预测函数控制在网络化控制系统中的研究与应用(EI收录)
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Proceedings of the 7th World Congress on Intelligent Control and Automation June 25 - 27, 2008, Chongqing, China
Study and Application of Predictive Functional Control in Networked Control System
m 0 h
yp(k i) CMi xp(k ) C*(m)Ph u (h< N ) F (h< N ) u iMT (i)
(3)
K
V (K )
(11)
ৃݭЎ˖
xp ( k i ) M xp (k i 1) K *(m)u T (k i m 1) v(k i 1)
ݭЎⶽ䰉ᔶᓣЎ˖
wj (i )
¦ M n « ¦ >C*mfj (i 1 n m)@» ,1 d j d N ,
ᠻ㸠఼㡖⚍䞛⫼џӊ偅ࡼᮍᓣ˗ ؛䆒 ˖㋏㒳ᄬ㔥㒰Ӵ䕧䖳ᓊˈৃ㛑Ўⷁᯊ䯈䖳ᓊ гৃ㛑Ў䭓ᯊ䯈䖳ᓊ˗ ؛䆒 ˖㋏㒳Ё㹿ᇍ䈵Ў㒓ᗻᯊϡব㋏㒳˗ 㗗㰥㋏㒳ాໄˈ㹿ᇍ䈵ৃҹ㸼冫བϟ˖
x(t ) M x(t ) Bu (t W k ) v(t ) (1) ® ¯ y (t ) Cx(t ) w(t ) ᓣЁ W k W sc W ca ˈv(t ), w(t ) ЎѦϡⳌ݇ⱘ䳊ഛؐⱑ
Wca Wsc
Wca
3.2
Wsc
2˖ᬍ䖯乘⌟ߑ᭄ࠊㅫ⊩ॳ⧚ᮍḚ
᳝䖳ᓊ⡍ᗻⱘ乘⌟ൟ ⬅ᓣ(2)ৃᕫ (k i) Ͼࠊ਼ᳳⱘ⢊ᗕЎ˖
6237
xp ( k i ) M xp (k i 1) ¦ *mu ( k i m 1) v (k i 1)
ᆊ㞾✊里ᄺ䞥乍Ⳃ˄䌘ࡽো˖50677021˅
ೄ䲒ˈ㔥㒰࣪ࠊ㋏㒳㡖⚍П䯈䗮䖛㔥㒰Ӵ䕧ֵᙃᯊᖙ ᇚᓩ䍋Ӵ䕧䖳ᓊˈ 䖭Ӯ䰡Ԣ㋏㒳ᗻ㛑⫮㟇ᓩ䍋㋏㒳ϡ〇ᅮDŽ NCSൟᰃᇍ݊ߚᵤࠊ఼㡖⚍䆒䅵ⱘ⸔ˈ᭛⤂[4]߽ ⫼њ㔥㒰Ӵ䕧䖳ᓊᇣѢϔϾ䞛ḋ਼ᳳⱘⷁᯊ䯈䖳ᓊNCS ൟ఼ࠊخ㡖⚍䆒䅵 ˈԚ㔥㒰Ӵ䕧䖳ᓊᇣѢϔϾ䞛ḋ਼ ᳳ䖭ϔ؛䆒ᅲ䰙㋏㒳Ёᐌᐌϡ㛑ᕫࠄ⒵䎇˗᭛⤂[5]ᡞ㔥 㒰Ёⱘϡ⹂ᅮᗻ䖳ᓊ䗮䖛䆒㕂㓧ކऎඳ䕀ᤶ៤⹂ᅮᗻ䖳 ᓊˈҢ㗠ᇚ㔥㒰࣪ࠊ㋏㒳Ң䱣ᴎ㋏㒳䕀࣪Ў⹂ᅮᗻᯊ⒲ ㋏㒳 ˈԚ㓧ކऎⱘ䆒ゟҎЎⱘᓊ䭓њ䖳ᓊᯊ䯈ˈ⬹ᰒ⡉ ᔎDŽ 乘⌟ߑ᭄ࠊ(Predictive Functional Control, ㅔ鹵PFC)
