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Tracking Control System of the Two Axes Passive Solar Tracker

description

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Tracking Control System of the Two Axes Passive Solar Tracker

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¼½ <¾ � 3 3 �¿3 3 73 3 ¿3 3 À3 3 �3 3 ¼3

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� * + < = > ? @ A B C D � E F G D H � � C D � 2 I �� � � � � � � �� � � �� � � �� � � �� � � � � � J K L � � 3 M N , O P Q�

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� � ~ � � [ � � � � 4 � � �� * � � �, - �O P 5 = l * = � � � � � � �� � �� � q r Q�

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I

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��Á  à � � Ä Å i Æ ¨ © i ® ¯ (high concentrated photovoltaic,

HCPV) ^ ¦ § ª « Ç È 5 { 0 É ¥ I � ª ­ ® ¯ �HCPV ^ Ê Ë ; Ì Í Î Ä Ï Ð

^ Ñ Ò Ó ¨ © Ô �Õ Ñ Ò Ó ¨ © Ô Ö · × u Ø Ù ^ ¨ © ¼Ú �: Û Ü Ý Ì Þ

ª « ¬ ^ ª « ß à Ì á � 0.5°�â ã ä Ù å æ ç è " ± é ¨ © Ô × u Ø Ù ¼

Ú ê ë ì +

¥ I � ª « ^ 9 T ; í î ï �# ^ a ð ñ ò ® ó ô * ¨ © * õ �Ü Ý ª «

¬ �ö a ÷ ^ ø à �ù à , kc ÷ ú û ü ¨ © ý å kp * å þ ¼� � ^ ��� ö

� I � � � � � � �� � 2 � Ì � · � � � � Ç È � � k � � p · � s ¨

© �� ^ � � � � � Ê � ö � � c � +

ª ­ ® ¯ ^ ¹ � , Labview � � $ % �í î Labview ^ � � � Ï · ! "

# � $ % � Ç & ' ^ ­ ( ¬ +) ¨ © ^ ý å kp * å þ � � 0.2°ª ­ ® ¯ * Y �

I � � + I ª « ¬ �ê , æ ç å à ; - � ß à � 0.1°̂ . / 0 (collimating

tube)�� � � f * 1 Ç 2 v 3 Ù ö . / 0 4 ^ ¨ © i 5 6 7 �~ 8 � ª « ¬ ^ å

à 9 ç +: �, ; f Ý < = · � > ª « ß à á � 0.5°�? @ A ¥ I � ª « p � Ã

� � HCPV ^ B | � +

C D E F Ä Å i¨ © · G Z �¥ I � ¦ § ª « ¬ �ª ¼­ ( +

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II

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The purpose of this research is to develop a passive sun-tracking control system

for high concentrated photovoltaics (HCPV), which uses two axes tracking

mechanisms. HCPV uses III-V solar cell which has higher efficiency and can only

absorb the direct solar irradiation. In order to reducing the error of incident angle,

which causing degradation of insolation absorption of the solar cell, the precision of

tracker is set to be smaller than 0.5°.

The passive tracking adopted in this study is utilizing the horizontal coordinates

of astronomy, which depends on the latitude, longitude and time zone of the tracker’s

location to calculate the altitude and azimuth of the solar. The stepping motor, which

drive the tracking mechanisms, is chosen to provide adequate rotating torque for

mechanism and rpm for coping with rapid motion of the solar trajectories (particularly

in the noon).

This control system is programming with Labview software. When the solar

altitude and solar azimuth move at angle of 0.2°, the controller drives the stepping

motor to actuate the tracker. A collimating tube with an accuracy of 0.1° is used to

measure the error of tracking angle, and recorded the light spot in the collimating tube

with a digital camera to analyzing the error distribution. At the outdoor test,

experiment results show that the average angle error is less than 0.5° and which prove

the feasibility of the passive sun-tracking system can be used in HCPV.

Key word: HCPV, two axes passive solar tracker, sun-tracking control system

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III

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· � � e �# � { f ü g h ^ 0 i ï �Â� ´ N O ^ J j � R �P ^ L k � l ;

A , m n +? Ê � L M o � ^ p q # r �s i# r , k t u v w ö x y � a

; z { R ^ | P } ~ Z � �� P > � " ^ | � +� �� L M ö � ; ^ c � � � P

z � � � � � ^ � [ � � � � ( ) �o � � � # r , k � � � N O �! P � �

� � +

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Z � c � ¡ l ¢ ^ � P } £ �a % ¤ ¥ U ^ � � # r �µ ¦ # r , kµ § # r �

L M � ¨ ö P & 0 c  P ^ Ú © ª? � Â# « ¨ F¬ ­ �® ¯ �° ¯ �� ± � ²

M M �M M ³ ¨ ö P & = J K c d + � P ´ � ^ µ ¶ ª�· � L M ^ ; · P 0 ¸

ö [ \ � ¹ º ^ » ¼ · � ½ � - P ö J K Þ # è ¹ � ¾ ¿ +

À 8 � L M P ^ F � , k Á Â Ã Ä Å ö J K c d 4 � P ^ Æ Ç k C R �ö P

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h � Ó � M M " F Â P ^ C Ú � ! P · � Ô � Õ Ö � ^ × è J K Þ # � Ò +

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IV

� Ø � ....................................................................................................................I�

Ù � Ø � .................................................................................................................. II�

é M ........................................................................................................................ III�

] v ........................................................................................................................ IV�

C] v ..................................................................................................................... VI�

] v ..................................................................................................................... IX�

Ú � � � .................................................................................................................. X�

Û 0 \ ¨ © ª « ¬ ................................................................................................. 1�

1-1 [ \ I Ç ..................................................................................................... 1�

1-2 ª « ¬ � Ü V © ........................................................................................ 3�

1-3 [ \ 4 Ý .................................................................................................... 4�

Û = \ ¨ © ª « T � .............................................................................................. 5�

2-1 ï Þ ñ ò ® ¯ ............................................................................................ 5�

2-1-1 ß à ñ ò ® ..................................................................................... 5�

2-1-2 á à ñ ò ® ...................................................................................... 5�

2-1-3 a ð ñ ò ® ..................................................................................... 6�

2-1-4 Ñ o ñ ò ® ^ â ã .......................................................................... 6�

2-2 a ð ñ ò å à C ä E c d å û ................................................................. 7�

2-2-1 c d æ ç � ..................................................................................... 7�

2-2-2 ¨ © á ø å ..................................................................................... 8�

2-2-3 ¨ © c å ......................................................................................... 8�

2-2-4 ¨ © ý å kp * å .......................................................................... 9�

2-3 è a ÷ ¨ © ý å E p * å � � ............................................................ 10�

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V

2-4 a ð ñ ò ® ú û y � æ ç ....................................................................... 10�

Û Ñ \ ª « ¬ � I � � ........................................................................................ 12�

3-1 ¦ § ª « ¬ Ç È ...................................................................................... 12�

3-2 � � & é .......................................................................................... 12�

3-3 � � 2 � .................................................................................................. 14�

3-4 � � ­ ( � � .......................................................................................... 15�

Û ê \ ª « ¬ ª ­ ® ¯ 5 { k , ; ..................................................................... 17�

4-1 ª ­ ® ¯ ë È .......................................................................................... 17�

4-2 ª « ® ¯ 5 { .......................................................................................... 18�

4-2-1 c d ì f ¹ � ............................................................................... 18�

4-2-2 å à ú û ¹ � ............................................................................... 19�

4-2-3 � I í î ï ¹ � ............................................................................ 20�

4-2-4 ª ­ ® ¯ ¹ � ............................................................................... 21�

4-3 ª ­ ® ¯ , ; .......................................................................................... 22�

4-3-1 � @ p q ....................................................................................... 23�

4-3-2 , ; ð ñ ....................................................................................... 23�

Û Ò \ ð � ........................................................................................................... 25�

5-1 ð � .......................................................................................................... 25�

5-2 ò ó ó p ô .......................................................................................... 25�

õ � Ü ................................................................................................................. 27�

ö v A ÷ ø ú û ¨ © �� ................................................................................ 30�

ö v B � � � � � � ú û .................................................................................... 38�

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VI

� � � �

C 1-1 � ¸ ¨ © Ô � å ù Ð â ã ...................................................................... 41�

C 1-2 ú ¯ û ü E Fresnel lens â ã ..................................................................... 41�

C 1-3 ý þ Æ Fresnel ü i · CPV���550�� iÐ� ................................. 42�

C 1-4 u � ¨ © { ·^ � i¬ �(a) � � ' Æ � i¬ [3]�(b) � � � � � � i¬ 42�

C 1-5 , � � ' j � � i¬ ^MicroDish t Æ �^ HCPV ® ¯ .................... 43�

C 1-6 PV-fibre �^ HCPV ® ¯�(a)ë È C�(b) = e � i¬ ��................. 43�

C 1-7 � ¸ �^¨ © ª « ¬ (a) � º � Tetra-Track ¦ § I� é I�(b) � �

Zomeworks � §¥ I� { � (thermal-liquid) é I�(c) � � Lorentz ¦ § I

� é I+ ..................................................................................................... 44�

C 1-8 ¨ © ä Ù åà 9 ç E ù Ð C ä C .............................................................. 44�

