Design of a Simultaneous Control System of Position and Force with a Pneumatic Cylinder Driving Apparatus

ᙽី⻝ ⱬ⌸᳜ ᛴᵡ ㄭ㟠⌄ ー〱㻤 䄠ᚄ れ㟠 ᵡⱤ ㆤ⼼ᙌ ⪬ᙌ

沫 滆 昷 ^*

Design of a Simultaneous Control System of Position and Force with a Pneumatic Cylinder Driving Apparatus

Ji-Seong Jang

Key Words : Low Stiffness(㩖 ṫ㎇), Pneumatic Cylinder (Ὃ₆㞫 㔺Ⰶ▪), Position and Force Control(䧮ὒ 㥚䂮 㩲㠊), Trajectory Tracking (Ὼ㩗 㿪㩗)

Abstract

In this study, position and force simultaneous trajectory tracking control system with pneumatic cylinder driving apparatus is proposed. The pneumatic cylinder driving apparatus that consists of two pneumatic cylinders constrained in series and two proportional flow control valves offers a considerable advantage as to non-interaction of the actuators because of the low stiffness of the pneumatic cylinders. The controller applied to the driving system is composed of a non-interaction controller to compensate for interaction of two cylinders and a disturbance observer to reduce the effect of model discrepancy of the driving system in the low frequency range that cannot be suppressed by the non-interaction controller. The experimental results with the proposed control system show that the interacting effects of two cylinders are eliminated remarkably and the proposed control system tracks the given position and force trajectories accurately.

1. ^昢ࣜ嵦

Ὃ₆㞫 㔺Ⰶ▪⯒ 㧊㣿䞲 ῂ☯ 㧻䂮⓪ Ὃ₆㦮 㞫 㿫㎇ὒ 㩖 Ṧ㐶 䔏㎇ ⹥ Ⱎ㺆⩻ὒ ゚ᾦ䞮㡂 ㌗╖

㩗㦒⪲ 㩗㦖 ῂ☯⩻㠦 㦮䞮㡂 㟧䢎䞲 㩲㠊 ㎇⓻㦚 㠑₆Ṗ 㣿㧊䞮㰖 㞠┺ἶ 㧎㔳 ♮㠊㪎 㧞₆ ➢ⶎ㠦

┾㑲䞲 ⹮⽋ 㧧㠛㠦 㭒⪲ ㌂㣿♮ἶ 㧞┺^(1,2). 㧊⩂

䞲 㧎㔳㦚 䌞䞒䞮㡂 ㌞⪲㤊 ⿚㟒㠦 Ὃ₆㞫 㔺Ⰶ▪

ῂ☯ 㧻䂮⯒ 㩗㣿䞮₆ 㥚䟊㍲⓪ Ὃ₆㞫 㔺Ⰶ▪ ῂ

☯ 㧻䂮Ṗ 㧻㩦㦚 Ṗ㰖⓪ 㦧㣿 㡗㡃㦚 䕢㞛䞮ἶ

゚ ㍶䡫 䔏㎇㦚 ⽊㌗䞶 㑮 㧞⓪ 㩲㠊₆⯒ ㍺Ἒ䞾 㦒⪲㖾 ῂ☯ 㧻䂮㦮 ἶ ㎇⓻䢪⯒ ╂㎇䟊㟒 䞲┺.

Ὃ₆㞫 㔺Ⰶ▪ ῂ☯ 㧻䂮⓪ ┺⯎ ῂ☯ ⹿㔳ὒ

゚ᾦ䞮㡂 ṫ㎇㧊 㧧㦒⸖⪲ 㥚䂮 Ὼ㩗㦚 㩫䢫䞮Ợ 㿪㫛䞮₆Ṗ 㣿㧊䞮㰖 㞠㰖Ⱒ ṫ㎇㧊 㧧┺⓪ ộ㦖 㿫 Ṛ㦮 Ṛ㎃㧊 㧧┺⓪ ộ㦚 㦮⹎䞮⸖⪲ ⽋㑮㦮 㞷㿪㠦㧊䎆⯒ ☯㔲㠦 ῂ☯䞮㡂 ṗ 㞷㿪㠦㧊䎆⪲⿖