ࠊ఼㡖⚍ᓩܹᬍ䖯乘⌟ߑ᭄ࠊㅫ⊩ˈ䆹ㅫ⊩乘⌟㋏㒳ᴹ䕧ߎᯊ㗗㰥њϸ辵ৃ㛑ⱘᯊ䯈䖳ᓊ㋴ˈᕫߎњ䗖⫼Ѣޣᇣ䭓ǃⷁᯊ䯈 䖳ᓊᕅડⱘࠊ䕧ߎㄪ⬹DŽ Matlab ⦃๗ϟ߽⫼ TrueTime Ꮉㆅᵘᓎњ㔥㒰ӓⳳ⦃๗ˈᇍ↨њϸ辵ᯊ䯈䖳ᓊᑊᄬᚙމϟϢᐌ㾘乘 ⌟ߑ᭄ࠊㅫ⊩ⱘࠊᬜᵰˈӓⳳ㒧ᵰ㸼ᯢᬍ䖯ৢⱘㅫ⊩ᇍޣᇣ䭓ǃⷁᯊ䯈䖳ᓊᕅડˈᦤ催ࠊક䋼᳝ⴔ㡃དᬜᵰDŽ ݇䬂䆡 㔥㒰࣪ࠊ㋏㒳ˈ䭓ᯊ䯈䖳ᓊˈⷁᯊ䯈䖳ᓊˈ乘⌟ߑ᭄ࠊ
乘⌟ߑ᭄ࠊ㔥㒰࣪ࠊ㋏㒳ЁⱘⷨおϢᑨ⫼
਼咢䕝 1,2
1)
⥟ 3
䶽⩲ 1
ᕤᑇ 3
3)
ढ࣫⬉ᄺࠊ里ᄺϢᎹᄺ䰶 ֱᅮ 071003 2) ⬉फҀ㞾ࡼ᳝࣪䰤݀ৌ फҀ 210003 ढ࣫⬉ᄺ㛑⑤ϢࡼᎹᄺ䰶 ࣫Ҁ 102206
ᨬ
㽕
㔥㒰࣪ࠊ㋏㒳Ё⬅Ѣ㔥㒰Ӵ䕧ৃ㛑ᓩ䍋ϡ⹂ᅮᗻ䭓ᯊ䯈䖳ᓊⷁᯊ䯈䖳ᓊDŽ䩜ᇍϸ辵ৃ㛑ߎ⦄ⱘᯊ䯈䖳ᓊ⡍ᗻˈ
ᬍ䖯乘⌟ߑ᭄ㅫ⊩ᴀॳ⧚
ᬍ䖯乘⌟ߑ᭄ࠊㅫ⊩ॳ⧚Ḛབ 2 ᠔冫ˈϢӴ㒳 ⱘ乘⌟ߑ᭄ࠊㅫ⊩Ⳍ↨ˈЏ㽕ऎ߿ᰃᅗՓ⫼㋏㒳ⱘ᳝ 䖳ᓊ⡍ᗻⱘ⢊ᗕぎ䯈ൟᴹ乘⌟ᇍ䈵ⱘ䕧ߎDŽ
a d T ˈ߭鹵䖭ḋⱘӴ䕧䖳ᓊЎⷁᯊ䯈䖳ᓊ˗ ᅮН ᔧ㔥㒰Ӵ䕧䖳ᓊऎ䯈 [0, a] ߚݙᏗˈϨ a t T ˈ߭鹵䖭ḋⱘӴ䕧䖳ᓊЎ䭓ᯊ䯈䖳ᓊ˗ ⊼˖⬅ᅮН ৃⶹˈ䭓ᯊ䯈䖳ᓊϡᰃϔᅮѢϔϾ䞛
(4)
F(h< N )ui
݊Ё˖
K *(m) [*0 , *பைடு நூலகம் ," * h ], u (k ) [u (k ), u (k 1)," , u (k h)]
䗮䖛䗦ᮍ⊩ᕫ˖
ª FT n(0) F T n(1) " F T n(i 1) º « T » T T « F n(1) F n(0) " F n(i 2) » « # » # # # « T » T T ¬F n(h) F n(1 h) " F n(i 1 h)¼ (h< N )ui K ªPn 0 0 º K P hu ( h < N ) « 0» «0 % K » « » n 0 0 P ¬ ¼ hu ( h < N )
ൟⱘ㔥㒰࣪ࠊ㋏㒳㒧ᵘЏ㽕⬅ϔϾ㔥㒰ഫ㢹 ᑆϾᱎ㛑㡖⚍㒘៤ˈབ ᠔冫DŽ
M
e AT , *m
³
k tm 1
k tm
k e A (T s ) Bds, t 1
k T ; th
0
ᔧӴ䕧䖳ᓊЎⷁᯊ䯈䖳ᓊᯊˈे 0 W k T ˈᓣ (2) Ё h=1ˈϔϾ䞛ḋ਼ᳳ [kT , (k 1)T ] ࠄݙ䖒㹿ᇍ䈵Ϟ ⱘࠊ䞣া᳝ϔϾ u(t)˗ᔧӴ䕧䖳ᓊЎ䭓ᯊ䯈䖳ᓊᯊˈे ˈᓣ(2)Ё h>1ˈϔϾ䞛ḋ਼ T W k hT ˄h Ўℷᭈ᭄˅ ᳳ [kT ,(k 1)T ] ࠄݙ䖒㹿ᇍ䈵ⱘࠊ䞣 u(t)ߚ↉䖲㓁Ϩ ᳔᳝ h+1 ϾϡৠⱘؐDŽ ҹϞݙᆍᓎゟњϔϾߚᏗᓣ㔥㒰࣪ࠊ㋏㒳ൟDŽ
1)