C 1-9 I¦ §ª « ¬ Í � � � � � � � i¬ ................................................... 45�

C 1-10 I�¦ §Ç È Í � � � � � � � i¬ E ý å � ô 40°^ � � � � � �

i¬ � u � ^¼Ú ê â ãC .......................................................................... 46�

C 1-11 ¥ I­ ( ^¦ §ª « ¬ Í � ¨ © Ø Ù ú· ý å � ô 32°^¨ © Ø Ù ú #

Ø Ù ¼Ú ê u � â ã ...................................................................................... 46�

C 1-12 � Q �ª « ® ¯ª « � ¹ C .................................................................... 47�

C 2-1 áà ñò ® ................................................................................................. 48�

C 2-2 a ðñò ® ................................................................................................. 48�

C 2-3 0 7 � c ç ��C .................................................................................. 49�

C 2-4 ï Þ= Ë C (a) ß à ' = Ë C�(b) ä Ù åE p *å = Ë C ..................... 49�

C 2-5 ¨ © á ø å0 7� ��C ...................................................................... 50�

C 2-6 è a ÷ ¨ © � � ���(a) � ��(b) � � .............................................. 51�

C 2-7 ñò ® ·÷ ø ö � �^ç � �l ÷ ø ,� ¸ 7 j úû (a) ý å�(b)

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VII

p *å+ ......................................................................................................... 52�

C 3-1 ¦ §ª « Ç È � úC .................................................................................. 53�

C 3-2 ¦ §ª « ¬ � � C...................................................................................... 53�

C 3-3 n � ��= Ë C (a) PM��(b)VR��(c) � Q �+ ...................... 54�

C 3-4 �� Ê � � � ...................................................................................... 54�

C 3-5 � � c þ 0.2°^�� � � �(a) ý å�(b)p *å ....................................... 55�

C 3-6 � � c þ 0.2°^�� � � �(a) ý å�(b)p *å ....................................... 56�

C 3-7 � p �� � � ......................................................................................... 57�

C 3-8 � p ��� � � � Ê � C�(a) RK564AA-T30�(b) RK564AA-T10 ....... 57�

C 3-9 ��� I¬ E �� � d ^ ï � = Ë C ....................................................... 58�

C 3-10 í � o E � I¬ ï � = Ë C .................................................................... 58�

C 4-1 ¹ � � ¹ C ................................................................................................. 59�

C 4-2 c d ì f¹ �C ...................................................................................... 60�

C 4-3 c d ì f� Ç & ' C .................................................................................. 60�

C 4-4 MathScript�� E ! ¹ � î ï C ................................................................ 61�

C 4-5 �� é I 8 " Ç ( �(a) ç # " � 0.2°�(b) ç # á � 0.2° ........................ 61�

C 4-6 åàúû ¹ �C ...................................................................................... 62�

C 4-7 � I í î ï ¹ �� Ç & ' .......................................................................... 62�

C 4-8 � I í Sequence $ ' 0 ............................................................................. 63�

C 4-9 � I í Sequence $ ' = ............................................................................. 63�

C 4-10 � I í Sequence $ ' Ñ ........................................................................... 64�

C 4-11 �� % _ ¹ � & �(a)��' � �(b)�� % _ ........................................ 65�

C 4-12 � I í Sequence $ ' ê ........................................................................... 65�

C 4-13 ª ­ ® ¯ Sequence $ ' 0 ....................................................................... 66�

C 4-14 ª ­ ® ¯ Sequence $ ' = ....................................................................... 66�

C 4-15 ª « fÝ K ( ) ü ¹ � & �(a) K ( % ä �(b) K ( � % ä ..................... 67�

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VIII

C 4-16 ª ­ ® ¯ Sequence $ ' Ñ ....................................................................... 67�

C 4-17 ª « ¬ m * ¹ � & �(a) � m * �(b) m * ................................................ 68�

C 4-18 ª ­ ® ¯ � � � C ................................................................................ 68�

C 4-19 . / 0 = Ë C ........................................................................................... 69�

C 4-20 + , öª « ¬ s^ . / 0 � - ' R l ................................................. 69�

C 4-21 ¨ © i.ö / à 0 s^ 6 7 � < = ý åÇ È 1 2 ¨ © *õ3 0.6°�p *

åÇ È 4 8 ¨ © *õ3 0.4° ........................................................................... 70�

C 4-22 ª « æ ç C�c d � 20087 6À 10¼�(a) ý å�(b) p *å ............. 71�

C 4-23 åàæ ç E c d C ä �(a) ý åæ ç �(b) p *åæ ç �(c) Ì · æ ç ..... 72�

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IX

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1.1 � ¸ �ª « ¬ { ù Ð â ã .................................................................... 40�

3.1 ý å· p *å � � � � kü 5 § � � � � õ f ......................................... 40�

4.1 . / 0 / à 0 ^ õ f � ú .......................................................................... 40�

Page 12: FW:

X

� � � � � � � � � � � �

a ý å(altitude)

ET � c ç (equation of time)

H ¨ © c å

Gs � 6 7 8 � â

Gw 9 7 9 : 8 � â

lst ) a c d ^ò / � � �

llocal ) a ^ù à

LST � ¨ © c

n 0 7 ; <^ï f

tsolar = ¨ © c

b > E ?

α á ù (right ascension)

β ß ø (latitude)

γ p *å(azimuth)

φ ) a ø à

ε ß á@å�obliquity of the ecliptic, ε = 23°26’20.512”�

λ ß ù (longitude)

δ á ø (declination)

θz ï A å

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� � �� � �� � �� � � � � ���� � ���� � ���� � ���

1-1����������������

Þ B � Z � C D CO2 E 6 ê F Ä � - � G 7ó ¤ H �� I Ì J = '  ^

� � �Ê K L Þ M N ·L O �; P Q ^~ � ·L ó 8 R Þ B � Z � · S N � T

U ( �� �·L V G ^w � W � +ö X � ~ � ·L �� I  ¨ © ·^� � �Y

Z [ \ +] % ù a r m � �� { ·}; ·�; ^ G ó V G � _ �l `,

¨ © ·{ À $ a 5 �: Û ^ b % r ¨ © · Ô c 5 { � � ^ d � � +

0 e ¨ © · { � ; � � ¨ © Ô (solar cell)}¤�i f Ô

(photovoltaic, PV)�ù ¨ © ¼Ú g Ù r i· � å H ·�l i � å ù Ð: x R

9 ( o I � ¸ Õ � �hC 1-1��] 2 ö¨ © Ô i d F � � ^ j k ¨ © Ô �

l i � å ù Ð3ö 15% ~ 20%� � � ö � o¨ © Ô � , III-V Ó l ± � �

Q � x R ^ � ï ' (multi-junction, MJ) ¨ © Ô ù Ð À Ä �Spectrolab y m ö 2007

7x R ^Ñ ï ' Ô ^i � å ù ÐÄ � 40.7%+Õ¨ © Ô ^ ù Ð;Y C D ¼

Ú ê n n Õ� Ä �B - � " ' <^Å i ü Å i�J o ? B ë ì ¨ © Ô ^ - � '

<�: Û J I ¨ © Ô Ì Í Î ¨ © · � i¬ (solar concentrator)�p ·u � ¨ ©

·�: Û `¤�Å iÆ ¨ © Ô (concentrated photovoltaic, CPV)� j k ¨ © Ô

·ÑÒ Ó � ï ' Ô p B # � CPV� ] ;8 �ù î Å i� Ä ^ ù Ð q Ä � 2 �

Í Î � i¬ +

¨ © · � i¬ ^� r ;� � i# �� ó n n Å � ^© i�: à - � Ì Þ Õ s

� ü � ¸ �^ � i¬ �] 2 à � ö CPV ® ¯^Å ii# �� ´ � � � Fresnel

lens û ü �E ú ¯ û ü � ¸ ö� t u v ü (Fresnel lens) w x ú ¯ û ü d � X y

��C 1-2��i� z è { � É Ù �> Å i]^[1]+� iÐ(concentration ratio, C)

B ô | �i# } S ' <(apearature area) E ¨ © Ô ' <(cell area)^ â # +C 1-3

Page 14: FW:

2

4 ; Araki ~ � [2]- � � Æ ^ ý þ Æ (dome-shaped) t u v ü ,; CPV ¨ © ·{

® ¯�� iÐ B �> 550�+CPV ® ¯ g 19707 N � � > � � �� � �� º

��� � k¼� ~ n � ^w . �: Õ 1 � 3 ä CPV � U ^[ { �] 2 [ { ^ CPV

^ � iÐ � 300 > 1000 � ~ �@ � Ä � iÐ � � �: Û `¤� HCPV (high

concentrated photovoltaic) ® ¯+

� � ' j � � i¬ (parabolic dish)[3]k � � � � � � i¬ (parabolic trough)[4]

