空间机械臂柔性关节轨迹跟踪自抗扰控制

Proceedings of the 30th Chinese Control ConferenceJuly 22-24, 2011, Yantai, China

グ䰪 Ủ㟸Ḋ 㢸䖞䘯䐕䑠㠠

怄㉦⒩ 䞿㿸 怄棂

┘ ъ 㡚 䲒, ┘ 150001

E-mail: [email protected]

㾷: 䪸 オ䰤 Ỡ㟲Ḅ 㢲Ⲵ儈㋮ 䖘䘩䐏䑚䰞仈ˈ ・ ⭥ н⺞ 亩 䍏䖭 亩ⲴḄ 㢲Ҽ䱦㓗㚄 〻ˈ 䈕Ѣ㓗㌫㔏 Ҿ㠚 (ADRC) 䇮䇑Ҷ єњ㠚 Ⲵ 䰝⧟ ㌫㔏DŽ 䙊䗷 ⣦ 㿲⍻ (ESO) ՠ䇑⭥ н⺞ ㍐ 䍏䖭 䗷〻ѝ ԕ㺕 DŽ䟷⭘䈕 䇮䇑Ⲵ 㜭┑䏣㌫㔏 䙏 っ ㋮ Ⲵ㾱≲ˈ Ҷ⭥ н⺞ ㍐ 䍏䖭 ㌫㔏Ⲵ DŽ ㇇⌅ㆰ ˈ Ҿ ⧠DŽԯⵏ㔃 㺘 䇮䇑Ⲵ 䰝⧟ ㌫㔏 ㋮ 儈ǃ励ἂ ㅹ㢟 Ⲵ 䍘ˈ а Ⲵ 〻 䱵 ѹDŽ

䭤䈃: オ䰤 Ỡ㟲, Ḅ 㢲, 䖘䘩䐏䑚, 㠚

Active Disturbance Rejection Control for Trajectory Tracking

of Space Manipulator Flexible Joint

ZHAO Zhigang, TIAN Hao, ZHAO Yang

School of Astronautics, Harbin Institute of Technology, Harbin 150001, P.R. China

E-mail: [email protected]

Abstract: The high-precision trajectory tracking control for space manipulator flexible joint is researched. The second-order cascade dynamics equations with motor uncertainties and load disturbance of flexible joint are established. A control strategy of active disturbance rejection control (ADRC) and double closed-loop control is presented based on cascade systems. Both the inner and outer loops are designed by active disturbance rejection controllers. In this method the disturbances are estimated using extended state observer (ESO) and compensated during each sampling period. The designed controller not only satisfies the quick response speed and steady-state accuracy demands, but also effectively resists to the motor uncertainties and the load disturbance. Control algorithm is simple and it is easy to digital implement. The simulation results indicate that the designed of the double closed-loop control system has high-precision and stronger robustness and has important engineering significance. Key Words: Space Manipulator, Flexible Joint, Trajectory Tracking, Active Disturbance Rejection Control

1. 䀶

䲿⵰オ䰤ㄉ 䖘 ǃ␡オ ⍻ㅹオ䰤 亶 Ⲵ䗵䙏 , Ҿオ䰤 Ỡ㟲 Ⲵ䴰≲䎺 䎺䘛 DŽオ䰤 Ỡ㟲 䖘 ǃ о㔤 Ⲵа亩 䭞 ˈ ⵰ 䱄Ⲵ ⭘ Ⲵ ⢥ о

> @

⭘DŽオ䰤 Ỡ㟲 㢲䙊 䴰㾱 䖳 䙏∄Ⲵ䰤 傡 㜭 ˈ Ѫ Ỡ㟲Ṩ 䜘 Ⲵ 㢲 ⭘䉀⌒喯䖞 䙏 Ѫ傡 䜘Ԧˈ䘉ṧⲴ 㢲 㔃 ㍗ ǃփ〟 ǃ䟽䟿䖫ǃ 䖭㜭 ǃՐ ⦷儈

> @

ㅹՈ⛩DŽն 䉀⌒喯䖞 䙏 䗷〻ѝ ⲴḄ 䙐 ㌫㔏ӗ⭏䉀 Ⲵѫ㾱 ㍐ˈ Ỡ㟲 㹼ԫ Ⲵ㋮ っ DŽ ˈオ䰤 Ỡ㟲Ⲵ ⧟ ˈ ⿽ 䜘 ⍻䟿 ㅹн⺞

> @

㍐䜭Պ ӗ⭏а ˈ ≲ 〻к䘲⭘Ⲵ儈 䍘励ἂ ањӏ䴰䀓 Ⲵ䰞仈DŽ

亩 㠚❦、 䠁䍴 ˈ亩ⴞ ˖50975056ǃ11072066.