䎆 ☛Ⱃ♲ 㿲⩻㦚 㤦䞮⓪ ἓ㤆㠦⓪ 㩖 ṫ㎇ 䔏㎇

㧊 㥶Ⰲ䞮Ợ 㧧㣿䞶 ộ㦒⪲ 䕦┾♲┺. Ὃ₆㞫 㞷 㿪㠦㧊䎆⯒ 㧊㣿䞮㡂 㥚䂮㢖 䧮㦚 ☯㔲㠦 㩲㠊䞲 㡆ῂ ἆὒ⪲⓪ 䞲 Ṳ㦮 Ὃ₆㞫 㔺Ⰶ▪⯒ 㧊㣿䞮㡂 㑮㰗 ⹿䟻㦮 㥚䂮㢖 䧮㦚 ☯㔲㠦 㩲㠊䞲 㡆ῂ, ἶ ⶊ 㧎Ὃ ⁒㥷㦚 㧊㣿䞲 㡆ῂ ❇㧊 㧞┺^(3,4). ⁎⩂⋮, 䞲 Ṳ㦮 Ὃ₆㞫 㔺Ⰶ▪⯒ 㧊㣿䞲 㡆ῂ㠦㍲⓪ 㥚䂮 㩲㠊⯒ ₆⹮㦒⪲ 䔏㩫 㥚䂮 㡺㹾 㧊⌊㠦 䞒㓺䏺㧊

☚╂䞮Ⳋ 䧮 㩲㠊⯒ 㔲㧧䞮₆ ➢ⶎ㠦 㓺䎳 䡫㦮

⳿䚲䂮㠦 ╖䞮㡂 㥚䂮㢖 䧮㦚 㩲㠊䞮⓪ ộ㦖 Ṗ⓻ 䞮㰖Ⱒ 㥚䂮㢖 䧮 Ὼ㩗㦚 ☯㔲㠦 㩲㠊䞮⓪ ộ㦖 㞚┞⸖⪲ 㩫䡚䕢 ❇㦮 Ὼ㩗㦚 ☯㔲㠦 㿪㩗䞮㰖 ⴑ 䞮㡖┺. ἶⶊ 㧎Ὃ ⁒㥷㦚 㧊㣿䞲 㡆ῂ㠦㍲⓪ 䗒 㰖 㩲㠊 㧊⪶㦚 ₆⹮㦒⪲ 㩲㠊₆⯒ ㍺Ἒ䞮㡖₆ ➢ ⶎ㠦 㩲㠊Ἒ㦮 㞞㩫㎇ 䘟ṖṖ 㣿㧊䞮㰖 㞠ἶ, ⡦ 䞲 䗒㰖 ′䂯㦚 㾲㩗㧊 ♮☚⪳ ㍶㩫䞮⓪ ộ㧊 㓓 㰖 㞠₆ ➢ⶎ㠦 䧮 㩲㠊㔲㦮 㰚☯㧊 䋂Ợ ⹲㌳䞮 ἶ 㧞┺.

⽎ ⏒ⶎ㠦㍲⓪ Ὃ₆㞫 㔺Ⰶ▪ ⚦ Ṳ⯒ 㰗⪂⪲

㡆ἆ䞲 㧻䂮⯒ ῂ㎇䞮ἶ 㥚䂮㢖 䧮 Ὼ㩗㦚 ☯㔲㠦 㩲㠊䞮⓪ 㩲㠊₆⯒ ㍺Ἒ䞲┺. 㩲㧧䞲 㧻䂮⓪ ㍺䂮

* 䣢㤦, ⿖ἓ╖䞯ᾦ ₆ἚὋ䞯⿖

E-mail : [email protected]