sAbstract—With regards to the characteristics of stochastic short time delay and long time delay induced by the network transmission in networked control system (NCS), the improved predictive functional control (PFC) algorithm is proposed in this paper. The two kind of network-induced time delays are specifically considered for predicting the future plant outputs in improved PFC algorithm. The control law is given by improved PFC which is introduced to controller nodes in NCS. A distributed NCS model is constructed based on TrueTime toolbox. Simulation experiments are practiced over this model which embraces both stochastic short time delay and long time delay. It is proved that the improved PFC algorithm can give better control performance compared with the standard PFC algorithm. Keywords—Networked Control System (NCS), Long Time Delay, Short Time Delay, Predictive Functional Control (PFC)
xp ( k i )
݊Ё M (i )
M i xp ( k ) * ( m )U huiM T (i ) V ( k ) M T (i )
[M i 1 , M i 2 ," ,1], V (k ) Ўⱑాໄ䞣ˈे˖
(5)
ᭈ⧚ᓣ(11)ᕫ˖
yp ( k i )
݊Ё˖
i 1
K C M i x p ( k ) P n <W j T (i ) V ( K ) Wj (i) [ w1(i ), w2(i )," , wj (i )] ,
ª
h
(12)
V (k ) [v(k ), v(k 1)," v(k i 1)] ˈ K K K U hui [u T (k ), u T (k 1)," , u T (k i 1)]
>@
DŽ
