Simulation and Experimental Verification of Model Based Opto-Electronic Automation

Drexel University

Department of Electrical and Computer Engineering

skb25@drexel.edu, kurzweg@ece.drexel.edu, guezal@drexel.edu

Shubham K. Bhat, Timothy P. Kurzweg, and Allon Guez

Motivation

Current State-of-the-Art Photonic Automation

Our Technique: Model Based Control

Optical Modeling Techniques

Learning Model Identification Technique

Conclusion and Future Work

Overview

No standard for OE packaging and assembly automation.

Misalignment between optical and geometric axes

Packaging is critical to success or failure of optical microsystems

60-80 % cost is in packaging

Automation is the key to high volume, low cost, and high consistency manufacturing ensuring performance, reliability, and quality.

Motivation

Current State-of-the-Art

LIMITATIONS:

Multi-modal Functions

Multi-Axes convergence

Slow, expensive

“Hill-Climbing” TechniqueVisual Inspect

and Manual Alignment

Initialization Loop

Move to set point (Xo)Measure Power (Po)

Stop motion Fix Alignment

ApproximateSet Point=Xo

Assembly Alignment Task Parameters

Off the shelfMotion Control (PID)

(Servo Loop)

StopStop

Model Based Control

ADVANTAGES:

Support for Multi-modal Functions

Technique is fast

Cost-efficient

Visual Inspect and Manual Alignment

Initialization Loop

Move to set point (Xo)Measure Power (Po)

Stop motion Fix Alignment

Set Point=Xo

Learning AlgorithmModel Parameter

AdjustmentOptical Power

Propagation Model

Correction to Model Parameter

{Xk}, {Pk}

FEED - FORWARD

Off the shelfMotion Control (PID)

(Servo Loop)

Assembly Alignment Task Parameters

Model Based Control Theory

)ˆ()(

)( 1p

d

KPsP

sR

1)(

)(

PK

P

sR

sP

p

r

)(

)(

)(

)(

)(

)(

sR

sP

sP

sR

sP

sP r

dd

r

Kp

Kp

Pd(s) Pr(s)++ +

-

R(s) E(s) P

1ˆ P

1)1

)(ˆ()(

)( 1

PK

PKP

sP

sP

pp

d

rIf = P,P

2),(1),(2r

eU

j

zyxU

jkr

Optical Modeling TechniqueUse the Rayleigh-Sommerfeld Formulation to find a Power Distribution model at attachment point

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 non-

monotonic (no 1-1 mapping)

Find “equivalent” set of monotonic functions

Inverse Model: Our Approach

Decompose complex waveform into Piece-Wise Linear (PWL) Segments

Each segment valid in specified region

Find an inverse model for each segment

The structure of the system and all of its parameter values are often not available.

Noise, an external disturbance, or inaccurate modeling could lead to deviation from the actual values.

Adjust the accuracy on the basis of experience.

Need for Learning Model

Real System

Adjustment Scheme

Model

+

- )(ˆ ty

)(tu )(ty

)(te

Input Output

ErrorEstimatedmodel

Learning Model IdentificationAlgorithm

)ˆ,,ˆ(ˆ uyfy

yye ˆ

It follows that )ˆ(ee and

ˆˆ

ee

Step 1: Assume system to be described as , where y is the output, u is the input and is the vector of all unknown parameters.

),,( uyfy

Step 2: A mathematical model with the same form, with different parameter values , is used as a learning model such that

Step 3: The output error vector, e , is defined as

Step 4: Manipulate such that the output is equal to zero.

Step 5:

Real System)(tu

Model

Sensitivity equations

)(ˆ t QtST )(

+

- )(ˆ ty

)(ty

)(te

Learning Model Identification Technique

Output Input

Output Error

Estimatedmodel ofunknown parameters

)(tS

We present a two unknown system having input-output differential equation Kuyay ( a and K are unknown )

The variables u, y, and are to be measuredy

Step 1: uK

xa

x

0

0

10 1xy and 2xy { }

Step 2: uK

xa

x ˆˆ0

ˆˆ0

10ˆ

{ Assume estimated model and }xxe ˆ

The Sensitivity coefficients are contained in

K

e

a

eK

e

a

e

S

ˆˆ

ˆˆ

22

11

Step 3:

where , Tyyyye ˆˆ a

x

a

eˆ

ˆ

ˆ

andK

x

K

eˆˆ

ˆ

Learning Model Identification example

Learning Loop of PWL Segment

1

1

1

2

sxu

x

)1(

1

sPowerDisplacement+

-

K

Input2x 1x yu

.

(x) (P)(u)

uxxt

x

122

Kaxt

x

22

For each PWL Segment:L-1

Learning for 2 Unknown Variables (PWL Segment)

a and K have initial estimates of 0.1 and 4

Actual values of a and K are 1.44 and 5.23

QeS T

S: Sensitivity matrix

Sxe

ˆˆ

Kaxt

x

22

: Updated Model

e: error matrixQ: weighting matrixe: tracking parameter

K

aˆˆ

Distance = 10um

No. of. Peaks = 10

Edge Emitting Laser Coupled To a Fiber

Aperture = 20um x 20um

Fiber Core = 4 um

Prop. Distance = 10 um

Example: Laser Diode Coupling

NEAR FIELD COUPLING

Nominal Model

dt

du

-

KK

KK

+ )1(

1

s

Proportional Gain

Proportional Gain

Motor Dynamics Plant Model

Derivative

Desired Power

Time Taken = 7 seconds

Model Based Control System

(1.41)

+InverseModel

+

+

20

18

16

14

12

Fiber Position(12.6 um)

1.5

1

0.5

0

1.5

1.3

1.1

0.9

0.7

Received Power(1.41 )

Experimental Setup of Laser-diode example

Test bed for Verification

Optical Power Sensor

Optical Source

X-Y Stage

Motion Control Card

X Amplifier

Y Amplifier

Laser Diode Driver

Pre-amplifiers, encoders

We acknowledge Kulicke and Soffa, Inc. for the donation of the XY Table

Test bed for Verification

Optical Power Sensor

X-Y Stage

Laser Diode Driver

Model based control leads to better system performance

Inverse model determined with PWL segments

Learning loop can increase accuracy of model

Shown increased performance in simulated systems

Hardware implementation

Evaluate other learning techniques

Error prediction in models

Conclusions and Future Work