where δϕ is a small phase shift. Then the following relation gives the balance B
B=
I D − IC 2.π .OPD = sin δϕ ≈ I D + IC λcontrol
Thus the balance B is directly proportional to OPD shift. We have a measurement of OPD shift as long as it does not exceed the linear zone of the cosine, i.e.
−
π
< δϕ
1, for a lag filter a