*

䘁 ˈ䪸 н⺞ ㍐ лḄ 㢲Ⲵ

> @> @> @

䰞仈ˈ励ἂ ǃ ╄ ǃ⾎㓿㖁㔌 ǃ

> @> @> @

ǃ━⁑ ǃ㠚䘲 ǃ⁑

> @

㋺ ԕк ⌅Ⲵ ⌅ㅹ㧧 Ҷ䖳␡ ⹄ウDŽ ⥞> @ ⌒⾎㓿—励ἂ ⧠Ḅ 㢲 Ӫ儈㋮ ս㖞䐏䑚˗ ⥞> @ а⿽ Ҿ ⨶䇪Ⲵ⾎㓿㖁㔌 ㆆ⮕ˈն䈕 ⌅䘲 㢲Ḅ 䖳 Ⲵ ˗ ⥞> @䙊䗷䇮䇑 㢲Ḅ 㺕 ⌅ Ѫа㡜ⲴḄ 㢲 ㌫㔏ѝˈ 䪸 㺕 Ⲵ ㌫㔏䇮䇑Ҷ㠚䘲 㿴 ˈ 㠚䘲 ㇇⌅ ⭘Ҿ Ӫ ՠ䇑ѝ˗ ⥞> @ Ҷа⿽⭡㠚䘲 ⁑㋺㌫㔏 䙀䘶 䇮䇑⴨㔃 Ⲵ䙂䱦 ⌅, ն ⌅⁑㋺㿴 , 䇑㇇䟿 DŽ

ок䘠ⲴḄ 㢲 ⌅н ˈ 䟷⭘㠚 䇮䇑єњ㠚 ѻ 䰝⧟ 㺕 Ḅ 㢲⁑ н⺞ 䍏䖭ㄟ 䜘н⺞ Ⲵ DŽ㠚 (Active

> @

Disturbance Rejection Control, ADRC) 丙Ӝ␵⹄

ウ Ⲵа⿽н 䎆㌫㔏㋮⺞⁑ Ⲵ DŽ ⭘ ⣦ 㿲⍻ ՠ䇑⭡Ҿ⁑ н⺞ ㍐ “ ” ⿽“ ” Ⲵ ˈ 䗷〻ѝ Ā ā ԕ㺕 ˈ 㓸 ⁑ н⺞ л ⧠㢟 Ⲵ 䍘ˈ 䎵䈳 ǃ ǃ㋮ 儈ǃ 㜭 ǃ㇇⌅ㆰ ㅹ⢩⛩ˈ ф Ҿ