Ê C 1-4 (a)�C 1-4 (b)� = �z � � � ¨ © { ·^u � �� ó n { � � � � � �

H I � 7 Ç { +] ? % Ã � ö HCPV ^ � i¬ s�Kusek ~ � [5]r � � j �

� i¬ � � h á �� E H t ^ ��Ê C 1-5� Í Î ÑÒ Ó Ñ ï ' ¨ © Ô +

� % Anton ~ � [6]- � = e � i^ � � ' Æ � i¬ �r Å � ^¨ © i= e Å �

�i � � s�í î i � � r ¨ © i ú ) �ÑÒ Ó Ñ ï ' ¨ © Ô �Ê C 1-6 (a)��

ÕÛ ® ¯ö= e � Ù ü i ^ - � s;� � ¦ � ' ü �J oi# � Q ¤�� � � ±

(Cassegrain)i# ® ¯�Ê C 1-6 (b)�+

� i¬ � � � Ä ï u ¨ © ·· ¨ © Ô ^ ù Ð�� Ì ·Â ¨ © # ß / ª « �

: Û � � ü � ¸ �^¨ © ª « ¬ �hC 1-7��é Ip � % é I} { � é I�

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¥ I�ª « ¬ ^ª « ­ ( ® ¯�! ª « ® ¯ $ � Ã Å Æ ­ & ' �� ¸ ª « ^ B Ç

à�� - ª « ¬ · � �> A � � Æ R �8 Ó � 5 K L È É�Û � ? r ö : � � -

ê , ª « ¬ � - ª « ^� ·+

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ó ¸ R ^ � � + � � ö ö v � � ÷ ø úû � ¹ ,kà � ö¨ © ª « ¬ s^

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õ+: Û B r ï Ð Ñ 7 H 0 � ï Þ�,a Þ�ï Þ R +ï � # Ò % ´ � � ¸ ^

p q ó ô | ï Þñò �,- & é Ño Ó � ^ï Þñò ® ¯�c � �J ß à ñò ®

¯(ecliptic coordinates)S�Jáà ñò ® ¯(equatorial coordinates)S·Ja ðñò ®

¯(horizon coordinates)S+

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a Þ ¹ º k × Ø � ï Þs^ Ü 5¤�ï Ü +áà ñò ® ;] 2 ï � # - � À ß

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á c ï Þ Y � I 15°(360°/24 = 15°)+

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® ^I � õ f�á ø å�c å��� � ò �á ø ö0 ï ^�Iê Ü á (±0.064°)�

h y �(2-3)+Â ª « ¬ ^Õ ó B 8 Ó ª ¼^ ª ·�Õ c å � ò � ^�I - _ ­ (

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ª « ¬ § � �+Û ñò ® ^ À 5�Ç È ^c å � §§ R d � �  D a Þ^ g �

§�Ê Û � · - _ Ç È � IE a Þg � 0 é �� h^ô *R q ;ö ô õ c r c å

� §§ R  / º Ü ÷ � E ï � � ¬ áà � 1 ¸ 9 T �� ] Û R q ^æ ç ¨ " �`

Ý ö � > ÷ 5 };l � � 5 : ø ¬ ­ ù w ß à+

ß à ñò ® � � ;,¨ © � I^ � � �G / ' �: Û r ß à ñò ® ^9 T �

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T *õ�Ê a ðñò ® ^ý å�p *å�+

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T Ë | § � �� 7 áà ñò ® � ô * Ü §^*õ�Ý ö � ` öª « ¬ Ç È ^ � ú

s�: Û � � ^¥ I�ª « ¬ ;� a ðñò ® �åà;, " úû ð ñ ~ ) ä �

� ­ ( ¬ í +

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kp *å�: Û Ì � 0 � Í Q � � û K ÷ b úû ¨ © � � ^y ��Á Â Û 0 Z �

Cucuno ~ � [22]� ü Í Q - � ö û 0 ÷ b k û 0 ù ø à^¨ © � � y ��Õñò

® ^úû � - � ^c d æ õ f· 0 e ¼ � � � ^ò / c d � ¸ �Goswami

~ � [23]ö� % � ü � � C � c d æ ^ ç � �,- á Ê � � c d æ ^ ç � ,

ka ðñò ® n åà^úû +

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¼ � � � ^ ý þ c d �`¤�� ¨ © c �mean solar time��; � a Þg �

å ½ ô | c d �g � 0 å � 360�56’�Ì c 24 á c �Õa ðñò ® Ü Ý ^c d æ

�Ø ï Ô , ¨ © � I}; Ô Õ ¨ © 6 r ���Ê ¼ � �� ô | �¤� . ¨ © c }

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= ¨ © c (true solar time)� = ¨ © c E � ¨ © c � Û ^ç # ¤�� c ç (equation

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a Þ | ¨ © 0 � � Ì ^ � - c d � 365.2422 ¼�� Ë r c d ^c � Y ß b ,

k � � ��: Û r þ 7 � ô � 365¼�� H a Þ E ¨ © 1  ^ = � c d �� > 0

e ý þ � - � ^ò / ð� c d +î - t y �[24]B å û ü ) a ^� ¨ © c

( ) 4min/ degsolar st localLST t ET l l= − − − + ⋅ (2-1)

l LST�� ¨ © c �lst� ) a c d � Ü Ý ò̂ / � � � �llocal� ) a ^ù à�

ET�� c ç

9.87 sin 2 7.53cos 1.5sinET B B B= − − � 360( 81) / 364 degB n= − (2-2)

2-2-2 * + � , �* + � , �* + � , �* + � , �

% C � á ø ^ô | B õ 2-1-2 Ê C � áà ñò ® ^ Î · �î C 2-1 B V �

a Þ ¨ © y � ^ð ' �¤� ß à ' � E a Þg � ^ð ' � > ð| �= � 1 ç

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7� �þ 0 ï ¨ © ^á ø å δö±23.45o � d ^�� � � �l úû y �[23, 24]

23.45 sin[360(284 ) / 365]o onδ = + (2-3)

l n� g 1À 1¼û � ^ï f�� n=1�4 � 1À 1¼�,Û I H �+

2-2-3 * + # �* + # �* + # �* + # �

: �a Þg � 0 � 3� 24 á c �¨ © þ á c g � � � � I3 15 �� ô |

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15 [ 12]osolarH t= − (2-4)

} B ó % H tsolar = 12�H×4 min/deg�l tsolar; = ¨ © c �c d � �� 24 á c

( ^c d �l c å� ¥ N c å � ò >� = ¨ © c ^ � � �� � c å� � N

¤ è = ¨ © c ^ � � +

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Ê - <

1or cos [ tan tan ]ss srH H ϕ δ−= ± − ⋅ (2-5)

l φ� ) a ø à+

2-2-4 * + - � . / 0 �* + - � . / 0 �* + - � . / 0 �* + - � . / 0 �

ý åkp *åî C 2-4 (b) _ V �� öa Þs Ô̂ ,��l � A � sp E ï Þ

^@5� P5�4 � ¡ ^ï A �Ô � �� � > ¨ © (S5) E ï A (P5) � d ^ ì å

θz H ;ä Ù å� ? ¤�ï A å�úû y �[23]Ê -

1cos [sin sin cos cos cos ]z Hθ ϕ δ ϕ δ−= + (2-6)

};Bó%Hýå a^y � �äÙ åEýå 1 O ��

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à�� ¹ p � × Ø � � d ^ ì å�l y � [22, 23]�

cos (sin sin sin ) / cos cosa aγ ϕ δ ϕ= − (2-8)

sin cos sin / cosH aγ δ= (2-9)

î �p * å^ � � ; & �±180°^� � �:Ûöú û � Ñ å X � ì f ^c

��Y A q b ô � b ^p * ååà �:�_>^ } > � 0 �� ; - � " ú û �

Ñ å X � ì f ��åà # � q � # � & �0° ~ 180°�Cucuno ~ � [22]� üy � (2-8)

ó ç � , s ^ l Û �ú û y � (2-8)�(2-9)^ cosγE sinγ�8 " I � ^ � ¥ � ç �

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p * ååà +

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V�¼ük¼ 4 cd � � ö & s ' 5�- � ê 5�¼Ú cd 3 � ( ác�ÂÚ p

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� ` � Â�ñ ò ® ú û � � ^æ ç �:Û� � � � ÷ ø (ephemeris)^ú û p q

ó @ A [25]� 1 C ú û � ¹ B h ö v A� ÷ ø Í �^7` � � � 2 2000 7�

� � 60007+

÷ ø ' � Ë ï � # ^ú û �ç � :� \ I · . ç ~ ï � ` � Õ � � 9 � ^

¨ © ýåkp * å�: l ö ÷ ø ^ú û % � >� ¸ 7 j ^�:�· ñ ò

® Ö Ö ) äï f � � 1 â �÷ ø ^ú û p � < w ã � ; < �� � â ã ñ ò ® E

÷ ø I � ö� ¸ 7 j ^¨ © ýåkp * åö � �^� � �:� � �) ï ^ýå

p * å� � ;0 7� À < D ^+l ö ÷ ø ^ú û � 7 j � � ^: ø �

:Ûc � % ü20057�20087k20117^ýåp * å � � · ñ ò ® â ã �C2-7

< = � �c ÷ ø Eñ ò ® ^ýåp * å� � �B � ü ê = � � � d ç � z á�

:Ûö� Crcd d � h áp B Ô Õ l ^ç � �î C _Vö 1 ¸ cd 5 �

-�åà ç � ^¹ à �Y " �0.2°�:Û�Y 6 � > ª « ¬ ª « ß à � Þ (<

0.5°)�:�ñ ò ® ^ú û è ¹ �Ì � � > ï � ` � ^ 6 � �:Ûy � â ÷ ø

^û � � § P �¹ � ú û ?Y %ù Ð �� , � � > ? ú û è ¹ ; < ^ ÷ ø �

- �ñ ò ® R �¥ I ª « ^f # ' û � Æ +

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������������ � � � � � � � � � � � � � � � � � � � �

