ＯＴＥＣ
Vol. 18 (2013)，５〜16

低温度差熱エネルギーを用いた超小型バイナリー発電プラントのモデリングと非干渉化 PID 制御系の設計ప ᗘᕪ⇕࢚ࢿࣝࢠ࣮ࢆ⏝࠸ࡓ㉸ᑠᆺࣂ࢖ࢼ࣮ࣜⓎ㟁ࣉࣛࣥࢺࡢࣔࢹࣜࣥࢢ࡜㠀ᖸ΅໬ PID ไᚚ⣔ࡢタィ㡑 ᘓᴿ*1㸪᭷⏣ ㆤ*2㸪ụୖ ᗣஅ*3㸪ᮤ㻌 ⩔㢅*1
Modeling and Design of Decouple PID Control for Ultra Compact Binary Power Plant
Using Low Temperature Difference Thermal Energy
Kun-Young HAN*1, Mamoru ARITA*2, Yasuyuki IKEGAMI*3, and Hee-Hyol LEE*1*1

Graduate school of Information, Product and Systems, Waseda University
2-7 Hibikino, Wakamatsu-ku, Kitakyushu-shi, Fukuoka 808-0135, Japan*2*3Kyushu Electronic Technology Co., Ltd.

Institute of Ocean Energy, Saga University

Linear transfer function models of three inputs-two outputs of a 10KW class ultra-compact binary power plant are
built to design control system in this paper. Decouple PID control systems using pre-compensators with parallel
connection for linearized transfer function matrix models are designed to reduce the interaction of a multivariable
control plant. In addition, control results of two inputs-two outputs system and three inputs-two outputs system arecompared to confirm the control performance.
Key Words : Low temperature difference, Ultra compact binary power generation, Decouple PID control

1. ⥴   ゝ㏆ᖺ㸪໬▼⇞ᩱᯤῬၥ㢟ࡸ⎔ቃၥ㢟࡞࡝࠿ࡽ㸪෌⏕ྍ⬟࢚ࢿࣝࢠ࣮࡜ࡋ࡚ᮍ฼⏝⇕࢚ࢿࣝࢠ࣮ࡢ᭷ຠά⏝ࡀ┈ࠎὀ┠ࡉࢀ࡚࠸ࡿ㸬ᮍ฼⏝⇕࢚ࢿࣝࢠ࣮※࡜ࡋ࡚ࡣ㸪ᾏὒ⾲ᒙ῝ᒙ ᗘᕪ⇕ࡸᕤሙᗫ⇕㸪 Ἠ⇕࡞࡝ࡀ࠶ࡿ㸬ࡇࢀࡽࡢᮍ฼⏝⇕࢚ࢿࣝࢠ࣮ࢆ⏝࠸ࡓⓎ㟁ࡣ㸪ⅆຊⓎ㟁ࡸཎᏊຊⓎ㟁࡜ẚ࡭࡚㸪ࡑࡢ⇕※࡜෭༷※ࡢ ᗘᕪࡀ㠀ᖖ࡟ప࠸ࡓࡵ⇕ຠ⋡ࡀపࡃ㸪Ⓨ㟁㔞࠶ࡓࡾࡢࢥࢫࢺࡀ㧗ࡃ࡞ࡿ㸬⌧ᅾࡲ࡛ࡢ࡜ࡇࢁ㸪⇕࢚ࢿࣝࢠ࣮ࢆ⏝࠸ࡓⓎ㟁࡜ࡋ࡚㸪100 ୓ KW ⣭ࡢ኱つᶍᆅ⇕Ⓨ㟁࠿ࡽ 50 KW ⣭ࡲ࡛ࡢᑠᆺⓎ㟁ࡣᐇ⏝໬ࡉࢀ࡚࠸ࡿࡀ㸪ᑠつᶍᕤሙࡸ Ἠ᪑㤋࡛ࡶタ⨨ྍ⬟࡞ 10 KW ⣭ࡢ㉸ᑠᆺࣂ࢖ࢼ࣮ࣜⓎ㟁ࣉࣛࣥࢺࡢᐇ⏝໬࡟ࡣ⮳ࡗ࡚࠸࡞࠸㸬ࡑࢀࡣ㸪ప ᗘᕪ⇕࢚ࢿࣝࢠ࣮࡛࠶ࡗ࡚ࡶ㸪௚ࡢ෌⏕ྍ⬟࢚ࢿࣝࢠ࣮࡜ẚ࡭㸪Ᏻ౯࡟㸪ࡲࡓᏳᐃ࡟Ⓨ㟁ࡀ⥔ᣢ࡛ࡁࡿ⇕஺᥮ჾ㸪ࢱ࣮ࣅࣥ㸪࣏ࣥࣉ࡞࡝࡟ࡼࡾᵓᡂࡉࢀࡓ⇕ࢧ࢖ࢡࣝࣘࢽࢵࢺࡢ㛤Ⓨࡸసື፹యࡢ㑅ᐃ㸪ไᚚࢩࢫࢸ࣒ࡀ༑ศ࡟㛤Ⓨࡉࢀ࡚࠸࡞࠸ࡓࡵ࡛࠶ࡿ㸬୍᪉㸪ࡇࡢࡼ࠺࡞Ⓨ㟁ࣉࣛࣥࢺࡣከධຊከฟຊከኚᩘࢩࢫࢸ࣒࡛࠶ࡾ㸪ࡲࡓ㠀⥺ᙧ≉ᛶ㸪↓㥏᫬㛫≉࡞࡝ࢆ᭷ࡍࡿື≉ᛶࡀ」㞧࡞ไᚚᑐ㇟࡛࠶ࡿ㸬ࡇࢀࡲ࡛ࡇࡢࡼ࠺࡞ࣉࣛࣥࢺ࡟ᑐࡋ㸪㠀⥺ᙧࣔࢹࣝ࡜ BP ࢆ⏝࠸ࡓไᚚᡭἲ>@ࡀᥦ᱌ࡋ࡚࠸ࡿࡀ㸪Ⓨ㟁ࣉࣛࣥࢺ඲యࡢື≉ᛶࢆ⾲ࡍ⥺ᙧ໬ࣔࢹࣝ࡜ไᚚ᪉ἲࡣ㸪ᮍࡔ㛤Ⓨࡉࢀ࡚࠸࡞࠸㸬ࡑࡇ࡛ᮏ◊✲࡛ࡣⓎ㟁ࣉࣛࣥࢺࡢືసⅬ㏆ഐ࡟࠾ࡅࡿື≉ᛶࢆ༑ศ࡟ᤊ࠼ࡓ⥺ᙧ໬ఏ㐩㛵ᩘ⾜ิࣔࢹࣝࢆᑟฟࡋ㸪᧯స㔞࡜ไᚚ㔞㛫ࡢ㢧ⴭ࡞┦஫ᖸ΅ࢆ⪃៖ࡋࡓ㠀ᖸ΅໬ PID ไᚚ⣔ࢆタィࡍࡿ᭦࡟㸪ไᚚ㔞ࡢᩘࡼࡾࡶ᧯స㔞ࡢᩘࡀከ࠸ไᚚ⣔ࡢไᚚᛶ⬟࡟ࡘ࠸᳨࡚ウࡍࡿ㸬*ཎ✏ཷ௜ 2013 ᖺ 8 ᭶ 21 ᪥᪩✄⏣኱Ꮫ኱Ꮫ㝔᝟ሗ⏕⏘ࢩࢫࢸ࣒◊✲⛉ 㸦ࠛ808-0135 ⚟ᒸ໭஑ᕞᕷࡦࡧࡁࡢ 2-7㸧
E-mail: kyhan@akane.waseda.jp*2஑ᕞ㟁Ꮚᢏ◊ᰴᘧ఍♫*3
బ㈡኱Ꮫᾏὒ࢚ࢿࣝࢠ࣮◊✲ࢭࣥࢱ࣮
*1