> @

⧠DŽADRC 䘲Ҿ ⨶ н⺞ ㍐ Ⲵ㌫㔏Ⲵ 䰞仈DŽ

ԕオ䰤 Ỡ㟲Ḅ 㢲Ѫ⹄ウ 䊑ˈ䙊䗷䇮䇑㲊 䟿 Ḅ 㢲㓗㚄㌫㔏 єњ㠚 㺕 ⁑ н⺞ ㍐ Ⲵ 䍏䖭ㄟ Ⲵ Ⲵ ⭘ˈ ⧠Ḅ 㢲Ѣ㓗㌫㔏㠚 DŽ

㢲䗃 䖤ս〫TL ⧠ 㢲䖘䘩䐏䑚ԫ ⲴѢ㓗㌫㔏DŽ

, y x , 䇠x 11 TL , x 12 T L , y 1 x 11, x 21 Tm , x 22 Tm 221

K 1a s , b , u Wm

NJ L J m

§C K s ·1

TL f 1(x 11, x 12, x 21, x 22, w L ) ¨L Tw L ¸L J L J L J L ¹

§C ·K 1

w L ¸ ¨L x 12 s x 11

J L J L J L ¹

§C K s Tm w ·

f 2(x 11, x 12, x 21, x 22, w m ) ¨m T( TL ) m ¸m

NJ m N J m ¹J m

§C K x w ·

¨m x 22 s (21 x 11) m ¸

NJ m N J m ¹J m

Ḋ 㢸㌱㔕 ⁗

2.1 Ḋ 㢸㌱㔕

オ䰤 Ỡ㟲Ḅ 㢲ѫ㾱⭡ Ⓚ( ⭘ժ ⭥

) ǃՐ ( ⭘䉀⌒ 䙏 ) ⍻䟿 Ԧ( ս㖞

> @

⍻䟿ǃ ⍻䟿ㅹ) ㅹ䜘 㓴 DŽ 㢲Ḅ а㡜⭡ 䙏 ǃ䖤 Ր 䬮ㅹ 䎧ˈ 㢲䘋㹼 ⁑㾱

> @

㘳㲁 㢲Ḅ Ⲵ ˈ 㢲㔃 ⽪ 1 ⽪DŽ

(1) лє

11 x 12­x °

12 f 1(x 11, x 12, x 21, x 22, w L ) ax 21 (2) 6L :x °y x

11¯1

21 x 22­x °

22 f 2(x 11, x 12, x 21, x 22, w m ) bu (3) 6m :x

°y x

21¯2

Ѫ Ҿ 䇮䇑ˈ f 1(x 11, x 12, x 21, x 22, w L )

L 1: Ḅ 㢲㌫㔏⽪

2.2 Ḋ 㢸 ⁗

㢲Ḅ ㅹ Ѫ㓯 䖜 ㉗ˈ ф 㘳㲁

⭥ ㄟⲴн⺞ 亩 䍏䖭㋈┎䱫 ⭼ ㅹ ㍐ˈ ・ Ỡ㟲 њḄ 㢲㌫㔏Ⲵ 〻ˈ (1) ⽪˖

­ K T w K s TJ C TTL L s L L m °°L L N

(1)

K Ts °J T (m TL ) w m Wm m m C m Tm °N N ¯

ѝ˖TL Ѫ 㢲䗃 䖤ս〫˗Tm Ѫ⭥ 䖤ս〫˗J L Ѫ䍏䖭 䟿˗J m Ѫ⭥ 䟿˗K s Ѫ 䖜 ㉗ ㌫ ˗N Ѫ 䙏∄˗C L Ѫ䍏䖭ㄟ䱫 ㌫ ˗C m Ѫ⭥ Ⲵ䱫 ㌫ ˗Wm Ѫ⭥ Ⲵ傡 ⸙˗w L Ѫ䍏䖭 ⭼ ˗w m Ѫ⭥ ㄟⲴн⺞ 亩DŽ䘉䟼 w L w m ⭼DŽ

⭡ (1) ⸕ˈ㌫㔏 䱵к ⭡⭥ Ⲵ傡 ⸙Wm 傡 ⭥ 䖤ս〫Tm ˈ㘼⭥ 䖤ս〫Tm 傡

f 2(x 11, x 12, x 21, x 22, w m ) Ⲵ ⭘䟿 Ⲵ⣦

13 ML ˈx 23 Mm ˈ (2) 䟿x 13 x 23ˈ 䇠x

(3)㓴 ⲴѢ㚄㌫㔏 ⲴѢ㓗㓯 ㌫㔏 (4) (5) ⽪

11 x 12­x °

' °x 12 x 13 ax 216L : (4)

Mx L °13°¯y 1 x 11

21 x 22­x °

' °x 22 x 23 bu 6m : (5) Mx m °23°¯y 2 x 21

䘉䟼 ԕ Ḅ 㢲㌫㔏ⴻ ⭡6L 6m

єњ ㌫㔏㓴 ⲴѢ㓗㌫㔏ˈ䘉䟼Ѣ㓗㌫㔏 Ⲵ 䟿u 傡 x 21ˈ㘼x 21 傡 x 11ˈӾ㘼䗮 ⴞⲴDŽ ⣦ 䟿x 21ⴻ Ѫ⣦ 䟿x 11ⲴĀ㲊 䟿āˈ䇠Ѫu 1DŽ