䆹ㅫ⊩ᡞࠊ䕧ܹⱘ㒧ᵘ㾚Ў݇䬂䯂乬ˈৃҹܟ᳡݊ᅗ ൟ乘⌟ࠊৃ㛑ߎ⦄㾘ᕟϡᯢⱘࠊ䕧ܹ䯂乬ˈৠᯊ᳝ 㡃དⱘ䎳䏾㛑ঞ䕗ᔎⱘ剕ẦᗻDŽ乘⌟ߑ᭄ࠊㅫ⊩гৃ ҹ䞛⫼䕗ⱘ䞛ḋ਼ᳳˈ↨䕗䗖⫼ѢᄬӴ䕧䖳ᓊⱘ㔥㒰 ࣪ࠊ㋏㒳ˈ⬅ѢӴ䕧䖳ᓊⱘᄬˈӴ㒳乘⌟ߑ᭄ࠊㅫ ⊩ϡ㛑ᕫࠄᕜདⱘࠊᬜᵰDŽᴀ᭛ᦤߎࠊ఼㡖⚍ᓩܹ 㛑䗖⫼Ѣⷁᯊ䯈䖳ᓊ䭓ᯊ䯈䖳ᓊⱘᬍ䖯乘⌟ߑ᭄ࠊㅫ ⊩ˈᑊℸ⸔Ϟ⫼䆒䅵ⱘ㔥㒰࣪ࠊ㋏㒳ൟ偠䆕݊ ࠊᬜᵰDŽ
1ˊᓩ㿔
㔥㒰࣪ࠊ㋏㒳˄ Networked Control System ˈㅔ鹵 NCS˅ⱘ⡍⚍ᰃড作ࠊಲ䏃䗮䖛辵㔥㒰ֵ䘧䖲㗠ᔶ ៤㋏㒳䯁⦃DŽϢӴ㒳ᛣНϞⱘࠊ㋏㒳Ⳍ↨᳝ᕜӬ⚍˖ བᅲ⦄䌘⑤݅ѿˈѸѦᗻད˗֓Ѣ㋏㒳ᅝ㺙ǃ㓈ᡸǃᠽሩ˗ ޣᇥ㋏㒳䖲㒓ˈ⠽⧚㒧ᵘⳌᇍㅔऩˈࡴњ㋏㒳ⱘ♉⌏ᗻ ৃ䴴ᗻDŽ㗠㔥㒰࣪ࠊ㋏㒳ℷ៤ЎҎӀⷨおⱘϔϾ⛁ ⚍ˈᑊᓩ䍋њ䍞ᴹ䍞ⱘᄺ㗙ⱘ݈䍷[1-3]DŽ Ԛᰃˈ 䗮䆃㔥㒰ⱘᓩܹՓ㋏㒳ⱘߚᵤ䆒䅵বᕫ䴲ᐌ1
ḋ਼ᳳˈ㗠ᰃ䖳ᓊߚᏗऎඳⱘϞ⬠ѢϔϾ䞛ḋ਼ᳳDŽ 㔥㒰࣪ࠊ㋏㒳Ёˈḍ㡖⚍ⱘ偅ࡼᮍᓣϡৠˈ㔥 㒰⦃๗ϟⱘࠊ㋏㒳ᓎг䱣ПϡৠDŽЎњⷨおᮍ֓ˈᴀ ᭛া㗗㰥㔥㒰࣪ࠊ㋏㒳ЁⱘӴ䕧䖳ᓊ㗠ϡ㗗㰥᭄϶ࣙ ᭄ࣙᯊᑣ䫭хᚙˈމϨخབϟ؛䆒˖ ؛䆒 ˖Ӵᛳ఼㡖⚍䞛⫼ᯊ䩳偅ࡼᮍᓣˈࠊ఼㡖⚍
>@ >@
978-1-4244-2114-5/08/$25.00 © 2008 IEEE.
6236
᳔ ᮽ ⬅ ⊩ ADERSA ݀ ৌ ⱘ Richalet ᖋ IITB ݀ ৌ ⱘ KuntzeㄝҎᑈҷЁৢᳳᦤߎˈᑊ៤ࡳᑨ⫼ѢᎹϮᴎ఼ Ҏⱘᖿ䗳催㊒ᑺࠊ ሲѢϝҷൟ乘⌟ࠊㅫ⊩
Lihui Zhou1,2, Tiankun Wang3, Pu Han1, Daping Xu3
2)
North China Electric Power University, Baoding 071003(E-mail: hp@ncepubd.edu.cn) Guo Dian Nan Jing Automation Co. LTD, Nanjing 210003 (E-mail: zhouli-hui@gmail.com) 3) North China Electric Power University, Beijing 102206 (E-mail: wangtiankun@gmail.com)
ాໄDŽ 㓐ড়㗗㰥Ӵ䕧䖳ᓊЎⷁᯊ䯈䖳ᓊ䭓ᯊ䯈䖳ᓊϸ辵ᚙ ˈމᡞ䖲㓁ൟ行ᬷ࣪ˈৃᕫ˖
h p p x ( k 1) M x ( k ) ° ¦ * m u ( k m ) v(k ) ® m 0 ° y p ( k ) Cx p ( k ) w ( k ) ¯
(2)
2ˊ㔥㒰࣪ࠊ㋏㒳ⱘߚᵤϢᓎ
Wca
Wsc
3ˊᬍ䖯乘⌟ߑ᭄ࠊㅫ⊩
1˖㔥㒰࣪ࠊ㋏㒳ⱘᴀ㒧ᵘ