TEL : (051)620-1583 FAX : (051)620-1574

ὋṚ㦚 㭚㧊₆ 㥚䞮㡂 䘎⪲✲ 㔺Ⰶ▪ ⚦ Ṳ⯒ 㰗

⪂⪲ 㡆ἆ䞮㡂 ῂ㎇䞮㡖ἶ, 䧮 ⹥ 㥚䂮 Ὼ㩗㦚 㩲 㠊䞮₆ 㥚䞲 㥶⨟ 㩲㠊 ⺎ぢ⯒ ṗ 㔺Ⰶ▪㠦 㡆ἆ 䞮㡖┺. 㩲㠊₆⓪ ṗ 㔺Ⰶ▪㦮 㤊☯ ⹿㩫㔳㦒⪲⿖

䎆 㥶☚♲ ㍶䡫䢪 ⳾◎㦚 ₆⹮㦒⪲ 㔺Ⰶ▪Ṛ㦮 ☯ 㩗㧎 ㌗䢎 Ṛ㎃㦚 㠋㩲䞮₆ 㥚䞮㡂 ㍺Ἒ䞲 ゚ Ṛ

㎃ 㩲㠊₆㢖 㩖㭒䕢 㡗㡃㦮 ⳾◎Ⱇ 㡺㹾⯒ ⽊㌗䞮

₆ 㥚䞲 㣎⧖ ὖ䁷₆⯒ ⼧㣿䞾㦒⪲㖾 㩲㠊 ㎇⓻㦚 䟻㌗㔲䋺⓪ ῂ㫆⪲ ♮㠊 㧞┺. 㩲㠊Ἒ㦮 ㎇⓻㦖

┺㟧䞲 䡫䌲㦮 ⳿䚲䂮㠦 ╖䞲 䧮ὒ 㥚䂮 Ὼ㩗 㿪 㩗 㔺䠮㦚 䐋䞮㡂 Ỗ㯳䞮㡖ἶ, 㓺䎳 䡫㦮 ⳿䚲 Ὼ 㩗㠦 ╖䞮㡂 㥚䂮 ⹥ 䧮 Ὼ㩗㦮 㿪㩗 㡺㹾Ṗ ⳿䚲 䂮㦮 0.5[%]㧊⌊㧎 㟧䢎䞲 ἆὒṖ 㠑㠊㪢┺.

2. ^{击匶橛 柪庶塚 割壟 沫獞汞 割昷}

㔺䠮ٻ㧻䂮㦮ٻῂ㎇㦚ٻFig. 1 㠦ٻ⋮䌖⌎┺ډٻὋ₆㞫ٻ 㔺Ⰶ▪ٻཛὒٻཝ㦖ٻ⌊ἓٻ40ڶౝڸڇٻ⪲✲ٻ㰗ἓٻ12ڶౝڸ,ٻ 䟟㩫ٻ₎㧊ٻ300ڶmmڸ㧎ٻ䘎⪲✲ٻ㔺Ⰶ▪ڃCA1B40-300,ٻ SMCڃ艧ڄڄ⯒ٻ 㧊㣿䞮㡖┺ډٻ 䞒㓺䏺㦮ٻ 㥚䂮⓪ٻ ㍶䡫ٻ 䙂䎦㑒⹎䎆ڃLTM300S,ٻGEFRANڃ艧ڄڄٻཞ⯒ٻ㔺Ⰶ▪ٻ ཝ䁷㦮ٻ ⪲✲㠦ٻ 㡆ἆ䞮㡂ٻ Ỗ㿲䞮㡖ἶڇٻ 㔺Ⰶ▪㠦㍲ٻ

⹲㌳䞮⓪ٻ䧮㦖ٻ⪲✲㎖ڃMNT-100L, CASڃ艧ڄڄٻཛྷ⯒ٻ 㟧ٻ 㔺Ⰶ▪㦮ٻ ⪲✲ٻ ㌂㧊㠦ٻ 㼊ἆ䞮㡂ٻ Ỗ㿲䞮㡖┺ډٻ 䧮ٻ 㩲㠊㣿ٻ ⺎ぢڃMPYE-5-1/4LF-010B, FESTOڃ艧ڄڄٻ ཟ⓪ٻ㾲╖ٻ㥶䣾ٻ┾Ⳋ㩗ٻ18.2ڶmm²ڸ㧎ٻڏ ⹿䟻ٻ゚⪖ٻ 㩲㠊ٻ ⺎ぢ⯒ٻ ㌂㣿䞮㡖ἶڇٻ 㥚䂮ٻ 㩲㠊㣿ٻ ⺎ぢڃMP YE-5-1/8HF-010B, FESTOڃ艧ڄڄٻའ㦖ٻ㾲╖ٻ㥶䣾ٻ┾