5

6

韓建榮，有田護，池上康之，李羲頡

2. ㉸ᑠᆺࣂ࢖ࢼ࣮ࣜⓎ㟁ࣃ࢖ࣟࢵࢺ࣭ࣉࣛࣥࢺࡢᵓᡂᮏ◊✲࡛ᑐ㇟࡜ࡋࡓ㉸ᑠᆺࣂ࢖ࢼ࣮ࣜⓎ㟁ࣃ࢖ࣟࢵࢺ࣭ࣉࣛࣥࢺࡣ㸪⵨Ⓨჾ㸪จ⦰ჾ㸪෌⏕ჾ㸪ศ㞳ჾ㸪ࢱ࣮ࣅࣥ㸪 Ỉ࣭෭Ỉ࣭సືὶయ࣏ࣥࣉ㸪సືὶయࢱࣥࢡ➼࡟ࡼࡾᵓᡂࡉࢀ࡚࠸ࡿ㸦ᅗ 1㸧㸬᧯స㔞ࡣ Ỉ࣏ࣥࣉᅇ㌿ᩘ࡜෭Ỉ࣏ࣥࣉᅇ㌿ᩘ㸪ཬࡧࢱ࣮ࣅࣥධཱྀ㟁☢ᘚ㛤ᗘ㸪ไᚚ㔞ࡣࢱ࣮ࣅࣥධཱྀᅽຊ࡜ฟཱྀᅽຊ࡛࠶ࡾ㸪ไᚚ┠ⓗࡣ㸪ࡇࢀࡽ 3 ࡘࡢ᧯స㔞ࢆ⏝࠸࡚ 2 ࡘࡢไᚚ㔞ࢆᡤᮃࡢ┠ᶆ್࡟㏣್ࡉࡏࡿࡇ࡜࡛࠶ࡿ㸬ࢱ࣮ࣅࣥධཱྀฟཱྀᅽຊࢆไᚚࡍࡿ᧯స㔞ࢆ㐺ษ࡟ㄪ⠇ࡍࡿไᚚ⣔ࢆタィࡍࡿࡓࡵ࡟ࡣ㸪ไᚚᑐ㇟ࣉࣛࣥࢺࡢື≉ᛶࢆ⾲ࡍᩘᏛࣔࢹࣝࡀᚲせ࡛࠶ࡿ㸬ࡑࡇ࡛㸪ḟ❶௨㝆㸪㉸ᑠᆺࣂ࢖ࢼ࣮ࣜⓎ㟁ࣃ࢖ࣟࢵࢺ࣭ࣉࣛࣥࢺࡢ⥺ᙧ໬ఏ㐩㛵ᩘ⾜ิࣔࢹࣝࡢᵓ⠏㸪ཬࡧไᚚ⣔タィ࡟ࡘ࠸࡚㏙࡭ࡿ㸬Fig1Structure of ultra-compact binary power generation system using low temperature difference thermal energy