3-1 ; < � � � � =; < � � � � =; < � � � � =; < � � � � =

%C � � - �^¦ §ª « Ç È ü Ê @ j Bõ A � ½[27] B · ^Ç È �

ú � ¹ �� ¦ §ª « Ç È Ä 3 1.5 m�� � C ë " á�60×60 cm2�Ç È Ì w ê ��

�HCPVi # � ���180 kg�;0 á � � � @ Ç �á � � ^ ð 5; ö � ç ó ,

k � @ ã �p * �� 0 p ' ?B , R � ò ó x R � � ª « ¬ ^9 Æ �l Ç È

^ g î à ;Ü Ú a ð ñ ò ® ^ýåkp * å I �åà þï ^� � �� � ¨ © |

^ � � +

Ç È ^ � ú C h C 3-1 [27]�¦ § p - � 1 ¸ ^= D 6 7 8 � �= D 8 � ^

] ^;� Ë - � � · � , ã á^ � � � I ýåkp * å^ � I �l Û 0 D 8 �

â � 1:6.25�; � � � 6 7 ^ � �ÕÛ = D 8 � â � 1:60�; � � 9 7 9 : ^

� �ª « ¬ ^ýå � I � � � 0°~90°�p * å � I � � �±120°�B­ � HCPV

� � w ê � 30 kg� E H 8 ^ª « ¬ � �C h C 3-2 [27]+

3-2 > ? @ A B C> ? @ A B C> ? @ A B C> ? @ A B C

� � ^9 T � û è k F � G z 8 � � ^ F 5 d H I � � �) ä0 � H

I ¢ � Ö Y � I 0 � f �Õ � I ^åà ¤ � å+ å + á = ß à +

Ä�B- �öÄß à � Þ ^ � � �n s � � ^ � I ·� � Ö Ì � ó� H I ) ä

^e f k J Ð �:Û � � Í Q - �5 £ � ­ ( § � ­ ( ® ¯+

� � Bc�Ñ o [28]< � \ F K (permanent magnet, PM)�B� F L

(variable reluctance, VR)�, k � Q � (hybrid)+

� \ F K � � �

PM � � � � ð È ÊC 3-3(a)� = �PM � � � ^ � � ;, � \ F K

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x H�æ PM � � � ^Ê �� � � �Ì � Ü Ç k F ô � � G * B , Ç � � ^

F �ö M _ c �   � � �Û � PM � � � ^ åY Ü Ú � � y ( � ¸ Õó

��á Ê N O P ® (alnico) F K � � � å ã " �� 45�} 90��Õ Q K ® (ferrite)

F K :B� Ü F � æ å ã á�� 7.5°k 15°+

B� F L � � �

C 3-3(b)� VR � � � ð È �· PM � � - � � \ F K R � � � �

¸ ^;�m^ � � ;, ı F y ( x H�ö � � � � ú % F �^ l Û -�A q ö

ô � � G ú %k F ^ l Û - �   � � +�è VR � � B , ù î � � ^ � ú ¿

_ ã " � � �z � ' ��Ì � ã " � � Eß b ô * � ¸ $ Ç s �J o � � ^

å0 e � � 15°+

� Q � � �

� Q � � � ;ð Q s · = o � � ^ ð 5�l È � ÊC 3-3 (c)��� � \

F K ^ � Ü Æ F d E��� G � ^ � Ü Æ F d O 1 R �-�$ %Ä � � , kÄ

ß à ^Ê �� å0 e & � 1.8°~3.6°� d +

� � Ê � � �

C 3-4 � � � ^Ê � � � �C ^ R §;þä^ H I f ] (pulses per

second, pps)�· 0 e � � � ¸ ^; � � %I = Ê � � � �c � � � I Ê � �

� ·î ¨ Ê � � � �ö � I Ê � � � -^÷ b ¤ � g � I ÷ (start-stop region)�

N Û÷ b � � B , C D ) ä ¢ � # ¸ � I �% _ �, k � � � �Õ À

" � I � � ;° � I H I Ð ì � 10 ppsc�· - � � E ) ä ¢ � ¸ � I �

% _ ^ À " � � �̧ T �À " g � I J Ð ° ^; � � öA ¥ � c�· -

� � E ) ä ¢ � ¸ � I �% _ ^ À " ) ä H I f ] �î ¨ Ê � � � E � I Ê �

� � � d ^÷ b ¤ � S � ÷ b (slew region)� � � öÛ÷ b · � · ) ä ¢

� ¸ ' � �] A q T c � I �% _ �0 U 1 è î ¨ Ê � � � ^÷ b � � �

rA q ' � +

î � � � ;��5 £ � ­ ( �A q 7 ¦ £ � ­ ( 0 o �� L , ¬ r � I

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åà æ ç V ú ç � �:Ûö2 � � � c�d � Ë } > � � ^ � � E � �

H� â �ö � · - ª « Ç È � � � I ^ � à -�Í )^ n n 6 7 8 � â � ÄB

¥ � ^ � � �%C � � ^¦ §ª « Ç È öýåkp * å� Ì � ­ � ^ � � , k '

� � à h ö v B+

3-3 @ A D E@ A D E@ A D E@ A D E

ýå @ j � � w ó g ÄÅ i ¨ © Ô � ��� � I ýå d � V W Å i � �

� I ^ S � �� � î C 3-5 (a)kC 3-6 (a) B_Výå � � G X � ~ � à ' I Õ

� � z - �:Ûýå � � ^Ê ��Ä � � ì � � �%C ýå @ j ^ � � k � � ú

û Bõ ö v B�� � � � �^ � � � � p � � [29]� � � ^ I Æ � � Q

� � � �:ÛB� >Ú Q Ç È Ì Þ ^Ä � � kÄß à +

Ç È � ú z � Y rú û ü^ � � Y s + ä f � � ; Z _ Ç È { � è �

^ l Û �á Ê [ ÷ � � H^ ÷ L �rY - ýå � � 1 è � � \ ô � � Õ � H Ç È

^ ] ^ +ö ê ÷ L ^ l -�r + ä f S 2+ õ C 3-6 � p � � ^

� � � � �2 �Æ � RK564AA-T30�4 � 1:30 8 � Ç �� � å� 0.024°

Õ À " M _ � � � 4 N•m�Ú Q Ç È Ì Þ +À 8 ÂÚ C 3-8 (a)�� ; � � � � �

� ú % 1 è \ ô � � ��Û � � BÍ ��ýå� I +

î C 3-5 (b)kC 3-6 (b) B_V p * åö � c K ^� � � à Y n n �:Û

w 5ö�2 / � � � � ^ � à ; _ · � Q � p * å � I ^ � à �2 �^ � ¹ ·ý

å � � 1 ¸ �õ ö v B ú û p * å^ � � � � �� � ^ + ä f ¸ o S 2+

õ C 3-7 � p � � ^ � � � � �2 �Æ � RK564AA-T10� 4 � 1:10

8 � Ç � � � å� 0.072°Õ À " M _ � � � 3 N•m� Ú Q Ç È Ì Þ + 6 7 @

j � �= D 6 7 ��Û 0 D 8 � 6 7 � 1:60 ^ 9 7 9 : �Û = D 8 � 6 7 �

1:6.25^ � 6 7 �� 8 ú û � � � � @ j � Ì � � +ÂÚ C 3-8 (b)�� ; � � �

� � � ú % 1 è \ ô � � ��Û � � BÍ ��p * å� I +

3-1;r ö v B ú û _>^ � � � Ì � � �� � õ f , k� Ê 2 �^ �

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� Æ � � � k 8 � â ` H � +

3-4 @ A F G@ A F G@ A F G@ A F G H IH IH IH I

� � � I ¬ ) ä^ ¢ � � H I �þ ) ä0 � H I * - _ � � k F |

° 0 � f � 0 e § ö ^ � � � I ® ¯B Ø ï - � H a � � ¬ �pulse

generator�� � ^ H I é I �Bû è b þä� � ^ H a � c ­ ( � à �Õà �

ö� � ^ � � d � rú û ¨ © ýå�p * ååà � å � H I ¢ � �l å

à ^ n 8 �> d ` �� � �:Û�· - � H a � � ¬ R �ª « Ç È ^­ ( ¬ -

��� [ \ , �� " R �ª « ¬ � I ® ¯^ ��û è ¹ � ^$ %råà K (

ú e � � � ­ ( � � � � � � � I ¬ �ï � í � � �k � � ­ ( f�l g �^�

� Ê-+

� � � I ¬

� � � I ¬ � � A q | ­ ( � � ^I R �Õ Õ � I ¬ � - s B. �

� � � �^0 @ c�l � Ï · ;r­ ( í ) ä^ ¢ � ú e � � � , k� � �

� L �C 3-9� � � ·� I ¬ d ^ ï � = Ë C+

ï � í � � �

- �[ � V G Adventech Æ � � ADAM-3952 � í � o �� DIN � � 50-Á

SCSI ï � í � � �+ h ï � í � � � i ´ § ö B Ç ^ ï j >� � ­ ( f^n �

Á k �l � R �; î ï ýå· p * å I §^ � � � � � (CW/CCW) ¢ � � �r

¢ � ú ) � � � � I ¬ , kV ú � � � ­ ( f�í � o E � � � I ¬ ï � ^p �

ÊC 3-10+

� � ­ ( f

® ¯ � - �^ � � ­ ( f� [ � V G Adventech ^ � l �Æ � �

PCI-1240U� � � ­ ( f À � B ­ ( ê §� 1 Ý � � � k m W � � ® ¯�:

Û Í Q �ó ­ ( ¦ §ª « Ç È �� � ­ ( f^Ï �ö�· � - �� "$ � n ­

� � ^· 5 �Bû è ¹ � ^$ %2 / Ì � ^Ï · �ö� � 4 ;��¹ � ú û ü

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åà K ( ú e � ­ ( f�û è ­ ( f� I � � ��r � � � I K ¢ V ú �

"+

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�� ��� ��� ��� � � � �� � �� � �� � � � �� �� �� � � � � � � � � � �� � � � �� � � � �� � � � �

4-1 � F � �� F � �� F � �� F � � J =J =J =J =

¥ I � ª « ¬ ^ª ­ ¹ � $ % - �� F � ¬ National Instrument ^É , �

� LabviewÛ 8o�Labview;0 p C­ � �� 4 � ^ ì f � , C p = �

- _¹ � ^$ %· � � ¹ � �¹ � $ %� q · , Ø Ô ^p � r %�� $ %� � �

^� Ç & ' �A � � � n ­ } ` K ( � s �s % Ü t ^ * ��+Õ Labview

4 � ^ I/OE z ¢ ¹ � u $ % z � î ð Ï · �Bî ï û K � ¬ �L , ¬ �} � �

& ' �:ÛB , ö�� " ð o s { f E ^ } ~ p v �æ ª « ¬ � I ® ¯ � �

Labview R �5 { ¹ � � �+

¹ � r % � ¹ ÊC 4-1 � = �ª « ¬ ^ w x * õ � ' ô a T ¹ Ü Õ> 0 e °

¹ Á� ° ^a F ¹ Ü �:Ûª « ¬ ö � - ' � � 2 Ì � rp * å y � � ' ô a T

¹ Ü �� ü ^ y � z Bõ A � ½[27]^p q +� 8 í î Û = \ & é ^y � ú

û ü¨ © ýåkp * å�råà f # ú e �� I � � í é I �¹ � � ô ¨ © ýå

kp * åþ � I 0.2°� I 0 e �Û { ;� � Ç È � � �, n ¸ æ ç , k w x *

õ æ ç � � H^åà 9 � �öª « ¬ � æ ç d � á� 0.5°^` ( -�þ 0.2°�

I 0 e ª « ¬ B � % 0.3°^æ ç | Ý # +� � � Ë c } ª « ðñ �d � ! ¹ � )

üþ 0.2°d � ^ � � � I ^cd E h cd Âà ^ú û ^ýåEp * å�~rs ·

K ( % C·n s ª « æ ç ^ýåEp * å # â ã +

î C 1-9kC 1-10BV 4 * ; - �¦ §ª « ¬ ª « ¨ © �� ¿ _^¼Ú ê

ö- � Ò 5 " ~ � 8 �:Û � ô - � Ò 5 l � 8 �¹ � * ï _ ª « � Õ m * � w

x * õ +

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4-2 � �� �� �� � � � K L� � K L� � K L� � K L

Ü Ý� ¸ Ï · c�Ñ @ j c 5 r %�À 8 ~ Q 0 � H $ % E ª « Ï · ^

¹ � �ÛR q ð 5ö�Br, � « ¹ � & r %^¹ � ¿ ��0 ! ¹ � � �(sub

VI)�ö Q � ¹ � c � Ì � î ð ! ¹ � ^f # ï í 5 4 B�Â� r % $ ' ^

§ P , k¹ � ^ x � | � z " +

J Ñ @ cc � �<cd ì f ¹ � �åà ú û ¹ � ·� I í î ï ¹ � ªcd ì

f ¹ � ;ð Q åà ú û ¹ � �Ü Ý "cd ú û üEcd Âà ^¨ © ýåp *

å�Õ� I í î ï ¹ � �;Bråà # ú e �� I í �é I � � �, -� � � �

¹ � ^ r % � ¹ +

4-2-1 # $ M N O 8# $ M N O 8# $ M N O 8# $ M N O 8

¨ © ýåkp * å � � f ;ó g cd ^� � �� � ) a cd , k0 7 ^

; < ï f �:Û r %cd ì f ¹ � Â�åà ú û ¹ � Ì � 0 �· � 4 c ¿ S cd

K ( ^ ! ¹ � � �+LabviewÂ�cd � � ^� f � å � � ´ � � �^��� �

- ��� , åà ú û ¹ � Ì � ^cd � f p · � , Labview 4 � ^��� � _

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^K ( î ð Y ± é ¹ � A q � | �:Û d � � Í )^rK ( � � # � å �ÊC

4-2 � = +

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' �� d � å �l � � � �� 8 � Ë � rcd R � ) äåà ú û ¹ � ^� f +

~2 � Format Date/Time String � � Ü � î ï c%H�c%M�ä%S R �cd

} S �� - � Decimal String To Number � � rcd E � � å �f E � � +Õú

û 0 7 ; < ï f ^ } ~ p q �; - � Get Date/Time In Seconds � � î ð

Seconds To Date/Time � � � ) ü^f # I Æ ; � Q K ( � � �:Û��

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UnBundle � � �r day of year^f # } S üó �B ) ü, f E � � < = ^0 7

; < ï f � E H 8 ^� Ç & ' ÊC 4-3�þ� | 0 e * Y g I } S "cd +

À 8 �rÛ¹ � , ! ¹ � � �^ � � � ��6 äåà ú û ¹ � +

4-2-2 �� 6 & O 8�� 6 & O 8�� 6 & O 8�� 6 & O 8

Labview ö ã Ä � ^o � 4 � B�ä M file ^ MathScript � ��B1 Ý

MATLAB %H^¨ © ýåp * åú û ¹ � �� d \ � � É cd , C ì f � �

a ð ñ ò ® ^ýåp * åy � +) äcd � f p ' ;, s 0 á Ê E H^cd ì f

¹ � # � ! ¹ � � ��c � r MathScript � � ^c�c�ä , k0 7 ^ ; <

ï f ·cd ì f ¹ � ^ ï í 5î ð�ÊC 4-4 � = +

) ü í 5 @ j �;þäý ú û ü0 �ýåkp * å^f # ��� £ G ð È

^ � * � � ¬ (shift register)rf # ú e >-0 e � | ^ £ G �rf # ·-0 e ú

û ü^ýåp * åf # # 1 8 ^I R �_>^ç # 4 N ýå· p * å� n n }

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cd � _>^ç # ? A q " � 0.2°�ýåö Ç G � ^cd ^åà � � � � ;

��� � p * åö � � � c K ^åà � � � à Y � Ä�þä� I 0.067°�� ,

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; true} false | I R �� ;ç # " � 0.2°�� true�ÊC 4-5 (a)�¹ � Y rÛ

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� � ;á� 0.2°�� false�ÊC 4-5 (b)+

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à ú û �ö r % $ ' n n millisecond multiple � � �Ü Ý ) ä^ä f (ms) ~ ô

¹ � ú û ^ × � cd �b � åà ú û ¹ � · � þd � 0.2°) ü0 �ýåp * åf

Ý�Û¹ � �ª ­ ® ¯^ ��:Û�Ì � � � � ! ¹ � � � E ¹ � & h C

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4-6+

4-2-3 P � Q R S O 8P � Q R S O 8P � Q R S O 8P � Q R S O 8

® ¯^� I í 4 ; � � ­ ( f�:ÛA q - � Labview 4 � ^ ì f C r %

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D ä H I f �0 � H I Y � I � � * � 0 �l AzE Alt^ ) ä � c

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� � � ; 6000 pps�B Ü Ý� ¸ ^Ì � ó�ýå}p * å^ � � �Movement mode

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I ;° )� � � I � ¬ � 8 �-0 V � ; � ¨ � I �;î % _ ^* õ � I ��

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'+

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. � � f �� ,ý å å àæ ç � > ­ ( ª '^ 6 � Ö ` �y �æ ç· ) ä cdæ

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ç � � � � BH�0 � ô ® ¯ [27]�: Û BH ° 4 - ï � � � ® } ³ ï �lª«

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ð Q I k¥ I I o ª« p �^ ð 5 �î �æ çB í î I � � � ç � �Â

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B h á ­ ( ® ¯ ^ � < �Ö Ì � x R ² ¼ ³ k Z © ^ � ´ Ç µ 4 Br cdõ

� : � +

3. ] 2 ê , ^ª« æ ç p ; ,� ¸ 8 � � ò ó B� � * õ L , , õ(position

sensitive device, PSD) [31]�r . / 0 ë@^/à0õ å � PSD � � �� �

ä � , � � ^ @i�^i�c¶�~ ô i� ! * õ� Õ Ý Û W � ¨ ©

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� � � �� � � �� � � �� � � �

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Akisawa, N. J. Ekins-Daukes, H. S. Lee, M. Yamaguchi “Development of

concentrator modules with dome-shaped Fresnel lenses and triple-junction

concentrator cells,” Prog. Photovolt: Res. Appl. 13, pp. 513-527, 2005.