Ⳋ㩗ٻ9.3ڶmm²ڸ㧎ٻڏ ⹿䟻ٻ゚⪖ٻ㩲㠊ٻ⺎ぢ⯒ٻ㌂㣿䞮 㡖┺ډٻṗٻ㎒㍲㠦㍲ٻỖ㿲♲ٻ㔶䢎ٻ⹥ٻ㩲㠊ٻ⺎ぢ⪲㦮ٻ 㿲⩻ٻ 㔶䢎⓪ٻA/D·D/A ⼖䢮₆ڃPCL-812PG,ٻ ⿚䟊⓻ٻ 12bit, Advantechڃ艧ڄڄ⯒ٻ㧊㣿䞮㡂ٻPC ⪲ٻ㧛ബ㿲⩻

䞮㡖┺ډ

3. ^{洢檺 堆旇汞 微塾廇}

3.1 割昷 愯洛柣

Ὃ₆㞫 㔺Ⰶ▪⯒ 㧊㣿䞲 ῂ☯ 㧻䂮㦮 Ṳ⨋☚⯒

Fig. 2 㠦 ⋮䌖⌎┺. 㔺Ⰶ▪ ⌊⿖㦮 㞫⩻ ⼖䢪⓪ ┺ 㦢 㔳㦒⪲ ₆㑶䞶 㑮 㧞┺. ┾, 㩚╂ ὖ⪲⓪ ┾㑲 䞲 㣿⨟ 㣪㏢⪲ 䀾 䞮ἶ, 㔺Ⰶ▪ ⌊⿖㦮 ㌗䌲 ⼖ 䢪⓪ ┾㡊 ⼖䢪⪲ Ṗ㩫䞲┺.







 +∆

∆

− ∆

∆ =

∆

1 1 1

1 1

1 a a a

a

a G RT

t A X V P

k t

P (1)







 −∆

∆

− ∆

∆ =

∆

2 2 2

2 2

2 a a a

a

a G RT

t A X V P

k t

P (2)







 +∆

∆

− ∆

∆ =

∆

1 1 1

1 1

1 b b b

b

b G RT

t A X V P

k t

P (3)







 −∆

∆

− ∆

∆ =

∆

2 2 2

2 2

2 b b b

b

b G RT

t A X V P

k t

P (4)

㔳 (1)ۙ(4)㠦㍲ k ⓪ ゚㡊゚⯒ ⋮䌖⌎┺. ῂ☯ 㧻䂮 㦮 㤊☯ ⹿㩫㔳 ⹥ ῂ☯ 㧻䂮㠦㍲ ⹲㌳䞮⓪ 䧮㦖 㔳 (5)㢖 (6)㦒⪲ ₆㑶♲┺.



 





∆

− ∆

∆

− ∆

∆ +

∆

−

∆

−

∆

∆ =

∆

t F X t B X P A P A P A P t A

M X2 1 _a1 2 _a2 1 _b1 2 _b2 _csgn

2 (5)

2 2 1 1 2 2 1

1 Pa A Pa A Pb A Pb

A

F= ∆ − ∆ + ∆ − ∆

∆ (6)

Fig. 2 Schematic diagram of the pneumatic cylinder driving system

X Z

Y

[

\ ]

X

X ZZ

Y Y

[ [

\\ ]] 

ཛ Cylinder for force control ཛྷGLoad cell ཝ Cylinder for position control ཞ PotentiometerG ཟའ Proportional flow control valve