3. ㉸ᑠᆺࣂ࢖ࢼ࣮ࣜⓎ㟁ࣃ࢖ࣟࢵࢺ࣭ࣉࣛࣥࢺࡢࣔࢹࣜࣥࢢ3.1 ࢫࢸࢵࣉᛂ⟅ࡢ ᐃ⥺ᙧ໬ఏ㐩㛵ᩘ⾜ิࣔࢹࣝࢆᵓ⠏ࡍࡿࡓࡵࡢࢫࢸࢵࣉᛂ⟅ ᐃᐇ㦂ࡣ㸪ḟࡢ᮲௳࡛⾜ࡗࡓ㸬ࡲࡎ㸪⇕※࡛࠶ࡿ Ỉ㔞㸦60ഒ㸧ࢆࢫࢸࢵࣉ≧>60 ε/min (10Hz) → 283 ε/ min (60Hz) ] ࡟ຍ࠼㸪ࢱ࣮ࣅࣥධཱྀฟཱྀࡢᅽຊࢫࢸࢵࣉᛂ⟅ࢆ ᐃࡍࡿ㸬ࡇࡢ࡜ࡁ㸪෭Ỉ㔞>265 ε/min (60Hz) ] ࡜సືὶయ㔞>࣏ࣥࣉᅇ㌿ᩘ 60 Hz@ࡣ୍ᐃ㸪ࢱ࣮ࣅࣥධཱྀ㟁☢ᘚࡣ඲㛤>100%@࡜ࡍࡿ㸬ḟ࡟㸪෭༷※࡛࠶ࡿ෭Ỉ㔞㸦8㹼9Υ㸧ࢆࢫࢸࢵࣉ≧>120 ε/min (20Hz) →265 ε / min (60Hz) @ ࡟ຍ࠼㸪ࢱ࣮ࣅࣥධཱྀ ฟཱྀࡢᅽຊࢫࢸࢵࣉᛂ⟅ ࢆᐃࡍࡿ㸬 ࡇࡢ࡜ࡁ㸪Ỉ㔞

>240L/min(50Hz)@࡜௚ࡢኚ㔞ࡣ୍ᐃ࡜ࡍࡿ㸬᭦࡟㸪㟁☢ᘚࡢ㛤ᗘࢆࢫࢸࢵࣉ≧>40᧡→100᧡@࡟ຍ࠼㸪ࢱ࣮ࣅࣥධཱྀฟཱྀࡢᅽຊࢫࢸࢵࣉᛂ⟅ࢆ ᐃࡍࡿ㸬ࡇࡢ࡜ࡁ㸪ࡑࡢ௚ࡢኚ㔞ࡣ୍ᐃ࡜ࡍࡿ㸬 ᐃ࡟࠾࠸࡚ࡣ㸪ධຊᢞධ
2 ศᚋ࡟ࢫࢸࢵࣉ≧࡟ࡋ㸪ᐃᖖ≧ែ࡟⮳ࡿ 4 ศ㛫ィ ࡋࡓ㸬ࡇࡢ࡜ࡁࡢࢧࣥࣉࣜࣥࢢ࿘ᮇࡣ 3 ⛊㸪ࢹ࣮ࢱᩘࡣ 240ಶ࡛࠶ࡿ㸬
3.2 3 ධຊ 2 ฟຊ⥺ᙧ໬ఏ㐩㛵ᩘ⾜ิࣔࢹࣝࡢᵓ⠏ࡇࡇ࡛ࡣ 3 ධຊ 2 ฟຊ⥺ᙧ໬ఏ㐩㛵ᩘ⾜ิࣔࢹࣝࢆᑟฟࡍࡿ㸬ࡑࡢࣈࣟࢵࢡ⥺ᅗࢆᅗ 2 ࡟♧ࡍ㸬ࡲࡓ㸪 Ỉ㔞ࢫࢸࢵࣉධຊ㸪෭Ỉ㔞ࢫࢸࢵࣉධຊ㸪ཬࡧࢱ࣮ࣅࣥධཱྀ㟁☢ᘚࢫࢸࢵࣉධຊ࡟ࡼࡾ ᐃࡋࡓࢱ࣮ࣅࣥධཱྀฟཱྀᅽ

低温度差熱エネルギーを用いた超小型バイナリー発電プラントのモデリングと非干渉化 PID 制御系の設計

7ຊࡢࢫࢸࢵࣉᛂ⟅ࢆᅗ 3㸪4㸪5 ࡟♧ࡍ㸬ణࡋ㸪෭Ỉ㔞ࢫࢸࢵࣉධຊࡣ㸪ࢱ࣮ࣅࣥฟཱྀᅽຊࢆపୗࡉࡏࡿస⏝ࢆࡍ
ࡿࡢ࡛㈇ࡢ್࡜ࡋ࡚࠸ࡿ㸬 Fig2Block diagram of 3inputs-2outputs transfer function model  Fig3 Real response by Hot water step input Fig4Real response by Cold water step input         Fig5Real response by Solenoid valve step inputࡇࡢᐇࢫࢸࢵࣉᛂ⟅࡟ᑐࡋ࡚ࣂ࢖࢔ࢫࢆ㝖ཤࡋ㸪ᘧ㸦1㸧ࡢ G1(s)ࢆ⏝࠸୍࡚ḟ㐜ࢀ↓㥏᫬㛫せ⣲࡛ࣔࢹࣝ໬ࡍ
ࡿ࡜ඹ࡟㸪᣺ືᡂศ࡟ᑐࡋ࡚ࡣ 2 ḟ᣺ືせ⣲ G2(s)࡛ࣔࢹࣝ໬ࡍࡿ㸬ࡲࡓ㸪 Ỉ㔞ࢆຍ࠼ࡓ࡜ࡁࡣ୍ᐃ㏿ᗘ࡛❧ࡕୖࡀࡿᛂ⟅ࡀぢࡽࢀࡿࡓࡵ㸪ࡑࢀࡣ✚ศせ⣲ G3(s)ࢆ⏝࠸࡚ࣔࢹࣝ໬ࡋ㸪ࡑࢀࡽࢆ୪ิ࡛⤖ྜࡍࡿ㸬