3. � � SES · L y m http://stirlingenergy.com/

4. � � � F ~ � · L � @ � NREL http://www.nrel.org

5. S. Kusek, J. Karni, M. Caraway, M. Lynn, “Description and performance of the

microdish concentrating photovoltaic system,” 4th International Conference on

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6. I. Anton, D. Silva, G. Sala, A.W. Bett, G. Siefer, I. Luque-Heredia, T. Trebst,

“The PV-FIBRE concentrator: a system for indoor operation of 1000X MJ solar

cells,” Prog. Photovolt: Res. Appl. 15, pp. 431-447, 2006.

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8. � � Zomeworksª« ¬ http://www.zomeworks.com

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2002.

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14. · � ¸ �¹ � i�¨ © i{ ª­ ® ¯ [ x º�� � o � " # Ç » ¸ ¹ # ®

&) � ��20037+.

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system,” Solar & Wind Technology 7, pp. 611-617, 1990.

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sun-tracking,” Renewable energy 29, pp. 393–402, 2004.

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Energy Conversion and Management 45, pp. 1931–1939, 2004.

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20. S. Abdallah, “The effect of using sun tracking systems on the voltage–current

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Conversion and Management 45, pp. 1671-1679, 2004.

21. á à ñ ò ® ¯ Ea ð ñ ò ® �h� G x V

http://zh.wikipedia.org/w/index.php?title=%E9%A6%96%E9%A1%B5&variant

=zh-tw

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29

22. M. Cucuno, D. Kaliakatsos, V. Marinelli, “General calculation methods for sorlar

trajectories,” Renewable Energy 11, pp. 223-234, 1997.

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Taylor & Francis, 2nd Ed., 1999.

24. ¼ � ( �ß ½ ¾ �¿ � � �± � � �À Á  “ ¨ © · ª¼® ¯ � [ \ <Û 0

Ã<y �^ / b � ” � ¾ � Û 25 Ä 5 ¸ ¹ [ 9 Y , pp. 2148-2153, 2004.

25. I. Reda, A. Andreas, “Solar position algorithm for solar radiation applications,”

NREL/TP-560-34302, January 2008.

26. a Þ c· Å Æ cd^ç # http://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html

27. A � ½ �¹ ¨ © ª« ¬ � � úE , ;º�� � ! " # Ç » ¸ ¹ # ® &) �

��20087+

28. � Ç t \ ���������� � V G C� y m �19947+

29. � p � � http://www.orientalmotor.com.tw/

30. [ � V G http://www.advantech.tw/

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Springer-Verlag Berlin Heidelberg 2007.

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� �� �� �� � A � � � ! " # $ %� � � ! " # $ %� � � ! " # $ %� � � ! " # $ %

A-1 ` a b B C` a b B C` a b B C` a b B C

Û úûp q ; Ü Ý Reda· Andreas [25]�� ¨ ç � úû¨ © ý å kp * å ^

õ f �� � ß ø �ß ù�á ø å �á ùå ,kcå �x Û � � �î �a Þ Ô Õ ¨

© ^* õY : � Ô Õ � � öa ^ � È �É à�Ê Ë Ä à� ¸Õ � � . ç�ö ÷ ø

^úû Y � J � : ø � ç � �ç � � 8 ^¨ © � � æ çê & �¬0.0003°�

Û ç � úû^p q Í � ^7` � � � 2 20007�� � 60007+

A-2 c d e 6 &c d e 6 &c d e 6 &c d e 6 &

÷ ø ^úû - � ^¼½ � Ì ê ¼(Julian day)�Ì ê ¼; 0 o � � 7À^

r ½ Í ¼q � § % � JD�; ° î y � 2 4713 7 1 À 1 ¼� Î b Å Æ c � 12

c5 x � ùè ^ï f �� �ï �# F � � �� ,R �ï �# ^ � 0 ø q �Ï � ¸

ø q ^7 ¯ 0 � ó �Ì ê ¼^úû; ÷ ø À w ? ; À w � ^ ) Ê �,ï f

úû^� Ë ö� � _ V ) ca Þ En ï � (��; Á ¨ © ) � d^ ' I l �l

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l Y�7j� á Ê 2000�2003 ~ ~ �M�Àj� á Ê 0 À H 2� 1�,Û I

H+� � Ð Ë ^; � M<3�� y � ^Mk Y Ì � ç � � Y=YÏ1�M=M +12+

D � decimal time�; rcd� H ï f ^ ��á Ê Ï � À^ 2� 12c 30

c 30 ä(UT)�D=2.521180556�Ì Ð Ë ^; � r ) a cd å ûH Å Æ c

B �úûü ó ^ JD<2299160�� = ) c� � � ^ ø q � Ì ê ø (Julian

calendar)�� B=0ª� JD>2299160�� = � � ^ ø q � � Ñ ø

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úû ø ¼(Julian Ephemeris Day, JDE)

86400T

JDE JD∆= + (A2)

úû Ì ê Í � (Julian century, JC),k ø Í � (Julian Ephemeris Century, JCE)

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c^ô | �a Þ '^cdò / +õ � � � F Ô Ð Õ ¨ Ð Ì Ö NASA [26]^�

$ % 1C ^ ∆Túûp ��î úû^�� B _ V ∆Tö0 7� p �ô # +

7j& � 1986> 2005dF

∆T = c0 + c1t3Ï c2t2 + c3t3 + c4t4 + c5t5 (A6)

l n � ä f c � � c0=64.86, c1=0.3345, c2=0.060374, c3=0.0017275,

c4=0.000651814, c5=0.00002373599�t = y – 2000�y = � � 7j + (Àj – 0.5)/12�

7j& � 2005> 2050dF

∆T = c0 + c1t + c2t2 (A7)

l n � ä f c � � c0=62.92, c1=0.32217, c2=0.005589�t· y^ô | ·(A6)�1

¸+

,s � % t ü ·` N ^7jï G ^û��l X 7j^ ∆TúûB,õ

NASA^� $ [26]�úû^7j � � î � � 2 19997> � � 30007+

A-3 6 & e f6 & e f6 & e f6 & e f � g� g� g� g hhhhe f � ,e f � ,e f � ,e f � , i .i .i .i . e fe fe fe f j � _ kj � _ kj � _ kj � _ k

¼ R ^ Ë × ; ,¨ © R úûa Þ * õ�Bõ [25]ö v � ö ^a Þ å ½

õ f æ(Earth periodic terms)� � ± úûa Þ ¼ R ùà^ L0æ

Page 44: FW:

32

0 cos( )i i i iL A B C JME= × + × (A8)

0 00

n

ii

L L=

=∑ (A9)

l Ai�Bi�Ci� A-1 L0æ^ Û i t õ f �n� L0æ � % ^t f �Õ¼ R ù

à^ L1�L2�L3�L4k L5æ^úû Ê ¸(A7)k(A8)

úûa Þ ¼ R ùà L ( Ö à)

2 3 4 50 1 2 3 4 5

810L L JME L JME L JME L JME L JME

L+ × + × + × + × + ×

=

(A10)

r Ö à å û�å à

(in radians) 180(in degree)

LL

π

×=

(A11)

l L^å à � � ; 0°~360°�a Þ ¼ R ^ø à B,k Ö à ô ê R^úû � ¹ ¸

�� (A8) ~ (A11)

A-4 � f� f� f� f * + � ,* + � ,* + � ,* + � , . � g. � g. � g. � g

r A-3 úû�� _ >^¼ R ß ù Lk¼ R ß ø B c � + ä - t I �� ú

ûa R ¨ © ß ø βk ß ù Θ:

180LΘ = + (A12)

l a R ê , ^ ß ù � � ; & � 0° ~ 360°

Bβ = − (A13)

A-5 � g l � . m l �� g l � . m l �� g l � . m l �� g l � . m l �

a Þ \ I ^H : ó g�¨ © EÀ Þ 5 6 5 ^ 6 � ��� (A14) ~ (A18)�úû

a Þ : D ¨ © y � EÀ Þ 6 � a § 9 ã ^õ f +,- ^ � * p �å à+

úûÀÞ·¨©�d^ð�Ø�à(elongation)

Page 45: FW:

33

32

0 297.85036 445267.11148 0.0019142189474JCE

X JCE JCE= + × − × + (A14)

úû¨©^ð�G 5 å (anomaly)

32

1 357.52772 35999.05034 0.0001603300000JCE

X JCE JCE= + × − × − (A15)

úûÀ¥^ð�G 5 å

32

2 134.96298 477198.867398 0.008697256250JCE

X JCE JCE= + × + × + (A16)

úûÀ¥^ø àå â (argument of latitude)

