pyconkr 20150627_simulation_on_optical_image_stabilizer_using_python

Simulation on Optical Image Stabilizer using Python

부제 : control library로 바로 해보는 system simulation

HyungKwan Kim

[email protected]

Today’s presenter is

• 김형관 주임

• LG Innotek (12’ 4~ 현재)

• Mobile OIS Camera 개발자

• G4/G3/G2/G-Flex2/Nexus5 (OIS engineering)

• MS in EE (Computer Vision, ITS)

© 2015 HyungKwan Kim

contents

• What is the Optical Image Stabilizer(OIS)?

• Motivation – Why? and Why Python?

• Library for System Simulation in Python

• Transfer Function & Bode Plot

• Generate Filters, PID, Time Delay

• Make Serial/Parallel/Feedback Connections

• Modelling Gyro & Actuator

• Let the system make “response”

• Measure the performance(Gain Cal., Trace Error)

• Usage of the simulation @ work

시스템 설계에 필요한 기본 요소 세팅

한땀, 한땀 이어서 시스템으로 완성

평가 및 활용

OIS 갂단한 설명


What is the Optical Image Stabilizer?

이미지 센서

렌즈

손떨림에 의한 광경로 변동

밀린 stroke만큼 Lens를 Shift시켜

떨림을 보정

흔들린 사진(떨림각:2도) 삼각대 촬영(무진동) © 2015 HyungKwan Kim

What is the Optical Image Stabilizer?

렌즈

홀센서 Y-axis

홀센

서 X

-axis

자이로 드라이버 컨트롤러

이미지 센서

• Very basic feedback system using Gyro, Hall, Actuator.

• Simple but enough to practice a closed-loop simulation


Motivation – Why Simulation?

• Closed-loop System Quality Control

현 Actuator Spec. 하에 안정성이 충분히 확보되는가? *

Step Response에 의한 정상상태 도달은 충분히 빠른가?

Gyro 열특성상, 품질 마짂은 얼마나 두어야 하는가?

• 샘플 제작 없이, 다양한 조합, 다양한 조건의 모듈 성능 검토 필요

A사 컨트롤러는 B사에 비해 추종오차가 얼마나 적을것인가? *

가격이 저렴한 A사의 Gyro의 노이즈는 성능에 영향을 줄 정도로 유의한가?

• Analystic Industrial Inspection

PCB 실장시 발생하는 SMT Rotation Angle은 얼마나 허용되는가?

Calibration 장비 정확도는 최소 얼마이상 확보되야 하는가?

• User에게 실제 의미가 있는 Spec. 정립 필요

성능이 얼마나 나와야 체감할 수 있을까?

감성평가가 가능한 이미지를 생성할 수 없을까? *

*표시 항목은 후반부에 결과 공유


Motivation – Why Python?

• It is free

M사의 프로그램도 좋지만… 돈도 돈이고 사내 구입 프로세스도 번거롭죠

각 Filter들을 Fully Customize가능하고, Fully Open된 홖경이 더 끌렸습니다.

• and easy to write code, easy to debug

출근길에 떠오른 idea를 퇴근 젂에 확인해 볼 수 있다는 점

C로는 쉽지 않죠?

• and even effective to debug one’s thought

컴파일 없는 즉각적인 실행, 시각화.

사고의 흐름을 놓치지 않게 하고, 잘못된 직관은 금방 바로 잡고.


Block Diagram of OIS

Gyro HPF/LPF

Servo Filter (PID)

Sine Wave

Gyro Phase Delay

Actuator (cmk

model)

Gyro Gain

Servo Gain

Integrator dps->deg.

Hall Filter

+ -


Library for System Simulation in Python

• Control Systems Library for Python (Murray, Caltech)

젂달 함수를 이용한 시스템 시뮬레이션

직렬, 병렬, 피드백 커넥션 함수 제공

Time Response(Impulse, Step 등) 계산 가능

Documentation도 충실하며, 지속적인 업데이트

• Getting Started

1. http://sf.net/projects/python-control/files lib 다운로드

2. python setup.py install

3. source code 상에서 import


http://sf.net/projects/python-control/files




Make Transfer Function & Bode Plot • General Form of Transfer Function

• Make Instance of Transfer Function F = control.tf([1, a0, a1, … , an], [1, b0, b1, … , bn])

• Make Bode Plot plt.figure() control.bode_plot(tf, freq_range)

𝑠𝑛 + 𝑎0 ∗ 𝑠𝑛−1 + ⋯ + 𝑎𝑛

𝑠𝑛 + 𝑏0 ∗ 𝑠𝑛−1 + ⋯ + 𝑏𝑛

• Transfer Function of HPF

• Make Transfer Function of HPF(10Hz)

• Make Bode Plot

𝐺 𝑠 = 𝑠 + 1

𝑠 + 𝑓



Gyro HPF/LPF

Servo Filter (PID)

Sine Wave

Gyro Phase Delay

Actuator (cmk

model)

Gyro Gain

Servo Gain


Hall Filter

+ -


Generate Filters, PID, Time Delay LPF

(Low Pass Filter)