G1 ( s )K  Lse 㸪 G ( s )2Ts  1wn2
㸪 G 3 (s)s 2  2]wn s  wn2

1Ts(1)

ࡇࡇ࡛㸪T㸪K㸪L㸪 wn 㸪 ] ࡣྛࠎ㸪᫬ᐃᩘ㸪ࢤ࢖ࣥ㸪↓㥏᫬㛫㸪ᅛ᭷ゅ࿘Ἴᩘ㸪ῶ⾶ẚࢆ⾲ࡍ㸬ࡲࡎ㸪ᅗ 6 ࢆ⏝࠸࡚ G1(s) ࡢ T㸪K㸪L ࢆ⟬ฟࡍࡿ㸬ࡲࡓ㸪2 ḟ᣺ືせ⣲ࡢ wn 㸪 ] ࡟ᑐࡋ࡚ࡣ㸪ᅗ 7 ࢆ⏝࠸࡚ G2(s) ࢆồࡵ㸪୍ᐃ㏿ᗘ࡛❧ࡕୖࡀࡿࢫࢸࢵࣉᛂ⟅࡟ᑐࡋ࡚ࡣ㸪ᅗ 3 ࡼࡾࣔࢹࣝ໬ࡍࡿ㸬 Ỉ㔞ࢫࢸࢵࣉධຊ࡟ࡼࡿࢱ࣮ࣅࣥධཱྀᅽຊࢫࢸࢵࣉᛂ⟅࠿ࡽᚓࡽࢀࡓ⤖ᯝࢆᘧ 2 ࡟♧ࡍ㸬8

韓建榮，有田護，池上康之，李羲頡 

Fig.6 Deducing method of 1st order + dead time transfer function   Fig.7 Deducing method of 2nd order transfer functionOS)
 ln(%max value  finalvalue
4
100%OSZn]
finalvalueTs] 㸬OS 㸪ణࡋ㸪
㸪S 2  ln 2 (%)
100

G1 ( s )0.28e  0.01s
G2( s )
0.01s  1
㸪

12G 3 (s)s  1.25 s  12 㸪
20.0056s ࡇࡢఏ㐩せ⣲ࡢ୪ิ᥋⥆ࡼࡾ㸪 Ỉ㔞ධຊ࡜ࢱ࣮ࣅࣥධཱྀᅽຊฟຊ㛫ࡢఏ㐩㛵ᩘࡣ㸪ᘧ㸦3㸧࡟࡞ࡿ㸬0.000056s 3  0.005663s 2  3.367s  0.0672 0.01s
G IH
e0.01s 4  1.007s 3  1.245s 2  12s
 



(2)(3)

௚ࡢ⥺ᙧ໬ఏ㐩㛵ᩘࣔࢹࣝࡶྠᵝ࡟ᚓࡽࢀࡿ㸬G OHG IC
G IV

0.000057s 3  0.00574s 2  3.14s  0.0672 0.01s
e0.01s 4  1.007s 3  0.81s 2  11s103
 0.001s
ee 0.001s
G OC
3232.5s  1.25s  50s  20
2.5s  2.9525s 2  15.77 s  6
㸪22.5e 0.01s G IV11s  1.22s 2  165s  15
㸪386.4e 0.01s
12.5s  4.5s 3  600.3s 2  48s
4

(4)
ᚓࡽࢀࡓ⥺ᙧ໬ఏ㐩㛵ᩘࣔࢹࣝࡢࢫࢸࢵࣉᛂ⟅࡜ ᐃࡋࡓᐇࢫࢸࢵࣉᛂ⟅ࡢẚ㍑ࢆ㸪ᅗ 8㸪9㸪10 ࡟♧ࡍ㸬   Fig8Responses of Real and Model by Hot water step input  Fig9Responses of Real and Model by Cold water step input