Ḋ 㢸 䰣⧥㠠 䇴䇗

ADRC 䶎㓯 䐏䑚- TD

> @

(Tracking differentiator)ˈ ⣦ 㿲⍻ ESO (Extended state observer) 䶎㓯 ⣦ 䈟 侸

> @

NLSEF (nonlinear state error feedback)йњ䜘 ˈ䘉й䜘 㜭 л˖

> @

ѝH1i sup

(1) 䐏䑚 (TD) 䗃 Ⲵ䗷⑑䗷〻

㔉 ˈ 䗷⑑䗷〻 ԕ 䀓 ㌫㔏 䙏 䎵䈳ѻ䰤Ⲵ⸋⴮˗

(2) ⣦ 㿲⍻ (ESO)ՠ䇑 䊑 ㌫㔏⁑ ⭘ˈESO Ҿ 䟿Ⲵ 㓯ՠ䇑 ㌫㔏 䭞⧟㢲ˈ ㌫㔏 㜭˗

(3) ⭘䶎㓯 ⣦ 䈟 侸(NLSEF) ՠ䇑䟿㺕 ӗ⭏ 㻛 ѪĀ〟 Ѣ㚄 āⲴ 䊑䘋㹼 DŽ

⣦ 䟿x 21 Ѫ⣦ 䟿x 11ⲴĀ㲊 䟿āu 1ˈ❦ ⭘ 䱵 䟿u ѝ䰤 䟿x 21 䐏䑚Ā㲊 䟿āu 1ˈԕ䗮 䱵 䟿u 㻛 䗃 y 1 x 11Ⲵԫ DŽ ⭘⣦ 䟿x 11 TL x 21 Tm 㜭 ⍻䟿ˈ 2 ⽪ⲴḄ 㢲䖘䘩䐏䑚㠚 䰝⧟ ㌫㔏DŽ 3.1 ⧥ADRC Ⲻ䇴䇗

L V1

^z 1i x 1i , i 1, 2,3ˈ⭡ (8) ⸕ˈ 㾱

E13䏣 ҾV1ˈ㌫㔏⣦ Ⲵՠ䇑䈟 䜭Պ䏣 DŽ 㿲⍻ ˈz 11ox 11ˈz 12ox 12ˈz 13ox 13ˈ ѝz 13ՠ䇑䍏䖭 ㌫㔏 Ⲵ Ā ā x 13ˈ 䍏䖭Ⲵ ㅹ н⺞ ㍐DŽ (3) NLSEF⭏ 䟿 㺕

­e 11(k ) v 11(k ) z 11(k ) °

e 12(k ) v 12(k ) z 12(k ) °°

u 01 fhan(e 11, e 12, r 1, h 1) (9) °

°u (k ) u z 13(k ) 101°a ¯

z 13(k )

Ѫ䍏䖭 ㌫㔏ⲴĀ āⲴ 㺕 䜘 DŽ a

3.2 ⧥ADRC Ⲻ䇴䇗

⧟ Ⲵ 䊑Ѫ (3)ˈ䇮䇑 ⧟ADRC

⧟ Ⲵ 䊑Ѫ (2)ˈѪҶ䇙 䰝⧟ADRC Ⲵѫ㾱ⴞⲴ 䇙⣦ 䟿x 21 䐏䑚 ⧟㔉 Ⲵ⌅㧧 Ⲵ ˈ䇮䇑 ⧟ ˈ䙊䗷 䗷㲊 䟿u 1ˈ ԕ ⧟ⲴADRC ѝ ⎸Ҷ⑑䗷〻 䟿 䇱䗃 u 1 ━аӋDŽ 䗷⑑䗷〻䘉а⧟㢲DŽ

⧟ADRC Ⲵ⿫ ㇇⌅ ԕлй䜘 ˖ ⧟ADRC Ⲵ⿫ ㇇⌅ ԕлє䜘 ˖ (1) TD 䗷⑑䗷〻 (1) ESOՠ䇑⣦

­fh fhan(v 11(k ) v (k ), v 12(k ), r 0, h ) 11­

e k u k y k e h e () () (),fe fal(, , ),fe fal(, , h ) °121° (6) v 11(k 1) v 11(k ) hv 12(k ) 24°°°v (k 1) v (k ) h fh(v (k ), v (k ), v (k ), r , h )

