Transcript Learning Identification Technique For Opto

Learning Identification Technique For
Opto-Electronic Automation
Shubham K. Bhat, Timothy P. Kurzweg, and Allon Guez
Drexel University
Department of Electrical and Computer Engineering
www.ece.drexel.edu/opticslab
[email protected], [email protected], [email protected]
Overview
Motivation
Current State-of-the-Art Photonic Automation
Our Technique: Model Based Control
Hardware Implementation
Learning Model Identification Technique
Hardware Implementation
Conclusion and Future Work
Motivation
MANUAL
Fiber-Fiber Alignment
SEMI-AUTOMATED
No standard for OE packaging and assembly automation.
Misalignment between optical and geometric axes.
Packaging is critical to success or failure of optical micro-systems.
60-80 % cost is in packaging.
Automation is the key to high volume, low cost, and high
consistency manufacturing ensuring performance, reliability,
and quality.
Current State-of-the-Art
Assembly
Alignment
Task
Parameters
Visual Inspect
and Manual
Alignment
LIMITATIONS:
ApproximateS
et Point=Xo
“Hill-Climbing” Technique
Stop
Stop
Initialization
Loop
Move to set point (Xo)
Measure Power (Po)
Multi-modal Functions
Multi-Axes convergence
Off the shelf
Motion Control (PID)
(Servo Loop)
Slow, expensive
Stop motion
Fix Alignment
***KEY LIMITATION : POWER IS NOT MAXIMIZED***
Model Based Control
FEED - FORWARD
Assembly
Alignment
Task
Parameters
Visual Inspect
and Manual
Alignment
Correction to Model
Parameter
Optical Power
Propagation Model
Set
Point=Xo
Learning Algorithm
Model Parameter
Adjustment
{Xk}, {Pk}
ADVANTAGES:
Initialization
Loop
Move to set point (Xo)
Measure Power (Po)
Support for Multi-modal Functions
Technique is fast
Off the shelf
Motion Control (PID)
(Servo Loop)
Cost-efficient
Stop motion
Fix Alignment
Model Based Control (Theory)
Pˆ 1
Pd(s)
Kp
Pr ( s )
P

R( s )
K pP 1
+
R(s)
+
R( s)
 ( Pˆ 1  K p )
Pd ( s )
E(s)
+
P
-
Kp
Pr ( s )
R ( s ) Pr ( s )


Pd ( s ) Pd ( s ) R( s )
If
P̂ = P,
Pr ( s)
P
1
ˆ
 ( P  K p )(
) 1
Pd ( s)
K pP 1
Pr(s)
Optical Modeling Technique
Use the Rayleigh-Sommerfeld Formulation to find a
Power Distribution model at attachment point.
z
U 2( x, y ) 
j
e jkr
 U1( , ) r 2  
Solve using Angular Spectrum Technique
– Accurate for optical Microsystems
– Efficient for on-line computation
Spatial Domain
Fourier Domain
Spatial Domain
Inverse Model
For Model Based control, we require an accurate
inverse model of the power.
However, most transfer functions are not invertible.
• Zeros at the right half plane
• Unstable systems
• Excess of poles over zeros of P
Power distribution is nonmonotonic (no 1-1 mapping).
Find “equivalent” set of
monotonic functions.
Inverse Model: Our Approach
Decompose complex
waveform into PieceWise Linear (PWL)
Segments.
Each segment valid in
specified region.
Find an inverse model
for each segment.
Example System
For the double slit aperture, the irradiance at any point
in space is given as:
I ( x)  A sin c 2(
kb
x
ka
x
sin (tan 1 ( ) ) ) cos2 ( sin(tan 1 ( )))
2
z
2
z
 = wavelength = 630 nm
k = wave number associated with the wavelength
a = center-to-center separation = 32 um
b = width of the slit = 18 um
z = distance of propagation =1000 um
Hardware Implementation
Video Screenshots from the hardware implementation experiment
Optical setup
Amplifiers, Encoders
Interpolators, Motion Controller
Power Meter readings
Visit www.pages.drexel.edu/~skb25/automation.htm to watch the video
Hardware Results
Power Levels Reached
Gradient Ascent 0.644 uW
Model Based Control 1.55 uW
Need for Learning Model
The structure of the system and all of its parameter
values are often not available.
Uncertainty in models or inaccurate modeling could lead to
deviation from the actual values.
Adjust the accuracy on the basis of experience.
u (t )
Input
y (t )
Real System
Adjustment
Scheme
Model
Output
e(t )
+
Error -
yˆ (t )
Estimated
model
Learning Model Identification
Step 1: Assume system to be described as y  f ( y, u,  ), where y
is the output, u is the input and  is the vector of all unknown
parameters.
Step 2: A mathematical model with the same form, with
ˆ as a
different parameter values , is used
yˆ  f ( yˆ , u, ˆ )
learning model such that
Step 3: The output error vector, e , is defined as e  y  yˆ
Step 4: Manipulate ˆ such that the error is equal to zero.
Step 5: It follows that
e  e( ˆ )
and
 e  
 ˆ
e  
 ˆ 