3.1 㔥㒰⦃๗ϟˈ ⫼᠋݅ѿ䗮䆃㒓䏃Ϩ⌕䞣ব࣪ϡ㾘߭ˈ ᔧϾ㡖⚍䗮䖛㔥㒰Ѹᤶ᭄ᯊᖙ✊ᇐ㟈Ӵ䕧䖳ᓊˈNCS ⱘӴ䕧䖳ᓊЏ㽕⬅ϸ䚼ߚᵘ៤˖Ӵᛳ఼㡖⚍ˉࠊ఼㡖⚍ ⱘӴ䕧䖳ᓊ W sc ࠊ఼㡖⚍ˉᠻ㸠఼㡖⚍ⱘӴ䕧䖳ᓊ W ca DŽӴ䕧䖳ᓊৃ㛑ѢϔϾ䞛ḋ਼ᳳ ⫼ T 㸼冫 ˈгৃ㛑 ᇣѢϔϾ䞛ḋ਼ᳳℸᦤߎབϟᅮН˖ ᅮН ᔧ㔥㒰Ӵ䕧䖳ᓊऎ䯈 [0, a] ߚݙᏗˈϨ
Study and Application of Predictive Functional Control in Networked Control System
m 0 h
yp(k i) CMi xp(k ) C*(m)Ph u (h< N ) F (h< N ) u iMT (i)
(3)
K
V (K )
(11)
ৃݭЎ˖
xp ( k i ) M xp (k i 1) K *(m)u T (k i m 1) v(k i 1)
ݭЎⶽ䰉ᔶᓣЎ˖
wj (i )
¦ M n « ¦ >C*mfj (i 1 n m)@» ,1 d j d N ,
ᠻ㸠఼㡖⚍䞛⫼џӊ偅ࡼᮍᓣ˗ ؛䆒 ˖㋏㒳ᄬ㔥㒰Ӵ䕧䖳ᓊˈৃ㛑Ўⷁᯊ䯈䖳ᓊ гৃ㛑Ў䭓ᯊ䯈䖳ᓊ˗ ؛䆒 ˖㋏㒳Ё㹿ᇍ䈵Ў㒓ᗻᯊϡব㋏㒳˗ 㗗㰥㋏㒳ాໄˈ㹿ᇍ䈵ৃҹ㸼冫བϟ˖
x(t ) M x(t ) Bu (t W k ) v(t ) (1) ® ¯ y (t ) Cx(t ) w(t ) ᓣЁ W k W sc W ca ˈv(t ), w(t ) ЎѦϡⳌ݇ⱘ䳊ഛؐⱑ
Wca Wsc
Wca
3.2
Wsc
2˖ᬍ䖯乘⌟ߑ᭄ࠊㅫ⊩ॳ⧚ᮍḚ
᳝䖳ᓊ⡍ᗻⱘ乘⌟ൟ ⬅ᓣ(2)ৃᕫ (k i) Ͼࠊ਼ᳳⱘ⢊ᗕЎ˖
6237
xp ( k i ) M xp (k i 1) ¦ *mu ( k i m 1) v (k i 1)
ᆊ㞾✊里ᄺ䞥乍Ⳃ˄䌘ࡽো˖50677021˅
ೄ䲒ˈ㔥㒰࣪ࠊ㋏㒳㡖⚍П䯈䗮䖛㔥㒰Ӵ䕧ֵᙃᯊᖙ ᇚᓩ䍋Ӵ䕧䖳ᓊˈ 䖭Ӯ䰡Ԣ㋏㒳ᗻ㛑⫮㟇ᓩ䍋㋏㒳ϡ〇ᅮDŽ NCSൟᰃᇍ݊ߚᵤࠊ఼㡖⚍䆒䅵ⱘ⸔ˈ᭛⤂[4]߽ ⫼њ㔥㒰Ӵ䕧䖳ᓊᇣѢϔϾ䞛ḋ਼ᳳⱘⷁᯊ䯈䖳ᓊNCS ൟ఼ࠊخ㡖⚍䆒䅵 ˈԚ㔥㒰Ӵ䕧䖳ᓊᇣѢϔϾ䞛ḋ਼ ᳳ䖭ϔ؛䆒ᅲ䰙㋏㒳Ёᐌᐌϡ㛑ᕫࠄ⒵䎇˗᭛⤂[5]ᡞ㔥 㒰Ёⱘϡ⹂ᅮᗻ䖳ᓊ䗮䖛䆒㕂㓧ކऎඳ䕀ᤶ៤⹂ᅮᗻ䖳 ᓊˈҢ㗠ᇚ㔥㒰࣪ࠊ㋏㒳Ң䱣ᴎ㋏㒳䕀࣪Ў⹂ᅮᗻᯊ⒲ ㋏㒳 ˈԚ㓧ކऎⱘ䆒ゟҎЎⱘᓊ䭓њ䖳ᓊᯊ䯈ˈ⬹ᰒ⡉ ᔎDŽ 乘⌟ߑ᭄ࠊ(Predictive Functional Control, ㅔ鹵PFC)
ࠊ఼㡖⚍ᓩܹᬍ䖯乘⌟ߑ᭄ࠊㅫ⊩ˈ䆹ㅫ⊩乘⌟㋏㒳ᴹ䕧ߎᯊ㗗㰥њϸ辵ৃ㛑ⱘᯊ䯈䖳ᓊ㋴ˈᕫߎњ䗖⫼Ѣޣᇣ䭓ǃⷁᯊ䯈 䖳ᓊᕅડⱘࠊ䕧ߎㄪ⬹DŽ Matlab ⦃๗ϟ߽⫼ TrueTime Ꮉㆅᵘᓎњ㔥㒰ӓⳳ⦃๗ˈᇍ↨њϸ辵ᯊ䯈䖳ᓊᑊᄬᚙމϟϢᐌ㾘乘 ⌟ߑ᭄ࠊㅫ⊩ⱘࠊᬜᵰˈӓⳳ㒧ᵰ㸼ᯢᬍ䖯ৢⱘㅫ⊩ᇍޣᇣ䭓ǃⷁᯊ䯈䖳ᓊᕅડˈᦤ催ࠊક䋼᳝ⴔ㡃དᬜᵰDŽ ݇䬂䆡 㔥㒰࣪ࠊ㋏㒳ˈ䭓ᯊ䯈䖳ᓊˈⷁᯊ䯈䖳ᓊˈ乘⌟ߑ᭄ࠊ