(10) 1211120z 21(k 1) z 21(k ) h (z 22(k ) E21e ) ¯12

°z 22(k 1) z 22(k ) h (z 23(k ) E22fe bu (k )) v 11(k ) v 12(k ) Ѫ䐏䑚 ѝv (k ) Ѫ 䗃 ˈ°° 䗃 ˈh Ѫ䟷ṧ䮯ˈr 0 ¯z 23(k 1) z 23(k ) h ( (E23) fe 1)

Ѫ䗷⑑䗷〻䙏⦷ ˈ 䐏䑚Ⲵ䙏 ˈ r 0䎺 ˈ ѝz 21ˈz 22 z 23 ESO ㌫㔏⣦ Ⲵՠ䇑 ˈ

E21!0ǃE22!0 E23!0Ѫ ⧟ ⣦ 㿲⍻ 䐏䑚䙏 䎺 ˈն ҏ䎺 DŽ

(2) ESOՠ䇑⣦ 䇮䇑 DŽ Mm V2, V2!0, о (8) ⨶ˈ

11­4­§V·°e (k ) z 11(k ) y 1(k ),fe fal(e , 2, h ),fe 1 fal(e , 4, h )

°lim z 21 x 21 ¨ H21¸°°z (k 1) z (k ) h (z (k ) Ee ) °t ofE23¹(7) 11121111°4°z 12(k 1) z 12 h (z 13(k ) E12fe au 1(k )) °§V· ° (11) H22lim z 22 x 22 E21¨¸t ofE°z 13(k 1) z 13(k ) h ( E13fe 1) ¯23¹°°4 ѝz 11ˈz 12 z 13 ESO ㌫㔏⣦ Ⲵՠ䇑 ˈ§V·°

EHlim z x ¨¸23232223E11!0ǃE12!0 E13!0Ѫ ⧟ ⣦ 㿲⍻ 䇮°t of

E23¹¯䇑 ˈ ESO Ⲵ 䍘DŽ䙊䗷 ⨶䘹 ˈ

ѝH2i sup ^z 2i x 2i `, i 1, 2,3ˈ 㿲⍻ ˈ ԕ ESO っ DŽADRC Ⲵっ ṩҾESO Ⲵ ՠ䇑䈟 DŽ ML V1, V1!0, ṩ 㘳 ⥞[19]

4­§V1·

°lim z 11 x 11 ¨ H11¸°t ofE13¹°4°§V1·

(8) H12lim z 12 x 12 E11¨¸t of13¹°

°4

§V1·°

EHlim z x ¨¸13131213°t of

13¹¯

m V2

z 21ox 21ˈz 22ox 22ˈz 23ox 23ˈ ѝz 23ԓ㺘㌫⭥

㔏 ⲴĀ ā Ѫx 23ˈ ⭥

⁑ ㅹн⺞ ㍐DŽ

(2) NLSEF⭏ 䟿 㺕

­e 21(k ) u 1(k ) z 21(k ) °

e 22(k ) z 22(k ) °°

u 02 fhan(e 21, e 22, r 2, h 2) (12) °

°u (k ) u z 23(k )

02

°b ¯

z 23(k )

Ѫ⭥ ㌫㔏ⲴĀ āⲴ 㺕 䜘 DŽ b

> @

䶎㓯 fal(e , D, G) fhan(x 1, x 2, r , h ) Ⲵ ѹ

Ѫ˖

e ­

, e dG°1 fal(e , D, G) G (13)

°e Dsign(e ), e !G¯

ѝG㺘⽪㓯 ⇥Ⲵ 䰤䮯 DŽ

fhan(x 1, x 2, r , h )

3ѪḄ 㢲 ㌫㔏 ս䱦䏳 DŽ⭡ ⸕ˈ㌫㔏 㓯 っˈ ⧠Ҷ 䎵䈳 ˈ ф 㓖㓿䗷2s Ⲵ 䰤 䗮 っ ˈ㺘 ㌫㔏 䙏ˈっ ㋮ 儈DŽ

㌫㔏 ­

°d rh 2, a 0 hx 2, y x 1 a 0°

°a 1 °

°a 2 a 0 sign(y )(a 1 d ) 2 (14) °S (sign(y d ) sign(y d )) 2 y °

°a (a 0 y a 2) S y a 2

°S (sign(a d ) sign(a d )) 2°a

a °

fhan (r sign(a )) S a r sign(a ) °d ¯

fhan(x 1, x 2, r , h ) 䙏 Ո 㔬 Ⲵ

䰤(s)