低温度差熱エネルギーを用いた超小型バイナリー発電プラントのモデリングと非干渉化 PID 制御系の設計

9

Fig10Responses of Real and Model by solenoid valve step input step input 

4. 㠀ᖸ΅໬๓⨨⿵ൾჾࡢከẁ㝵᥋⥆ᑐ㇟࡜ࡋ࡚࠸ࡿⓎ㟁ࣉࣛࣥࢺࡣከධຊከฟຊከኚᩘࢩࢫࢸ࣒࡛࠶ࡾ㸪ࡇࡢࣉࣛࣥࢺ࡟࠾ࡅࡿ ᗘ㸪ᅽຊ㸪ὶ㔞࡞࡝ࡢ᧯స㔞ࡸไᚚ㔞ࡣ┦஫࡟ᖸ΅ࡋ࠶࠺ሙྜࡀከ࠸㸬ࡇࡢࡼ࠺࡞ࢩࢫࢸ࣒࡟ᑐࡋ࡚ไᚚᛶ⬟ࢆ㧗ࡵࡿࡓࡵ࡟ࡣ㸪ࡑࢀࡽᙉ࠸┦஫ᖸ΅ࢆྲྀࡾ㝖ࡃᑐ⟇ࢆᚲせ࡜ࡍࡿ㸬ࡑࡇ࡛㸪ࡇࢀࡽᙉ࠸┦஫ᖸ΅ࢆ✚ᴟⓗ࡟ᡴࡕᾘࡍไᚚჾ࡜ࡋ࡚㸪INA㸦㏫ࢼ࢖࢟ࢫࢺ㓄ิ㸧ࢆ⏝࠸࡚࿘Ἴᩘ㡿ᇦ࡛タィࡉࢀࡓ㠀ᖸ΅໬๓⨨⿵ൾჾࡀ᭷ຠ࡛࠶ࡿ㸬ࡑࡢタィἲ࡛࠶ࡿ୍⯡໬ᨃఝᑐゅ໬ἲࡣ㸪ᚲࡎࡋࡶධຊᩘ࡜ฟຊᩘࡀ➼ࡋ࠸࡜ࡣ㝈ࡽ࡞࠸୍⯡ࡢከධຊከฟຊไᚚᑐ㇟ࢆ㠀ᖸ΅໬ࡍࡿᨃఝᑐゅ໬ἲ࡛㸪ฟຊᩘ࡜➼ࡋ࠸ᅛ᭷್ၥ㢟࡟ᖐ╔ࡉࡏ㸪㠀ᖸ΅໬๓⨨⿵ൾჾࢆタィࡍࡿ㸬ࡇࡢ᫬㸪᏶඲࡞㠀ᖸ΅໬ࢆ㐩ᡂࡍࡿࡇ࡜ࡣᅔ㞴࡞ࡢ࡛㸪୍ᕠఏ㐩㛵ᩘ⾜ิ࡟࠾ࡅࡿᑐゅᡂศࡢ⤯ᑐ್ࡼࡾ㠀ᑐゅᡂศ⤯ᑐ್ࡢ⾜ ิ ⥲࿴ࡀᑠࡉ࠸ᑐゅ⾜ ิ ඃໃ࡟ࡼࡗ࡚㸪㠀ᖸ΅໬ࡢ⛬ᗘࢆุᐃࡍࡿ>@㸬
4.1 ୍⯡໬␲ఝᑐゅ໬࡟ࡼࡿ㠀ᖸ΅໬๓⨨⿵ൾჾタィ࡜ᑐゅ⾜ ิ ඃໃุูᮏ◊✲࡛ࡣ㸪3 ධຊ 2 ฟຊఏ㐩㛵ᩘ⾜ิࣔࢹࣝᘧ㸦5㸧࡟ᑐࡋ࡚㸪୍⯡໬ᨃఝᑐゅ໬࡜㏫ࢼ࢖࢟ࢫࢺ㓄ิ࡟ࡼࡾ㠀ᖸ΅໬๓⨨⿵ൾჾࢆタィࡍࡿ㸬

Gp( s)ª 0.000056 s3  0.005663 s 2  3.367 s  0.0672«e  0 .01s
0.01s 4  1.007 s 3  1.245 s 2  12 s«« 0.000057 s 3  0.00574 s 2  3.14 s  0.0672  0 .01se«
0.01 s 4  1.007 s 3  0.81 s 2  11s¬10e  0 .001s
2.5 s  1.25 s 2  50 s  203e  0 .001s
2.5 s 3  2.9525 s 2  15.77 s  63º22.5e  0 .01s »211s  1.22 s  165 s  15»»86.4
 0 .01se»
12.5 s 4  4.5 s 3  600 .3 s 2  48 s
¼3(5)
ࡲࡎ㸪௚᪉ࡢไᚚ㔞ࢆእ஘࡜ࡳ࡞ࡋ࡚࣮ࣝࣉẖ࡟ PID ไᚚჾࢆタィࡋ PID ไᚚࢆ⾜ࡗࡓ⤖ᯝࢆᅗ 11 ࡟♧ࡍ

10

韓建榮，有田護，池上康之，李羲頡 Fig11PID control result of 3input 2out systemᅗ 11 ࡣ㸪ࣉࣛࣥࢺ࡟࠾ࡅࡿ ᗘ㸪ᅽຊ㸪ὶ㔞࡞࡝ࡢไᚚ㔞ࡀ┦஫࡟ᖸ΅ࡋ࠶࠸㸪PID ไᚚ࡛ࡣᏳᐃࡋࡓไᚚࡀᅔ㞴࡛࠶ࡿࡇ࡜ࢆ♧ࡋ࡚࠸ࡿ㸬ᚑࡗ࡚㸪ఱࡽ࠿ࡢ㠀ᖸ΅໬ࡢᑐ⟇ࡀᚲせ࡜࡞ࡿࡇࡢ࡜ࡁࡢ᣺ື࿘ᮇࡣ 1.46 ⛊࡛࠶ࡾ㸪
ࡇࡢ PID ไᚚ⤖ᯝ࠿ࡽᚓࡽࢀࡓࣁࣥࢳࣥࢢ࿘Ἴᩘ w01=4.3 ࢆ⏝࠸࡚㠀ᖸ΅໬๓⨨⿵ൾჾ Gc1 ࢆタィࡍࡿ㸬୍⯡໬ᨃఝᑐゅ໬ἲ࡟ࡼࡾタィࡋࡓ๓⨨⿵ൾჾ Gc1 ࡣᘧ(6) ࡢࡼ࠺࡟࡞ࡾ㸪ࡇࡢ࡜ࡁࡢ ㏫ࢼ࢖࢟ࢫࢺ⥺ᅗ࡜ࢤࣜࢩࣗࢦࣜࣥᖏࢆᅗ 12 ࡟♧ࡍ㸬ª- 0.0127  0.7259ºGc1 «« - 0.2071  0.0689»»«¬ 0.9782  0.6843»¼ 