Fig. 1 Schematic diagram of the experimental apparatus

3.2 昦笛筚 微塾

ῂ☯ 㧻䂮㦮 䘟䡫 ㌗䌲⯒ Pa1 = Pb1 = P10, Pa2 = Pb2

= P20, Va1 = Va2 = Vb1 = Vb2 = V0, Ta1 = Ta2 = Tb1 = Tb2 = T_atm⪲ ⚦ἶ, 㩫㰖 Ⱎ㺆⩻㧊 㠜┺ἶ Ṗ㩫䞮㡂 㩚╂

䞾㑮⯒ ῂ䞮Ⳋ ┺㦢 㔳㦒⪲ ⋮䌖⌒ 㑮 㧞┺.



 



= 



 





) (( ) ) ) (

( ) (

s u

s s u s H

X s F

b

a , _^











= −

) ( )

() ( )

) (

( Hba s Hbb s ab s H aa s s H

H

) ( ) ) (

( H s

s s H

H

aad

aa = aan ,

) ( ) ) (

( H s

s s H

H

abd ab = abn

) ( ) ) (

( H s

s s H

H

bad

ba = ban ,

) ( ) ) (

( H s

s s H

H

bbd bb = bbn

) (

) ( )

(s H s k A1 A2

H_aan = _ban =Γ _qa + ) (

) ( )

(s H s k A₁ A₂ H_abn = _bbn =Γ _qb +

/ 0

) (kRT_atm V

=

Γ , Haad(s)=Habd(s)=s+Γkp0

s K B k s B M k Ms s H s

H_abd( ) _bbd( ) ( _p ) 2 ( _p0 2 _E)

3+ Γ 0 + + Γ +

=

=

0

20 22 0 10

12 V

A kP V A kP

K_E = + (7)

㔳 (7)㠦㍲ kq[(kg/s)/V]⓪ 㩲㠊 ⺎ぢ 㥶⨟㧊✳, k_p[(kg/s)/Pa]⓪ 㩲㠊 ⺎ぢ 㞫⩻-㥶⨟㧊✳, u [V]⓪ ⺎ ぢ⪲㦮 㩲㠊 㧛⩻㦚 ⋮䌖⌊ἶ, 㔺䁷䞲 ṗ 㩲㠊 ⺎ ぢ㦮 㞫⩻-㥶⨟㧊✳㦮 㹾㧊Ṗ ⹎㏢䞮⸖⪲ kpa = kpb

= kp0⪲ Ṗ㩫䞮㡖┺.

4. 洢檺匶ࣜ昪凊

4.1 捊儊昳 洢檺匶 昪凊

Fig. 3 㦖 ┾㥚 䞒✲⺇㦚 㧊㣿䞲 㩲㠊Ἒ㦮 な⪳

㍶☚㧊ἶ,ٻR(s)⓪ [Fr(s) Xr(s)]^T, Y(s)⓪ [F(s) X(s)]^T⯒

⋮䌖⌎┺.ٻ Fig. 3 㠦㍲ H(s)⯒ 㞞㩫䢪䞮⓪ ⽊㌗₆ C_n(s)㦮 㰧䞿㦖 Youla parametrization⁽⁵⁾㦚 㧊㣿䞮㡂

┺㦢ὒ ṯ㧊 ⋮䌖⌒ 㑮 㧞┺.

, )) ( ) ( )

~ ( ))(

( ) ( )

~ ( (

)) ( ( ) (

1

− −

+

= Ω

=

s U s N s Z s U s D s W

s H s C

H H

H H

n

I s Z s D s W s

N~_H( )~_H( )+ ~_H( )~_H( )=

(8) H(s)ଲRHೂ㧊⸖⪲ 㔳 (8)㦮 Ἒ㑮 䟟⪂㦖 ┺㦢ὒ ṯ㧊 ῂ䞶 㑮 㧞┺.

) ( )

~ ( )

(s N s H s

N_H = _H = ,D_H(s)=D~_H(s)=I, 0

)

~ (s =

W_{H ,} Z~_H(s)=I ₍₉₎

㔳 (8)㠦㍲ U(s)⓪ Ὃ䃃 㩚╂䞾㑮 䟟⪂ Hm(s)⯒

㧊㣿䞮㡂 ┺㦢 㔳㦒⪲ ῂ䞶 㑮 㧞┺.