3: Ḅ 㢲 ㌫㔏 ս䱦䏳

⿫ DŽ

Եⵕ㔉

Ѫ傼䇱 䇮䇑Ⲵ 䰝⧟ADRC Ⲵ ˈԕ 1 ⽪ⲴḄ 㢲㌫㔏Ѫ 䘋㹼䖘䘩䐏䑚Ⲵ ԯⵏ䈅傼DŽḄ 㢲 ㌫㔏Ⲵ⢙⨶ 㺘1 ⽪ˈ ѝ㌫㔏䜘 㘳Ҷ ⥞> @ѝⲴ DŽ䘉䟼䇮 䍏䖭 ㅹн⺞ 亩Ѫw L 0.1sin t N m ˈ⭥ ⁑ ㅹн⺞ 亩Ѫw m 0.01sin t N m DŽ

㺘1. Ḅ 㢲㌫㔏

ㅖ

⢙⨶ 䍏䖭 䟿 ⭥ 䟿 䍏䖭ㄟ䱫 ㌫ ⭥ 䱫 ㌫ 䖜 ㉗ ㌫

䙏∄

Ḅ 㢲 㹼ԫ 㜭Պ ⧠ 䙏䘀 ㅹ ˈѪҶ Ⲵ㘳 Ⲵ 㜭ˈ 䘹 Ѫ1u10 3rad ǃ Ѫ4s Ⲵ↓ 㓯 Ѫ 䖘䘩䘋㹼䐏䑚ˈ Ⲵ ѫ㾱䇮䇑 䘹 㺘3 ⽪DŽ

㺘3. ADRC

ㅖ ㅖ

r 0

10

h

0.001

r 1 h 1 r 2 h 2

0.5

1000

E11

100

E12E13 E21 E22E23

2000

J L J m C L C m K s N

2.5u10 3kg m 2

3.2u10 4kg m 2 0.006N m s/rad

0.002N m s/rad 5.5u10N m/rad

60

3

Ѫオ䰤 Ỡ㟲Ḅ 㢲 䘀 䖘䘩о 䱵䘀 䖘䘩Ⲵ∄䖳 DŽ⭡ ⸕ˈ Ỡ㟲Ḅ 㢲 10s Ⲵԯⵏ䗷〻ѝ䗮 Ҷ䖳儈Ⲵ䐏䑚㋮ ˈ⭥ н⺞ 亩 䍏䖭 亩 Ⲵ㺕 ˈ㺘 ㌫㔏 ⭥ н⺞ 亩 䍏䖭 亩 ⭘ л Ⲵ励ἂ ˈ䗮 Ҷ䖳 Ⲵ䖘䘩䐏䑚 DŽ

-3

䐏䑚䖘䘩(r a d )

л䶒䙊䗷䗃 ս䱦䏳 㘳 ㌫㔏Ⲵ㔬 㜭ˈ ⲴADRC ѫ㾱 䘹 㿱㺘2DŽ

㺘2. ADRC

ㅖ ㅖ

r 0 h r 1 h 1 r 2 h 2

1000.65

E11 E12 E13

E21 E22 E23

700 䰤(s)

4: Ḅ 㢲㌫㔏䐏䑚䖘䘩

5ѪḄ 㢲⭥ 傡 ⸙ԯⵏ ˈ⭡ ⸕⭥ 䗃 ⸙ 㓖-0.7Nm ̚0.7Nm ѻ䰤ˈ ф 䗃 ⸙䘎㔝 ━ˈ㺘 䇮䇑 㜭㢟 DŽ

㘹 ⥤

[1] ҾⲫӁ, Ӝ, 傜 ⪎. オ䰤 Ỡ㟲 䇞. 咹⮸

⣷ぴ䲚, 2007, 16(4):1865-1870.