(6)




Fig12Inverse Nyquist Array and Gershgorin band byGc1

低温度差熱エネルギーを用いた超小型バイナリー発電プラントのモデリングと非干渉化 PID 制御系の設計

114.2 㠀ᖸ΅໬๓⨨⿵ൾჾࡢከẁ㝵᥋⥆ไᚚ㔞㛫ࡢ┦஫ᖸ΅ࡀⴭࡋ࠸ไᚚᑐ㇟࡟ᑐࡋ࡚ࡣ㸪୍ࡘࡢ๓⨨⿵ൾჾ࡛㠀ᖸ΅໬ࡀ㐩ᡂ࡛ࡁ࡞࠸ሙྜࡀከ࠸㸬ࡑࡢࡼ࠺࡞ሙྜ㸪㠀ᖸ΅໬๓⨨⿵ൾჾࢆከẁ㝵᥋⥆ࡍࡿࡇ࡜ࡀ᭷ຠ࡛࠶ࡿ>@㠀ᖸ΅໬๓⨨⿵ൾჾࡢ᥋⥆ᙧែ࡜ࡋ࡚ࡣ㸪┤ิ᥋⥆㸪୪ิ᥋⥆㸪ࡲࡓࡑࢀࡽࡢ⤌ࡳྜࢃࡏ࡜ࡋ࡚┤୪ิ㸪୪┤ิ᥋⥆ࡀ࠶ࡿ㸬ᮏ◊✲࡛ࡣ㸪┦஫ᖸ΅ࢆࡶࡓࡽࡍ」ᩘࡢ᣺ືᡂศࢆẚ㍑ⓗ⡆༢࡟㍍ῶ࡛ࡁࡿ୪ิ᥋⥆ࢆ⏝࠸ࡿ㸬๓⨨⿵ൾჾࡢ୪ิ᥋⥆タィἲࡣ㸪」ᩘࡢ࿘Ἴᩘ w0i, i=1,2,…,nࡑࢀࡒࢀ࡟ᑐࡋ࡚ n ಶࡢ๓⨨⿵ൾჾ Gciࢆタィࡋ㸪ࡑࢀࡽ๓⨨⿵ൾჾࢆ୪ิ࡟᥋⥆ࡍࡿ᪉ἲ࡛࠶ࡿ㸬ࡶ࠺୍ࡘࡢタィἲ࡜ࡋ࡚ࡣ㸪㢧ⴭ࡞୍ࡘࡢࣁࣥࢳࣥࢢ࿘
Ἴᩘ࡟ᑐࡍࡿ๓⨨⿵ൾჾ࡛ᑐゅඃໃࡀ㐩ᡂ࡛ࡁ࡞࠸࡜ࡁ㸪㢧ⴭ࡞᣺ືᡂศ࡟ᑐࡋ࡚᪂ࡓ࡟๓⨨⿵ൾჾࢆタィࡋ㸪ࡑࢀࢆ୍ࡘࡎࡘ୪ิ࡟㡰ḟ᥋⥆ࡋ࡚࠸ࡃ᪉ἲ࡛࠶ࡿࡀ㸪ᮏ◊✲࡛ࡣᚋ⪅ࡢ᪉ἲࢆ⏝࠸ࡿ㸬
1 ẁ┤ิ᥋⥆࡛㍍ῶ࡛ࡁ࡞࠿ࡗࡓ┦஫ᖸ΅ࡢ୰࡛㸪ࡑࡢ┦஫ᖸ΅ࡀⴭࡋ࠸୍ࡘࡢ࿘Ἴᩘ w02=11 ࡟╔┠ࡋ࡚๓⨨⿵ൾჾ Gc2 ࢆタィࡋ㸪୪ิ᥋⥆ࡍࡿ㸬ࡑࡢࣈࣟࢵࢡ⥺ᅗࢆᅗ 13 ࡟♧ࡍ㸬ࡇࡢ࡜ࡁࡢ ㏫ࢼ࢖࢟ࢫࢺ⥺ᅗ࡜ࢤࣜࢩࣗࢦࣜࣥᖏࢆᅗ 14 ࡟♧ࡍ㸬
Fig13Block diagram of Gc1+Gc2 parallel connection