𝐺 𝑠 =

1

𝑠 + 𝑓𝑐 𝐺 𝑠 =

𝑠 + 𝑓𝑙

𝑠 + 𝑓ℎ 𝐺 𝑠 =

𝑠 + 𝑓ℎ

𝑠 + 𝑓𝑙

𝐺 𝑠 = 𝑠2 +

𝐴𝑄

𝑓𝑝𝑠 + 𝑓𝑝2

𝑠2 +1

𝐴𝑄𝑓𝑝𝑠 + 𝑓𝑝

2

LBF (Low Boost Filter)

HBF (High Boost Filter)

PKF (Peaking Filter)

P (Proportional)

I (Integrator)

D (Derivate)

𝐺 𝑠 = 𝐺𝑎𝑖𝑛

0 ∙ 𝑠 + 1 𝐺 𝑠 =

1

𝑠 𝐺 𝑠 = 𝑠

HPF (High Pass Filter)

𝐺 𝑠 =

𝑠 + 1

𝑠 + 𝑓𝑐



Gyro HPF/LPF

Servo Filter (PID)

Sine Wave

Gyro Phase Delay

Actuator (cmk

model)

Gyro Gain

Servo Gain


Hall Filter

+ -


• Make the transfer function of time delay

𝑠𝑛 + 𝑎0 ∗ 𝑠𝑛−1 + ⋯ + 𝑎𝑛

𝑠𝑛 + 𝑏0 ∗ 𝑠𝑛−1 + ⋯ + 𝑏𝑛

Generate Filters, PID, Time Delay

N-deg. Pade estimation

(−1.0)𝑠 + 2.0

(1.0)𝑠 + 2.0 𝑒− 1.0 𝑠

𝑒−𝑡𝑠



Gyro HPF/LPF

Servo Filter (PID)

Sine Wave

Gyro Phase Delay

Actuator (cmk

model)

Gyro Gain

Servo Gain


Hall Filter

+ -


w/ white noise w/ ZRO Shift

• Generate Wave Choose the frequency that simulates hand shaking

• Add Degrading Factors Sensitivity shift over temperature Zero rate offset shift over static noise ( sqrt/root(Hz) )

2Hz 6Hz 10Hz

Modelling Gyro

w/ Sensitivity Change © 2015 HyungKwan Kim

Modelling Actuator • Spring-Damper Model (c-m-k model)

• Add Degrading Factors

𝐺 𝑠 =𝑤𝑛

2

𝑠2 + 2 ∗ 𝑡𝑎𝑢 ∗ 𝑠 + 𝑤𝑛2

Figure from http://ocw.mit.edu Freq(wn)=60, ampQ1(1/(2tau))=30db

Q1 amp-range variation Add harmonics Q1 f-range variation



Gyro HPF/LPF

Servo Filter (PID)

Sine Wave

Gyro Phase Delay

Actuator (cmk

model)

Gyro Gain

Servo Gain


Hall Filter

+

-

System Of

Single Transfer Function


Make Serial/Parallel/feedback connections

From http://www.cds.caltech.edu/~murray/books/AM05/pdf/am06-xferfcns_16Sep06.pdf, Chapter 8. Transfer Functions, p. 253,

http://www.cds.caltech.edu/~murray/books/AM05/pdf/am06-xferfcns_16Sep06.pdf




Gain + LPF = HBF꼴, 역시 제대로 표현 됨.


Serial Connection

Parallel Connection

= G G2 HPF

G1 HBF

= G

G2 Gain

G1 LPF

HBF x HPF 이며, 곱셈에 따라서 Gain 수렴 지점 두 곳이 제대로 표현 됨.



feedback Connection = G

G1 HPF

G2 HBF

+ -



System Total

Transfer Function

Gyro HPF/LPF

P I D

Sine Wave

Gyro Phase Delay

Actuator (cmk

model)

Gyro Gain

Servo Gain


Hall Filter

+

-

Servo Total

Transfer Function

Gyro Total

Transfer Function

Hall Filter

+

-

By Serial, Parallel

Connection

By Feedback

Connection


Let the system make “response”


Let the system make “response”

LPF( 𝒇𝒄 : 6Hz)

HPF(𝒇𝒄 : 6Hz)

INPUT SINWAVE

2Hz 6Hz 10Hz


Measure the performance (Gain Cal., Trace Error) • Gain Calibration

(minimize the gap between Input sinwave & output lens position

• Trace error OIS 성능(dB) 홖산

Gain:0.18 Gain:0.20 Gain:0.22

Input(Hand Shake) & Output(Lens Position)

Trace Error (Hand Shake

–Lens Position)

OIS 성능(=20*log10(hand_shake

/trace_error))


Usage#1 – actuator maker별 제어 안정성 비교

A사

B사


Usage#2 – controller chip maker별 OIS성능 비교

Minimal Performance 23.0 dB

A사

B사 Minimal Performance 14.8 dB


Usage#3 - 시뮬레이션 된 OIS 성능을 화상으로 확인

OIS Off OIS ON Grade B

OIS ON Grade A

Very useful when to decide “Target Spec.”


Usage#3 - 시뮬레이션 된 OIS 성능을 화상으로 확인

Overlaping images cropped with the offset of trace-error during pre-set exposure time

Trace error overlaping

offset


transfer functions, coefficients on this presentation are not necessirily reflecting the real characteristics of the product for confidential reason.


들어주셔서 감사합니다.

Thank you very much for your attending.


pyconkr 20150627_simulation_on_optical_image_stabilizer_using_python

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