∞

− ∈

=H s H s RH s

U( ) ¹( ) m( ) ,



 



=

) ( 0

0 ) ) (

( H s

s s H

H

bbm

m aam (10)

㔳 (9)㢖 (10)㦚 㧊㣿䞮㡂 (8)㦚 㩫Ⰲ䞮Ⳋ Cn(s)

⓪ ┺㦢ὒ ṯ㧊 ⋮䌖⌒ 㑮 㧞┺.

1

1( ) ( )( ( ))

)

(s =H⁻ s H s I−H s ⁻

C_{n m m (11)}

4.2ࣜ歾岆ࣜ分猧匶ࣜ昪凊ࣜ

⽎ 㩞㠦㍲⓪ ゚ Ṛ㎃ 㩲㠊₆⯒ 䙂䞾䞲 㩲㠊Ἒ H₀(s)=(1+Cn(s)H(s))^-1C_n(s)H(s)⯒ ⌊⿖ ⳾◎⪲ 㧊㣿 䞮⓪ 㣎⧖ ὖ䁷₆⯒ ㍺Ἒ䞲┺. 㣎⧖ ὖ䁷₆⯒ 㧊 㣿䞲 㩲㠊Ἒ⯒ Fig. 4 㠦 ⋮䌖⌎┺. Fig. 4 㠦 ⋮䌖⌎

㩲㠊Ἒ⓪ Fig. 5 㢖 ṯ㧊 ❇Ṗ ⼖䢮 䞶 㑮 㧞ἶ⁽⁶⁾, Fig. 5 㠦 ⋮䌖⌎ C1(s), C2(s)⓪ Youla parametric- zation 㦚 㧊㣿䞮㡂 ┺㦢ὒ ṯ㧊 ⋮䌖⌒ 㑮 㧞┺.

0 1 0 0

1(s)=K(s)(Z~ (s)−N (s)U (s))⁻

C _{H H}

,

0 1 0 0

0 0

0 0

2

)) ( ) ( )

~ ( ))(

( ) (

)

~ ( ( )) ( ( ) (

− −

+

= Ω

=

s U s N s Z s U s D

s W s H s C

H H

H

H (12)

U₀(s)⯒ Hm-1(s)J(s)ଲRH∞⪲ ㍶㩫䞮Ⳋ C1(s), C2(s)

⓪ ┺㦢 㔳㦒⪲ 䚲䡚♲┺.

1(s)=K(s)(I −J(s))⁻1

C _,

1 2(s)=H ⁻1(s)J(s)(I−J(s))⁻

C m (13)

yOšPG j•OšPG oOšPG €OšPG

RG TG

Fig. 3 Block diagram of a unity feedback control system

R(s) K(s)

d(s)

H₀(s) Y(s)

n(s) +

-

+ +

+ J(s) - + H_m-1(s) + R(s) K(s)

d(s)

H₀(s) Y(s)

n(s) +

-

+ +

+ J(s) - + H_m-1(s) +

Fig. 4 Block diagram of the control system with disturbance observer

R(s)

d(s)

H₀(s) Y(s)

n(s) +

- + +

+ + C₁(s)

C₂(s) R(s)

d(s)

H₀(s) Y(s)

n(s) +

- + +

+ + C₁(s)

C₂(s) 

Fig. 5 Equivalent system of the Fig. 4

zz

5. 柪竞ࣜ冶刂ࣜ愕ࣜ処然ࣜ

Fig. 6 ὒ 7 㦖 䧮 F 㢖 㥚䂮 X 㦮 㽞₆䂮 F0 ⹥ X0⯒ ṗṗ 0[N]ὒ 0.143[m]⪲ ㍺㩫䞲 䤚, 㓺䝢⧒㧎 Ὼ㩗㦚 㧊㣿䞮㡂 ㌳㎇♲ 㓺䎳䡫 ⳿䚲 Ὼ㩗㠦 ╖䞮 㡂 䧮ὒ 㥚䂮 Ὼ㩗㦚 ☯㔲㠦 㩲㠊䞲 ἆὒ⯒ ⋮䌖

⌊ἶ, 㔺㍶㦖 ⳿䚲 Ὼ㩗, 䕢㍶㦖 㔺䠮 ἆὒ㧊┺.