Fig.14 Inverse Nyquist array and Gershgorin band byGc1+ Gc2

12韓建榮，有田護，池上康之，李羲頡ࡇࢀࡼࡾ࿘Ἴᩘ w01㸻4.3 ࡜ w02=11 ࡟ᑐࡍࡿࢤࣜࢩࣗࢦࣜࣥᖏࡀཎⅬࢆྵࡲ࡞ࡃ࡞ࡾ㸪ࡲࡓ௚ࡢゅ࿘Ἴᩘࡢࢤ
ࣜࢩࣗࢦࣜࣥᖏ༙ᚄࡶᑠࡉࡃ࡞ࡿࡇ࡜ࡀศ࠿ࡿ㸬᭦࡞ࡿ㠀ᖸ΅໬ࢆᅗࡿࡓࡵ࡟㸪w03 = 20.0㸪w04 = 40.0㸪w05 = 4.1㸪w06 = 4.4㸪w07 = 7.0 ࡟ᑐࡍࡿ Gc3㸪Gc4㸪Gc5㸪Gc6㸪Gc7 ࢆタィࡋ㸪7 ẁ୪ิ᥋⥆ࡋࡓ࡜ࡁࡢࣈࣟࢵࢡ⥺ᅗࢆᅗ
15 ࡟㸪 ㏫ࢼ࢖࢟ࢫࢺ㓄ิࢆᅗ 16 ࡟♧ࡍ㸬ࡇࡢ࡜ࡁࡢ 7 ẁ୪ิ᥋⥆㠀ᖸ΅໬๓⨨⿵ൾჾࡣ㸪ᘧ(7)ࡢࡼ࠺࡟࡞ࡿ㸬ࢤࣜࢩࣗࢦࣜࣥᖏࡀཎⅬࢆྵࢇ࡛࠸࡞࠸ࡇ࡜࠿ࡽ㸪୍ᕠఏ㐩㛵ᩘ⾜ิ G(s) = Gp(s) ( Gc1+Gc2+Gc3+Gc4+Gc5+Gc6+Gc7 ) ࡢᑐゅิඃໃࡀ㐩ᡂࡉࢀ࡚࠸ࡿ

Gc Gc1  Gc2  Gc3  Gc4  Gc5  Gc6  Gc7ª- 0.1086 1.6104 º« - 1.4708 2.1950»«»«¬ 6.8428 3.5541»¼ 



(7)




Fig.15 Block diagram of Gc1+Gc2+Gc3+Gc4+Gc5+Gc6+Gc7 parallel connection

Fig.16 Inverse Nyquist Array and Gershgorin band byGc1+ Gc2+ Gc3+ Gc4+ Gc5+ Gc6+ Gc7

低温度差熱エネルギーを用いた超小型バイナリー発電プラントのモデリングと非干渉化 PID 制御系の設計

135. 㠀ᖸ΅໬ PID ไᚚ⣔ࡢタィ


5.1 3 ධຊ 2 ฟຊࣉࣛࣥࢺ࡟ᑐࡍࡿ㠀ᖸ΅໬ PID ไᚚ᧯స㔞ࢆ Ỉ㔞࡜෭Ỉ㔞㸪ཬࡧࢱ࣮ࣅࣥධཱྀ㟁☢ᘚ㸪ไᚚ㔞ࢆࢱ࣮ࣅࣥධཱྀᅽຊ࡜ฟཱྀᅽຊ࡜ࡋ㸪ไᚚ┠ᶆࢆࢱ࣮ࣅࣥධཱྀᅽຊ 1100 [KPa]㸪ฟཱྀᅽຊ 700[KPa]࡜ࡍࡿ㠀ᖸ΅໬ไᚚ⣔ PID ࢆタィࡍࡿ㸦ᅗ 17㸧㸬
Fig.17 Block diagram of Decouple PID control system
3 ධຊ 2 ฟຊࣉࣛࣥࢺ Gp(s) ࡟ᑐࡋ࡚㸪㝈⏺ឤᗘἲ࡟ࡼࡾタィࡉࢀࡓ PID ࣃ࣓࣮ࣛࢱ࡜ไᚚ⤖ᯝࢆ⾲ 1 ࡜ᅗ 18࡟♧ࡍ㸬Table 1Ỉ࣮ࣝࣉ࡜෭Ỉ࣮ࣝࣉࡢ PID ࣃ࣓࣮ࣛࢱỈ࣏ࣥࣉ෭Ỉ࣏ࣥࣉ

Kp

0.04340.6552Ti

0.70360.4475Td

0.17590.1119
Fig.18 3inputs-2outputs Decouple PID Control by 7-stage parallel connection14

韓建榮，有田護，池上康之，李羲頡

5.2 2 ධຊ 2 ฟຊࣉࣛࣥࢺ࡟ᑐࡍࡿ㠀ᖸ΅໬ PID ไᚚࡇࡇ࡛ࡣ᧯స㔞ࡢᩘࡀไᚚᛶ⬟࡟୚࠼ࡿຠᯝࢆ᳨ウࡍࡿࡓࡵ࡟㸪๓⠇ࡼࡾ᧯స㔞ࡢᩘࡀᑡ࡞࠸ Ỉ㔞࡜෭Ỉ㔞
ࡢ 2 ࡘࢆ᧯స㔞࡜ࡍࡿ 2 ධຊ 2 ฟຊࣉࣛࣥࢺ࡟ᑐࡍࡿไᚚࢆヨࡳࡿ㸬3 ධຊ 2 ฟຊࣉࣛࣥࢺ࡜ྠᵝ࡟㸪7 ẁ୪ิ᥋⥆๓⨨⿵ൾჾࢆタィࡋ㠀ᖸ΅໬ PID ไᚚࢆ⾜ࡗࡓ㸬㝈⏺ឤᗘἲ࡟ࡼࡾタィࡉࢀࡓ PID ࣃ࣓࣮ࣛࢱࢆ⾲ 2㸪ไᚚ⤖ᯝࢆᅗ 19 ࡟♧ࡍ㸬Table 2Ỉ࣮ࣝࣉ࡜෭Ỉ࣮ࣝࣉࡢ PID ࣃ࣓࣮ࣛࢱỈ࣏ࣥࣉ෭Ỉ࣏ࣥࣉKp