乘⌟ߑ᭄ࠊ㔥㒰࣪ࠊ㋏㒳ЁⱘⷨおϢᑨ⫼
਼咢䕝 1,2
1)
⥟ 3
䶽⩲ 1
ᕤᑇ 3
3)
ढ࣫⬉ᄺࠊ里ᄺϢᎹᄺ䰶 ֱᅮ 071003 2) ⬉फҀ㞾ࡼ᳝࣪䰤݀ৌ फҀ 210003 ढ࣫⬉ᄺ㛑⑤ϢࡼᎹᄺ䰶 ࣫Ҁ 102206
ᨬ
㽕
㔥㒰࣪ࠊ㋏㒳Ё⬅Ѣ㔥㒰Ӵ䕧ৃ㛑ᓩ䍋ϡ⹂ᅮᗻ䭓ᯊ䯈䖳ᓊⷁᯊ䯈䖳ᓊDŽ䩜ᇍϸ辵ৃ㛑ߎ⦄ⱘᯊ䯈䖳ᓊ⡍ᗻˈ
ᬍ䖯乘⌟ߑ᭄ㅫ⊩ᴀॳ⧚
ᬍ䖯乘⌟ߑ᭄ࠊㅫ⊩ॳ⧚Ḛབ 2 ᠔冫ˈϢӴ㒳 ⱘ乘⌟ߑ᭄ࠊㅫ⊩Ⳍ↨ˈЏ㽕ऎ߿ᰃᅗՓ⫼㋏㒳ⱘ᳝ 䖳ᓊ⡍ᗻⱘ⢊ᗕぎ䯈ൟᴹ乘⌟ᇍ䈵ⱘ䕧ߎDŽ
a d T ˈ߭鹵䖭ḋⱘӴ䕧䖳ᓊЎⷁᯊ䯈䖳ᓊ˗ ᅮН ᔧ㔥㒰Ӵ䕧䖳ᓊऎ䯈 [0, a] ߚݙᏗˈϨ a t T ˈ߭鹵䖭ḋⱘӴ䕧䖳ᓊЎ䭓ᯊ䯈䖳ᓊ˗ ⊼˖⬅ᅮН ৃⶹˈ䭓ᯊ䯈䖳ᓊϡᰃϔᅮѢϔϾ䞛
(4)
F(h< N )ui
݊Ё˖
K *(m) [*0 , *பைடு நூலகம் ," * h ], u (k ) [u (k ), u (k 1)," , u (k h)]
䗮䖛䗦ᮍ⊩ᕫ˖
ª FT n(0) F T n(1) " F T n(i 1) º « T » T T « F n(1) F n(0) " F n(i 2) » « # » # # # « T » T T ¬F n(h) F n(1 h) " F n(i 1 h)¼ (h< N )ui K ªPn 0 0 º K P hu ( h < N ) « 0» «0 % K » « » n 0 0 P ¬ ¼ hu ( h < N )
ൟⱘ㔥㒰࣪ࠊ㋏㒳㒧ᵘЏ㽕⬅ϔϾ㔥㒰ഫ㢹 ᑆϾᱎ㛑㡖⚍㒘៤ˈབ ᠔冫DŽ
M
e AT , *m
³
k tm 1
k tm
k e A (T s ) Bds, t 1
k T ; th
0
ᔧӴ䕧䖳ᓊЎⷁᯊ䯈䖳ᓊᯊˈे 0 W k T ˈᓣ (2) Ё h=1ˈϔϾ䞛ḋ਼ᳳ [kT , (k 1)T ] ࠄݙ䖒㹿ᇍ䈵Ϟ ⱘࠊ䞣া᳝ϔϾ u(t)˗ᔧӴ䕧䖳ᓊЎ䭓ᯊ䯈䖳ᓊᯊˈे ˈᓣ(2)Ё h>1ˈϔϾ䞛ḋ਼ T W k hT ˄h Ўℷᭈ᭄˅ ᳳ [kT ,(k 1)T ] ࠄݙ䖒㹿ᇍ䈵ⱘࠊ䞣 u(t)ߚ↉䖲㓁Ϩ ᳔᳝ h+1 ϾϡৠⱘؐDŽ ҹϞݙᆍᓎゟњϔϾߚᏗᓣ㔥㒰࣪ࠊ㋏㒳ൟDŽ
1)
sAbstract—With regards to the characteristics of stochastic short time delay and long time delay induced by the network transmission in networked control system (NCS), the improved predictive functional control (PFC) algorithm is proposed in this paper. The two kind of network-induced time delays are specifically considered for predicting the future plant outputs in improved PFC algorithm. The control law is given by improved PFC which is introduced to controller nodes in NCS. A distributed NCS model is constructed based on TrueTime toolbox. Simulation experiments are practiced over this model which embraces both stochastic short time delay and long time delay. It is proved that the improved PFC algorithm can give better control performance compared with the standard PFC algorithm. Keywords—Networked Control System (NCS), Long Time Delay, Short Time Delay, Predictive Functional Control (PFC)
xp ( k i )
݊Ё M (i )
M i xp ( k ) * ( m )U huiM T (i ) V ( k ) M T (i )
[M i 1 , M i 2 ," ,1], V (k ) Ўⱑాໄ䞣ˈे˖
(5)
ᭈ⧚ᓣ(11)ᕫ˖
yp ( k i )
݊Ё˖
i 1
K C M i x p ( k ) P n <W j T (i ) V ( K ) Wj (i) [ w1(i ), w2(i )," , wj (i )] ,
ª
h
(12)
V (k ) [v(k ), v(k 1)," v(k i 1)] ˈ K K K U hui [u T (k ), u T (k 1)," , u T (k i 1)]
>@
DŽ
䆹ㅫ⊩ᡞࠊ䕧ܹⱘ㒧ᵘ㾚Ў݇䬂䯂乬ˈৃҹܟ᳡݊ᅗ ൟ乘⌟ࠊৃ㛑ߎ⦄㾘ᕟϡᯢⱘࠊ䕧ܹ䯂乬ˈৠᯊ᳝ 㡃དⱘ䎳䏾㛑ঞ䕗ᔎⱘ剕ẦᗻDŽ乘⌟ߑ᭄ࠊㅫ⊩гৃ ҹ䞛⫼䕗ⱘ䞛ḋ਼ᳳˈ↨䕗䗖⫼ѢᄬӴ䕧䖳ᓊⱘ㔥㒰 ࣪ࠊ㋏㒳ˈ⬅ѢӴ䕧䖳ᓊⱘᄬˈӴ㒳乘⌟ߑ᭄ࠊㅫ ⊩ϡ㛑ᕫࠄᕜདⱘࠊᬜᵰDŽᴀ᭛ᦤߎࠊ఼㡖⚍ᓩܹ 㛑䗖⫼Ѣⷁᯊ䯈䖳ᓊ䭓ᯊ䯈䖳ᓊⱘᬍ䖯乘⌟ߑ᭄ࠊㅫ ⊩ˈᑊℸ⸔Ϟ⫼䆒䅵ⱘ㔥㒰࣪ࠊ㋏㒳ൟ偠䆕݊ ࠊᬜᵰDŽ