32

3 93.27191 483202.017538 0.0036825327270JCE

X JCE JCE= + × − × + (A17)

úûÀ¥^ ¼ @ 5 ù à(longitude of the ascending node)

32

4 125.04452 1934.136261 0.0020708450000JCE

X JCE JCE= − × + × + (A18)

N ä A-2 ^ õ f � � � (A19)·(A20)�úû ∆ψik ∆εi

4

,0

( ) sin( )i i i j i jj

a b JCE X Yψ=

∆ = + × × ×∑ (A19)

4

,0

( ) cos( )i i i j i jj

c d JCE X Yε=

∆ = + × × ×∑ (A20)

l ai, bi, ci, di � õ f a, b, c, dÛ i t ^ õ f �Xj � ; � � (A14) ~ (A18)úûü ^

X0 ~ X4�Yi,j � ; Y0 ~ Y4 ö Û i t ^ õ f �úû� õ Ú ^ � B õ [25]� ö^ å

½ +

À 8 B úûü ß ù \ I ∆ψk � \ I ∆ε

0

36000000

n

ii

ψψ =

∆∆ =

∑ (A21)

0

36000000

n

ii

ε

ε =

∆∆ =

∑ (A22)

Page 46: FW:

34

A-6 ������������������������������������

y � (A13) _ > ^ ß ø f # 4 � = � ^ ß ø �:� � � a § ^ . ç } \ I

` � Ê K � I �¨©^ ß ø d ô ï G 0°�:� ¨©^ ß ø ; ð| ö ß à s �ö

v A-5 úû^g á � ê * Ø � a Þ � > E � Þ� �Õ ; 0 ê 0 ^Þ� +Õ a R

, ê ^ ß ù � Y � > \ I ^ 6 � �õ Ú öv A-2 % 1 C ç � ä f ^úû�ç �

^ ß ù λúûy � Ê - F( � * � å à)

λ ψ τ= Θ+ ∆ +∆ (A23)

l

20.48983600R

τ∆ = −� 0 ç � õ f �∆ψ � ß ù \ I

A-7 � � � �� � � �� � � �� � � �

ß á @ å ; ° ß à ' · a Þá à ^ ì å �ö � � a § \ I ` � c B r Û ì

å . � ô # (ε = 23°26’ 20.512” )�ö ÷ ø ^úû :� � \ I ` � �� , = �

^ ß á @ å Ì � r a § 9 � ^f # ( � \ I ∆ε) n s ð� ß á @ å (mean obliptic

of the ecliptic, ε0)�úûy � Ê - F

úûð� ß á @ å ε0� � * � Ù ä � 2 3 4 5

0

6 7 8 9 10

84381.448 4680.93 1.55 1999.25 51.38 249.67

39.05 7.12 27.87 5.79 2.45

U U U U U

U U U U U

ε = − − + − −

− + + + + (A24)

l U=JME/10+

úû = � ß á @ å ε� � * � å à�

0

3600ε

ε ε= +∆ (A25)

A-8 � � � � � � � � �� � � � � � � � �� � � � � � � � �� � � � � � � � �

Ú ÷ c ^� Ë ; � úûü ) a ^c å �Ú ÷ c � � � ; c d � * �Õ ; · c

d 1 C ^å à+

Page 47: FW:

35

úû� Ú ÷ c (mean sidereal time in Greenwich, ν0)

0

32

280.46061837 360.98564736629 ( 2451545)

0.00038793338710000

JD

JCJC

ν = + × − +

× − (A26)

A-9 � �� �� �� � � � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � � α � �� �� �� � δ � �� �� �� �� � � �� � � �� � � �� � � �

ç � E a § \ I ^: ø �8 �* Ì � r ß à ñ ò ® � å � á à ñ ò ® �- t

� � � úûî a Þ R , ê ^ á ù αk á ø δ , k ) a c å (observer local angle,

H)F

sin cos tan sintan

cosλ ε β εα λ

−=

(A27)

sin sin cos cos sin sinδ β ε β ε λ= + (A28)

l áù α ^ åà �� & � 0° ~ 360°� d

localH lν α= + − (A29)

l ν�Ú ÷ c �llocal� Ô , � ^ a T ùà �� ù� � � � ù� ¥ �

A-10 ����� !"#����� !"#����� !"#����� !"#

�� (A27)~(A29) � ú û ^ áù�á ø kc å p ; , a Þ R � Ô , * õ �

ú û ^ �Õ � - s 0 e Ô , ¨ ©* õ Y : �a T = � ^ � ¸ � � . ç �� , ö ú

û ¨ ©^ ý åkp * å� 2 � d � ± ç � . ç (parallax) + ó ^ åà ç �

ú û ¨ ©^ © ð . ç åà

8.7943600 R

ξ =× (A30)

ú û . ç ç � õ f æ u� Ö à �

tan 0.99664719 tanu ϕ= × (A31)

Page 48: FW:

36

l φ�a T ø à +

ú û . ç ç � õ f æ x

cos cos6378140

Ex u ϕ= + ×

(A32)

l E� Ô Õ � ^ ) a Ê Ë Ä à � � * �y � �+

ú û . ç ç � õ f æ y

0.99664719 sin sin6378140

Ey u ϕ= × + ×

(A33)

A-11 � �� �� �� � $$$$ � � � � � � � � � � � � � � � �

ú û : � . ç ± é áù^ åà � ê ∆α

sin sintan( )

cos sin cosx H

x Hξα δ ξ

−∆ =− (A34)

ç � � = � á ø δ’

(sin sin )cos( )tan '

cos sin cosy

x Hδ ξ αδ δ ξ− ∆=− (A35)

ç � � = � c å H’

'H H α= − ∆ (A36)

l . ç ç � æ ξ, x, y ^ ú û p �ö ö v A-10 % � � +

A-12 � % & ' � � ( ) �� % & ' � � ( ) �� % & ' � � ( ) �� % & ' � � ( ) �

r�� (A35)�(A36) ú û _ ü ^ = � á ø �c å�N ä y �(2-7) ú û ¨ ©ý

å�_ > ç � 8 ^ ý å a0�x Û� � a d � � " � É Ù ^ Z � �ç � y � Ê - <

00

283 1.0210.31010 273 60 tan( )

5.11

Pa

T aa

∆ = × ×+ +

+ (A37)

l P� ) a ÷ b ^ " � È 5 �T� ) a ÷ b 7 � É

À 8 ry �(2-7)·(A37) 1 n B _ > = � ¨ ©ý å a'

0'a a a= +∆ (A38)

Page 49: FW:

37

¸ T �r�� (A35) ~ (A38) ú û _ ü ^ = � áø �c åk = � ¨ ©ý å�N

ä p * åy �(2-8)�(2-9) I ��ú û c ¸ o Ì � 8 " � � E X � ^ � ¥ � �B _

ü ç � 8 ^ p * å γ’+

Page 50: FW:

38

�������� B � � � � � � � � � � � � � � � � � � � � � � � � � � � �

B-1 * + ,* + ,* + ,* + , - . / ��- . / ��- . / ��- . / ��

õ C 3-4k 3-5 ý åp * åö � � � � ) ï þ � I 0.2°� d � ^ c d �

Õ � 0 ; ý å} ; p * å�d � c d ö Ç G � � c K p Y h �� 4 åà ^ � �

ê ã " �3-2 Ê � > � � ^ � � E � � H � â �: Û d � ± ú û ý åkp

* å � �� � ^ À " # �Õ � � ; 7à åà � � ê À " ^ 0 ï �æ � � � � �

� · � Ú Q � � ) ï � � � � ^ � à �* � Ì � � l� Ê � ^ åà � � � à +

� � ) ï ý å � � ^ À " # � 0.00033°/sª p * å � � ^ À " # � 0.06°/s+

î � � � Ó � ^ � � � * � rpm�þ c ý V � f ��� , d � � rs · ^ ý

åp * å � �å û F

ý å � �

0.00033°/s×π/180°[rads]×60/2π[rpm] = 0.00055 rpm (B1)

p * å � �

0.06°/s×π/180°[rads]×60/2π[rpm] = 0.01 rpm (B2)

�� (B1)k(B2) ú û ^ � �� 6 7 ) ü í � Ì � ^ � ��î � ¦ § ª « ÇÈ

% ùè = D 6 7 8 ��� � � 6 7 8 �â (Gs)· 9 7 9 : 8 �â (Gw)�: Û � �

) ü í ^ � à d � � · 8 �â 1 Y F

ý å � �

0.00055 rpm×6.25�Gs�×60�Gw� Û 0.21 rpm (B3)

p * å � �

0.01 rpm×6.25�Gs�×60�Gw� Û 3.75 rpm (B3)

Page 51: FW:

39

B-2 * + , - . 0 ��* + , - . 0 ��* + , - . 0 ��* + , - . 0 ��

� � ^ ú û B rp * å § � H 0 � ¥ � w � ^ ¾ � o �ý å � B § � H 0 �

Ü Ý w � ^ Ý Þ �w � ^ w ê ; î � � w ê n s p * ås p ÇÈ ^ w ê �Ì w 3

� 100 kg+l Ì � Ð Ë ^ ; 9 7 9 : ^ 5 � ú ) ù Ð z ì �3� 50%�Õ � 6

7 ^ 5 � ú ) ù Ð � ã Ä �3� 80%+

ö p * å � � ^ ú û �� � � � ; Ø ï ö p * ås p �w ê ; Ý Ø ô - �

: Û d � ú û R � ö 9 7 s ^ w ê c ê �Û c ê ^ " á S ~ � 9 7 ^ 6 ååà �

� ÇÈ � - � ^ 6 ååà � 5.72°� æ B _ > R � ö 9 7 s ^ w ê c ê <

100 kg × sin(5.72°) = 9.965 kg (B4)

� - s � � ã 9 7 % K â ã �3� 0.35 m�� , � � ð � ô T ú û 9 7 s

^ � � T<

T = 9.965 kg × 0.35 m × 9.81 m/s2 = 34.22 N.m (B5)

x , 8 �â �ú û p * å � � ) ü í � � 8 �À 8 Y , + ä f � � ÇÈ �

� ^ + ä f � 2��_ > p * å � � � Ì � � T0<

T0 = 34.22 N.m / (60×6.25×0.8×0.5)×2 = 0.43 N.m (B6)

ý å � � � B § � ú û H 0 Ü Þ � w ^ á � �l� w ^ 5 Þ ; � � > ý å �

§ ^ â ã �Û â ã r à � 0.2 m� æ B � 4 ú û ü ý å � � ) ü í � � � À 8 ¸

o Y , + ä f �_ > ý å � � � Ì � � T1<

T1 = (100 kg×0.2 m×9.81 m/s2) / (60×6.25×0.8×0.5)×2 = 1.31 N.m (B7)

Page 52: FW:

40

1-1 � ¸ �ª « ¬ { ù Ð â ã

3-1 ý å· p * å � �� � kü 5 § � �� � õ f

� �(rpm) 8 �â � � 2 � Æ � � � ü 5 §

� � (N•m)

� � � � �

�(rpm)

ý å 0.00055 9 7 9 : :

1:60

� 6 7 :

1:6.25

RK564AA-T30

( 4 � 1:30 8 �

Ç)

1.31 0.21

p * å 0.01 9 7 9 : :

1:60

� 6 7 :

1:6.25

RK564AA-T10

( 4 � 1:10 8 �

Ç)

0.43 3.75

4-1 . / 0 / à 0 ^ õ f � ú

����� � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � H � � � ���� � � � �

2 2 0 400 0 0 02.69812 2 0.69812 400 0.0017453 0.10004894 0.13.39556 2 1.39556 400 0.0034889 0.19999983 0.24.09335 2 2.09335 400 0.00523338 0.29999965 0.34.79116 2 2.79116 400 0.0069779 0.40000051 0.46.18682 2 4.18682 400 0.01046705 0.60000006 0.67.5825 2 5.5825 400 0.01395625 0.79998787 0.8

8.97894 2 6.97894 400 0.01744735 1.00006509 1

Page 53: FW:

41

C 1-1 � ¸ ¨ © Ô � å ù Ð â ã [3]+

C 1-2 ú ¯ û ü E Fresnel lens â ã [1]+

Page 54: FW:

42

C 1-3 ý þ Æ Fresnel ü i · CPV � � �550 � � iÐ �[2]+

(a) (b)

C 1-4 u � ¨ © { · ^ � i¬ �(a)� � ' Æ � i¬ [3]�(b) � � � � � � i¬ [4]+

Page 55: FW:

43

C 1-5 , � � ' j � � i¬ ^ MicroDish t Æ �^ HCPV ® ¯ [5]+

(a)

(b)

C 1-6 PV-fibre �^ HCPV ® ¯ �(a)ë È C�(b) = e � i¬ � � [6]+

Page 56: FW:

44

(a) (b) (c)

C 1-7 � ¸ �^ ¨ ©ª « ¬ (a) � º � Tetra-Track ¦ § I� é I[7]�(b)�

� Zomeworks � § ¥I� { � (thermal-liquid)é I[8]�(c) � � Lorentz ¦ § I

� é I+

C 1-8 � i â 500 � - ¨ ©ä Ù åà 9 ç E ù Ð C ä C[10]+

� � â #

) ü Ï Ð â #

Page 57: FW:

45

C 1-9 I¦ § ª « ¬ Í � � � � � � � i¬ [16]+

Page 58: FW:

46

C 1-10 I�¦ § ÇÈ Í � � � � � � � i¬ E ý å � ô 40°̂ � � � � � �

i¬ � u � ^ ¼Ú ê â ã C� ß § � � � � 8 ^ ¼Ú ê �[16]+

C 1-11 ¥I­ ( ^ ¦ § ª « ¬ Í � ¨ ©Ø Ù ú · ý å � ô 32°̂ ¨ ©Ø Ù ú #

Ø Ù ¼Ú ê u � â ã [18]+

Page 59: FW:

47

C 1-12 � Q �ª « ® ¯ ª « � ¹ C[19]+

Page 60: FW:

48

C 2-1 áà ñ ò ® [21]+

C 2-2 a ð ñ ò ® <p * åî º 5 ( à Ë) 5 x �} ; � ¹ 5 ( á Ë) ô � p �ý å(�

Ë) [21]+

Page 61: FW:

49

C 2-3 0 7 � c ç � � C+

(a) (b)

C 2-4 ï Þ = Ë C (a) ß à ' = Ë C�(b) ä Ù åE p * å = Ë C[23]+

Page 62: FW:

50

C 2-5 ¨ ©á ø å0 7� � � C+

Page 63: FW:

51

(a)

(b)

C 2-6 è a ÷ ¨ © � � � � �(a) � � �(b) � � +

Page 64: FW:

52

(a)

(b)

C 2-7 ñ ò ® ·÷ ø ö � � ^ ç � �l ÷ ø , � ¸ 7 j ú û (a) ý å�(b)

p * å+

Page 65: FW:

53

C 3-1 ¦ § ª « ÇÈ � ú C[27]+

C 3-2 ¦ § ª « ¬ � � C+

Page 66: FW:

54

(a) (b) (c)

C 3-3 n � � � = Ë C[28] (a) PM��(b)VR��(c) � Q �+

C 3-4 � � Ê � � � [28]+

Page 67: FW:

55

(a)

(b)

C 3-5 è � � c � � � I J Ð þ 0.2°̂ � � � � �(a) ý å�(b) p * å+

Page 68: FW:

56

(a)

(b)

C 3-6 è � � c � � � I J Ð þ 0.2°̂ � � � � �(a) ý å�(b) p * å+

Page 69: FW:

57

C 3-7 � p � � � � [29]+

(a) (b)

C 3-8 � p � � � �� � Ê � C�(a) RK564AA-T30�(b) RK564AA-T10 [29]+

Page 70: FW:

58

C 3-9 � � � I¬ E � � � d ^ ï � = Ë C+

C 3-10 í � o E � I¬ ï � = Ë C+

Page 71: FW:

59

C 4-1 ¹ � � ¹ C+

Page 72: FW:

60

C 4-2 c d ì f ¹ �C +

C 4-3 c d ì f � Ç & ' C+

Page 73: FW:

61

C 4-4 MathScript � � E ! ¹ � î ï C+

(a) (b)

C 4-5 � � é I 8 " Ç ( �(a) ç # " � 0.2°�(b) ç # á � 0.2°+

Page 74: FW:

62

C 4-6 åà ú û ¹ �C +

C 4-7 � I í î ï ¹ �� Ç & ' +

Page 75: FW:

63

C 4-8 � I í Sequence $ ' 0 +

C 4-9 � I í Sequence $ ' = +

Page 76: FW:

64

C 4-10 � I í Sequence $ ' Ñ +

Page 77: FW:

65

(a) (b)

C 4-11 � � % _ ¹ � & �(a) � � ' � �(b)� � % _ +

C 4-12 � I í Sequence $ ' ê +

Page 78: FW:

66

C 4-13 ª ­ ® ¯ Sequence $ ' 0 +

C 4-14 ª ­ ® ¯ Sequence $ ' = +

Page 79: FW:

67

(a) (b)

C 4-15 ª « f Ý K ( ) ü ¹ � & �(a) K ( % ä �(b) K ( � % ä +

C 4-16 ª ­ ® ¯ Sequence $ ' Ñ +

Page 80: FW:

68

(a) (b)

C 4-17 ª « ¬ m * ¹ � & �(a) � m * �(b) m * +

C 4-18 ª ­ ® ¯ � � � C+

Page 81: FW:

69

C 4-19 . / 0 = Ë C+

C 4-20 + , ö ª « ¬ s ^ . / 0 � - ' R l +

Page 82: FW:

70

C 4-21 ¨ ©i. ö / à 0 s ^ 6 7 � < = ý åÇÈ 1 2 ¨ ©* õ 3 0.6°�p *

åÇÈ 4 8 ¨ ©* õ 3 0.4°+

Page 83: FW:

71

(a)

(b)

C 4-22 ª « æ ç C�c d � 20087 6À 10¼�(a) ý å�(b) p * å+

Page 84: FW:

72

(a)

(b)

(c)

C 4-23 åà æ ç E c d C ä �(a) ý åæ ç �(b) p * åæ ç �(c) Ì · æ ç +