Learning Model Identification
y (t )
u (t )
Real System
Input
Output
̂
ˆ (t )


Estimated
model of
unknown parameters
Model
Sensitivity
equations
e(t )
T
S (t )Q
Output
Error
S (t )
+
-
yˆ (t )
Learning Model Algorithm
We present a two unknown system having input-output
differential equation y  ay  Ku ( a and K are unknown )
The variables u, y, and
Step 1:
y are to be measured
0 1 
0
x  
 x  K  u
0

a


 
0 1  0
Step 2: xˆ  
xˆ   ˆ uˆ

0  aˆ   K 
Step 3:
{ y  x1 and y  x 2 }
{ Assume estimated model and e  x  xˆ }
The Sensitivity coefficients are contained in
 e1
 aˆ
S
 e 2
 aˆ
e1 

Kˆ  where e  y  yˆ
e 2 
Kˆ 


T
e
xˆ
e
xˆ
and ˆ   ˆ

y  yˆ ,
K
K
aˆ
aˆ
Learning Identification TechniqueExample System
“a” is unknown and
has to be learned.
For the double slit aperture, the irradiance at any point
in space is given as:
I ( x)  A sin c 2(
kb
x
ka
x
sin (tan 1 ( ) ) ) cos2 ( sin(tan 1 ( )))
2
z
2
z
 = wavelength = 630 nm
k = wave number associated with the wavelength
a = center-to-center separation = 32 um
b = width of the slit = 18 um
z = distance of propagation =1000 um
Learning Identification TechniqueExample System
y  my  Ku
y1  0.34 y1  27.07
Initial Estimate of “m” = 0.34
“a” of 72 um
Actual Value of “m” = 1.86
“a” of 32 um
Hardware Implementation- Flowchart
Video
Screenshots
Visit http://www.pages.drexel.edu/~skb25/learning.htm to watch the entire video
Hardware Implementation- Results
X and Y encoder setpoints
Initial X encoder position = 10477
Final X encoder position = 10810
Initial Y encoder position = 24
Final Y encoder position = 25
Efficiency and Accuracy
Reached Power Level
Final Results
Learning Identification Technique
Learned Initial Power Level = 1.24 uW.
Maximum Power Received = 1.675 µW.
Model Based Control
FeedForward Initial Power Level = 0.87uW.
Maximum Power Reached = 1.55 µW.
Gradient Ascent Technique
Maximum Power Received = 0.645 µW.
Conclusions
Model based control leads to better system
performance.
Inverse model determined with PWL
segments.
Learning increases accuracy of model.
Shown increased performance in simulated
systems.
Hardware implementation.
Future Work
Advanced
Optical Modeling
(Finite-Difference-Time-Domain)
Create advanced, yet efficient,
nano-scale device and optical
propagation models (FDTD).
Advanced
Learning Control
(Simulated Annealing, Genetic Algorithms)
Develop critical and accurate learning
loop algorithms (Adaptive Control,
Neural Networks).
Nano-assembly
(Nano-tubes, Nano-fibers, Nanomanipulators)
Develop user interfaces for existing
nano-positioners and nanomanipulators.
Hardware Implementation and Verification in Nano Test-bed