1ˊᓩ㿔
㔥㒰࣪ࠊ㋏㒳˄ Networked Control System ˈㅔ鹵 NCS˅ⱘ⡍⚍ᰃড作ࠊಲ䏃䗮䖛辵㔥㒰ֵ䘧䖲㗠ᔶ ៤㋏㒳䯁⦃DŽϢӴ㒳ᛣНϞⱘࠊ㋏㒳Ⳍ↨᳝ᕜӬ⚍˖ བᅲ⦄䌘⑤݅ѿˈѸѦᗻད˗֓Ѣ㋏㒳ᅝ㺙ǃ㓈ᡸǃᠽሩ˗ ޣᇥ㋏㒳䖲㒓ˈ⠽⧚㒧ᵘⳌᇍㅔऩˈࡴњ㋏㒳ⱘ♉⌏ᗻ ৃ䴴ᗻDŽ㗠㔥㒰࣪ࠊ㋏㒳ℷ៤ЎҎӀⷨおⱘϔϾ⛁ ⚍ˈᑊᓩ䍋њ䍞ᴹ䍞ⱘᄺ㗙ⱘ݈䍷[1-3]DŽ Ԛᰃˈ 䗮䆃㔥㒰ⱘᓩܹՓ㋏㒳ⱘߚᵤ䆒䅵বᕫ䴲ᐌ1
ḋ਼ᳳˈ㗠ᰃ䖳ᓊߚᏗऎඳⱘϞ⬠ѢϔϾ䞛ḋ਼ᳳDŽ 㔥㒰࣪ࠊ㋏㒳Ёˈḍ㡖⚍ⱘ偅ࡼᮍᓣϡৠˈ㔥 㒰⦃๗ϟⱘࠊ㋏㒳ᓎг䱣ПϡৠDŽЎњⷨおᮍ֓ˈᴀ ᭛া㗗㰥㔥㒰࣪ࠊ㋏㒳ЁⱘӴ䕧䖳ᓊ㗠ϡ㗗㰥᭄϶ࣙ ᭄ࣙᯊᑣ䫭хᚙˈމϨخབϟ؛䆒˖ ؛䆒 ˖Ӵᛳ఼㡖⚍䞛⫼ᯊ䩳偅ࡼᮍᓣˈࠊ఼㡖⚍
>@ >@
978-1-4244-2114-5/08/$25.00 © 2008 IEEE.
6236
᳔ ᮽ ⬅ ⊩ ADERSA ݀ ৌ ⱘ Richalet ᖋ IITB ݀ ৌ ⱘ KuntzeㄝҎᑈҷЁৢᳳᦤߎˈᑊ៤ࡳᑨ⫼ѢᎹϮᴎ఼ Ҏⱘᖿ䗳催㊒ᑺࠊ ሲѢϝҷൟ乘⌟ࠊㅫ⊩
Lihui Zhou1,2, Tiankun Wang3, Pu Han1, Daping Xu3
2)
North China Electric Power University, Baoding 071003(E-mail: hp@ncepubd.edu.cn) Guo Dian Nan Jing Automation Co. LTD, Nanjing 210003 (E-mail: zhouli-hui@gmail.com) 3) North China Electric Power University, Beijing 102206 (E-mail: wangtiankun@gmail.com)
ాໄDŽ 㓐ড়㗗㰥Ӵ䕧䖳ᓊЎⷁᯊ䯈䖳ᓊ䭓ᯊ䯈䖳ᓊϸ辵ᚙ ˈމᡞ䖲㓁ൟ行ᬷ࣪ˈৃᕫ˖
h p p x ( k 1) M x ( k ) ° ¦ * m u ( k m ) v(k ) ® m 0 ° y p ( k ) Cx p ( k ) w ( k ) ¯
(2)
2ˊ㔥㒰࣪ࠊ㋏㒳ⱘߚᵤϢᓎ
Wca
Wsc
3ˊᬍ䖯乘⌟ߑ᭄ࠊㅫ⊩
1˖㔥㒰࣪ࠊ㋏㒳ⱘᴀ㒧ᵘ
3.1 㔥㒰⦃๗ϟˈ ⫼᠋݅ѿ䗮䆃㒓䏃Ϩ⌕䞣ব࣪ϡ㾘߭ˈ ᔧϾ㡖⚍䗮䖛㔥㒰Ѹᤶ᭄ᯊᖙ✊ᇐ㟈Ӵ䕧䖳ᓊˈNCS ⱘӴ䕧䖳ᓊЏ㽕⬅ϸ䚼ߚᵘ៤˖Ӵᛳ఼㡖⚍ˉࠊ఼㡖⚍ ⱘӴ䕧䖳ᓊ W sc ࠊ఼㡖⚍ˉᠻ㸠఼㡖⚍ⱘӴ䕧䖳ᓊ W ca DŽӴ䕧䖳ᓊৃ㛑ѢϔϾ䞛ḋ਼ᳳ ⫼ T 㸼冫 ˈгৃ㛑 ᇣѢϔϾ䞛ḋ਼ᳳℸᦤߎབϟᅮН˖ ᅮН ᔧ㔥㒰Ӵ䕧䖳ᓊऎ䯈 [0, a] ߚݙᏗˈϨ