0.0493

1.8347Ti

0.190114.6086

Td

0.04670.7950

Fig.19 2inputs-2outputs Decouple PID control Result by 7-stage parallel connectionᅗ 18 ࡜ᅗ 19 ࡼࡾ㸪ᩚᐃ᫬㛫ࡣྛࠎ⣙ 700 ⛊࡜⣙ 2200 ⛊࡛࠶ࡿ㸬ࡇࡢ⤖ᯝࡼࡾ㸪᧯స㔞ࡀ୍ࡘከ࠸ 3 ධຊ 2 ฟຊࣉࣛࣥࢺ࡟ᑐࡍࡿᩚᐃ᫬㛫ࡀ⣙ 30%࡟▷⦰ࡉࢀࡿࡇ࡜ࡀศ࠿ࡿ㸬
5.3 ไᚚᛶ⬟ࡢ᳨ウࡇࡇ࡛ࡣ 3 ධຊ 2 ฟຊࣉࣛࣥࢺ࡜ 2 ධຊ 2 ฟຊࣉࣛࣥࢺ࡟ᑐࡍࡿไᚚᛶ⬟ࢆࢤ࢖ࣥవ⿱࡜఩┦వ⿱ࡢほⅬ࠿ࡽ᳨ウࡍࡿ㸬ᅗ 20 ࡣ 3 ධຊ 2 ฟຊ࡟ᑐࡍࡿ Ỉ࣮ࣝࣉࡢ Nyquist ⥺ᅗ࡜ Bode ⥺ᅗࢆ㸪ࡲࡓᅗ 21 ࡣ෭Ỉ࣮ࣝࣉࡢࡑ
ࢀࡽࢆ⾲ࡋ࡚࠸ࡿ㸬ࡇࢀࡽࡢ⤖ᯝࡼࡾ㸪 Ỉ࣮ࣝࣉࡢࢤ࢖ࣥవ⿱ࡣ-180 [ ° ] ௜㏆ࡢȰ 4.5 [ rad/sec ] ࡛ 5.55 [ dB ]࡛࠶ࡾ㸪෭Ỉ࣮ࣝࣉࡢࢤ࢖ࣥవ⿱ࡣȰ 6.99 [ rad/sec ] ࡛ 1.82 [ dB ] ࡛࠶ࡿ

低温度差熱エネルギーを用いた超小型バイナリー発電プラントのモデリングと非干渉化 PID 制御系の設計

15



Fig.20㸬 Nyquist and Bode diagram of Hot water loop of 3inputs-2outputs plant







Fig.21 Nyquist and Bode diagram of Cold water loop of 3inputs-2outputs plant
Table 3 3 ධຊ 2 ฟຊࣉࣛࣥࢺ࡜ 2 ධຊ 2 ฟຊࣉࣛࣥࢺࡢไᚚᛶ⬟ࡢẚ㍑
ไᚚᛶ⬟ᮃࡲࡋ࠸್

ࢤ࢖ࣥవ⿱

3~10 [dB]

఩┦వ⿱

ᩚᐃ᫬㛫

20~70[deg]༊ศ

3 ධຊ 2 ฟຊ2 ධຊ 2 ฟຊỈ⣔

5.55[dB]

0.262[dB]෭Ỉ⣔

1.92[dB]

48.2[dB]Ỉ⣔91.2[deg]

4.17[deg]෭Ỉ⣔

29.5[deg]

19.6[deg]

700 ⛊2200 ⛊࣭ไᚚᛶ⬟ࢆẚ㍑ࡋࡓࡶࡢࡀ⾲ 3 ࡛࠶ࡿ㸬௨ୖࡼࡾ㸪3 ධຊ 2 ฟຊ㠀ᖸ΅໬ PID ไᚚ⣔ࡢ᪉ࡀࢤ࢖ࣥవ⿱㸪఩┦వ⿱཮᪉ࡢᮃࡲࡋ࠸್࡟㏆ࡃ㸪ไᚚᛶ⬟ࡣ㧗ࡲࡿࡇ࡜ࡀ☜ㄆ࡛ࡁࡿ㸬
6. ⤖  ㄒⓎ㟁ࣉࣛࣥࢺࡢືసⅬ㏆ഐ࡟࠾ࡅࡿື≉ᛶࢆ༑ศ࡟ᤊ࠼ࡓ⥺ᙧ໬ఏ㐩㛵ᩘ⾜ิࣔࢹࣝࢆᑟฟࡋ㸪ᐇࢹ࣮ࢱ࡜ࡢẚ㍑࡟ࡼࡾ㸪ࡑࡢጇᙜᛶࢆ♧ࡋࡓ㸬ࡲࡓ㸪᧯స㔞࡜ไᚚ㔞㛫ࡢ㢧ⴭ࡞┦஫ᖸ΅ࢆ⪃៖ࡋࡓ㠀ᖸ΅໬ PID ไᚚ⣔ࢆタィࡋ㸪㠀ᖸ΅໬๓⨨⿵ൾჾ࡟ࡼࡿไᚚᛶ⬟ࢆ♧ࡋࡓ㸬᭦࡟㸪᧯స㔞ࢆቑࡸࡍຠᯝ࡟ࡘ࠸᳨࡚ウࡋ㸪ࡑࡢ᭷ຠᛶࢆ♧ࡋࡓ㸬

16

韓建榮，有田護，池上康之，李羲頡ᩥ  ⊩(1) W.L.Owens, “OTEC plant response and control analysis”, ASME J Solar Energy Eng, vol.104,no.3(1982), pp.208-215.
(2) Satomi S, Han K-Y, S J-S, Lee H-H, “A learning control of unused energy power generation”, 15th International Symposium
on AROB,vol.15,no.4(2010), pp.450-454.
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