[2] Makoto Iwasaki, Masafumi Yamamoto, Hiromu Hirai, et

al ˊModeling and Compensation for Angular Transmission Error of Harmonic Drive Gearings in High Precision Positioning. 09 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Suntec Convention and Exhibition Center Singapore, July 14-17, 2009: 662-667. [3] 䉒㇝, 㢟, 仌цր, ㅹ. Ҿ⾎㓿㖁㔌Ⲵн⺞ オ䰤

Ӫ㠚䘲 ⌅⹄ウ. ⸖咹ⷵ㔴, 2010, 31(1): 123-129.

i

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≹ , 㽊 , 䍮 䖙 Ḅ 㢲 н⺞ 㺕 Ⲵ

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⌒⾎㓿——励ἂ 㧉㬿ぴ䲚ⷵ㔴, 2010, 46 .

呹┷▥ⷵ㔴ˈ ˈ

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[10] Huang A CˈChen Y C. Adaptive sliding control for

single-link flexible-joint robot with mismatched uncertainties. IEEE Transactons on Control Systems Technology ˈ2004ˈ12(5) 770-775.

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[4]

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5: Ḅ 㢲㌫㔏⭥ ⸙

6ѪḄ 㢲⭥ 䖤ս〫ԯⵏ ˈ⭡ ⸕ˈ⭥ 䖤ս〫 㓯 ━ っˈ㺘 ∄䖳⨶ DŽ

[6]

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[8] ⍾ṩˈ ˈ҄㓒 Ḅ 㢲 Ⲵ⾎㓿㖁㔌

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ԯⵏ 4̚6㺘 ˈ 㘳㲁⭥ н⺞ 亩 䍏䖭 亩Ⲵ лˈ 䇮䇑Ⲵ ㌫㔏㜭 䙏㘼っ 䐏䑚 䖘䘩DŽ

[11] Chien M CˈHuang A C. Adaptive control for flexible-joint

electrically driven robot with time-varying uncertainties. IEEE Transactions on Industrial Electronicsˈ θ [12] ь, 䍮 䖙, ≹ , ㅹ オ䰤 ӪḄ 㢲䖘䘩

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(01): 19-23.

[14] 丙Ӝ␵ˊ㠚 ˊⓜ㽎䱠ⷵˈ2007ˈ1˖24-31. [15] 傜㓒䴘 㣿 ⌒ Ҿ㠚 Ⲵ Ӫ ḷ й

㔤 ⵬ 䈳. 呹┷▥ⷵ㔴 2004, 30(3): 400-406.

[16] 丙Ӝ␵ ⦻Տˊ䶎㓯䐏䑚- ˊ侊兮䱠ⷵ₝㟿ⷵˈ

1994ˈ14(2) 177-183ˊ [17] +XDQJ

QRQOLQHDU FRQWLQXRXV H[WHQGHG VWDWH REVHUYHU Chinese Science Bulletin - . [18] 丙Ӝ␵. 䶎㓯 ⣦ 䈟 侸 üNLSEF. 㘶Ⓟ₝⑂

䷥, 1995, 10 (3): 221-225.

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䪸 オ䰤 Ỡ㟲Ḅ 㢲䖘䘩 䰞仈, ⭘ADRC 㘳㲁⭥ н⺞ ㍐ 䍏䖭 ㍐ⲴḄ 㢲㌫㔏ˈ䇮䇑Ҷ 䰝⧟ADRC DŽ⭥ н⺞ 亩 䍏䖭 亩 䙊䗷 ⧟ ⣦ 㿲⍻ ⧟ ⣦ 㿲⍻ 㠚 ՠ䇑 㔉Ҹ㺕 DŽԯⵏ 㺘 ˈ 䇮䇑Ⲵ 㢲䖘䘩䐏䑚 䰝⧟ADRC 㜭 Ḅ 㢲 䙏㘼っ 䐏䑚 䖘䘩˗ 䇮䇑 ⧠ Ѿ 䎵䈳ˈ㌫㔏Ⲵ 䙏 ⺞ㅹ⢩⛩ˈ ф ㌫㔏 䖳 Ⲵ励ἂ DŽ Ⲵ ㆆ⮕ ԕ њḄ 㢲㌫㔏 ѝDŽ

[19] 䱸 ḻ, 䍮 . Ҿ ⣦ 㿲⍻Ⲵ Ӫ 励ἂ䐏

䑚 . 呹┷▥ⷵ㔴, 2008, 34(7) 828-832.

2: Ḅ 㢲 䰝⧟ADRC ㌫㔏Ṷ