Fig. 6 㦖 ゚⪖ 㩲㠊₆⯒ ῂ㎇䞲 㔺䠮 ἆὒ㧊ἶ, 㩫

㌗ 䘎㹾Ṗ 䋂Ợ ⹲㌳䞾㦚 㞢 㑮 㧞┺. ⡦䞲, ⳿䚲

Ὼ㩗㦮 ⼖䢪㠦 ➆⧒㍲ 䧮 ⹥ 㥚䂮 Ὼ㩗㦮 ☯ 䔏㎇

㧊 ⼖䢪䞮ἶ 㩫㌗ ㌗䌲㠦 ☚╂䞲 㧊䤚㠦☚ 㢚Ⱒ䞲 㰚☯㧊 ⋮䌖⋮ἶ 㧞⓪ ἓ㤆Ṗ 㧞㦢㦚 㞢 㑮 㧞┺.

Fig. 7 㦖 4 㧻㠦㍲ ☚㿲䞲 㩲㠊₆⯒ 㧊㣿䞮㡂 Fig.

4 㦮 㩲㠊Ἒ⯒ ῂ㎇䞲 㔺䠮 ἆὒ㧊ἶ, ⳿䚲 Ὼ㩗㦚 㧮 㿪㫛䞮ἶ 㧞㦢㦚 㞢 㑮 㧞┺. ⁎Ⰲἶ, 㥚䂮 㿪 㩗㡺㹾 ex 㢖 䧮 㿪㩗 㡺㹾 ef ⓪ 䘟‶㧊 ṗṗ - 0.021[mm], 0.093[N], 䚲㭖 䘎㹾Ṗ ṗṗ 0.2[mm], 2.3[N]㦒⪲ ⳿䚲䂮㦮 0.44[%]㢖 0.48[%]㧊⌊㧚㦚 䢫㧎䞮㡖┺.

(a) step width of Fr : 500[N], Xr : 0.05[m]

(b) step width of Fr : -500[N], Xr : -0.05[m]

Fig. 6 Trajectory tracking control results in case of a step trajectory tracking with proportional controller

(a) step width of Fr : 500[N], Xr : 0.05[m]

(b) step width of Fr : -500[N], Xr : -0.05[m]

Fig. 7 Trajectory tracking control results in case of a step trajectory tracking with the proposed controller

zz

Fig. 8 㦖 F0 ⹥ X0⯒ Fig. 6 ὒ ☯㧒䞮Ợ ㍺㩫䞲 䤚, 㩫䡚䕢 ⳿䚲 Ὼ㩗ὒ 㓺䎳䡫 ⳿䚲 Ὼ㩗㠦 ╖䞮 㡂 䧮ὒ 㥚䂮 Ὼ㩗㦚 ☯㔲㠦 㩲㠊䞲 㔺䠮 ἆὒ⯒

⋮䌖⌊ἶ, 䕢㍶㦖 ⳿䚲 Ὼ㩗, 㧒㩦 㐚㍶㦖 ゚⪖ 㧊

✳㦚 㧊㣿䞲 ἓ㤆, 㔺㍶㦖 4 㧻㠦㍲ ㍺Ἒ♲ 㩲㠊₆

⯒ 㧊㣿䞲 ἓ㤆㧊┺. (a)⓪ ⳿䚲 䧮 Ὼ㩗㦚 㩫䡚䕢

⪲ ㍺㩫䞮ἶ ⳿䚲 㥚䂮 Ὼ㩗㦚 㓺䎳䡫㦒⪲ ㍺㩫䞲 ἆὒ㧊ἶ, 㩲㞞䞲 㩲㠊₆⯒ 㧊㣿䞲 ἓ㤆㠦 ⳿䚲 Ὼ㩗㦚 㧮 㿪㫛䞮ἶ 㧞㦢㦚 㞢 㑮 㧞┺. 㥚䂮 Ὼ 㩗㦖 䧮 Ὼ㩗 Ṗ㏣☚㦮 ⹿䟻㧊 ⹪≢Ⳋ 㧒㔲㩗㦒⪲

㰚☯㩗㧎 Ệ☯㦚 ⽊㧊㰖Ⱒ, 㣎⧖ ὖ䁷₆㦮 㧧㣿㠦 㦮䞮㡂 㰚☯㧊 ㌂⧒㰖ἶ 㧞㦢㦚 㞢 㑮 㧞┺. (b)⓪

⳿䚲 䧮 Ὼ㩗㦚 㓺䎳䡫㦒⪲ ㍺㩫䞮ἶ ⳿䚲 㥚䂮

Fig. 9 ⓪ 㩫䡚䕢 ⳿䚲

Ὼ㩗㦚 㩫䡚䕢⪲ ㍺㩫䞲 ἆὒ㧊ἶ, ⳿䚲 Ὼ㩗㦚 㧮 㿪㫛䞮ἶ 㧞㦢㦚 㞢 㑮 㧞┺. 䧮 Ὼ㩗㠦⓪ 㥚 䂮 Ὼ㩗 Ṗ㏣☚㦮 ⹿䟻㧊 ⹪≢Ⳋ 㧒㔲㩗㦒⪲ 㰚☯

㧊 ⽊㧊㰖Ⱒ, 㣎⧖ ὖ䁷₆㦮 㧧㣿㠦 㦮䞮㡂 㰚☯

㧊 ㌂⧒㰖ἶ 㧞㦢㦚 㞢 㑮 㧞┺.

Fig. 9 ⓪ 㩫䡚䕢 ⳿䚲 Ὼ㩗㠦 ╖䞮㡂 䧮ὒ 㥚䂮 Ὼ㩗㦚 ☯㔲㠦 㩲㠊䞲 㔺䠮 ἆὒ⯒ ⋮䌖⌎┺. Fig.

9 㠦㍲ (a)⓪ ⳿䚲 䧮 Ὼ㩗ὒ ⳿䚲 㥚䂮 Ὼ㩗㦚 ☯ 㧒䞲 㭒䕢㑮㦮 㩫䡚䕢⪲ ㍺㩫䞲 ἆὒ㧊ἶ 㥚䂮 Ὼ 㩗㦮 㽞₆ 㦧╋㠦 㰚☯㧊 ⽊㧊㰖Ⱒ 㰚☯㧊 ㌂⧒㰚 㧊䤚⓪ ⳿䚲 Ὼ㩗㦚 㧮 㿪㫛䞮ἶ 㧞┺. (b)⓪ ⳿䚲 䧮 Ὼ㩗ὒ ⳿䚲 㥚䂮 Ὼ㩗㦮 㭒䕢㑮⯒ ┺⯊Ợ ㍺ 㩫䞲 ἆὒ㧊ἶ (a)㢖 ☯㧒䞮Ợ 㥚䂮 Ὼ㩗㦮 㽞₆ 㦧╋㠦 㰚☯㧊 ⽊㧊㰖Ⱒ 㰚☯㧊 ㌂⧒㰚 㧊䤚⓪ ⳿ 䚲 Ὼ㩗㦚 㧮 㿪㫛䞮ἶ 㧞┺.

(a) Fr : sinusoidal input, Xr : step input

(b) Fr : step input, Xr : sinusoidal input Fig. 8 Trajectory tracking control results in case of

a step trajectory and a sinusoidal trajectory tracking

(a) frequency of Fr : 0.5[Hz], Xr : 0.5[Hz]

(b) frequency of Fr : 0.5[Hz], Xr : 1[Hz]

Fig. 9 Trajectory tracking control results in case of sinusoidal trajectory tracking

zz

6. 冶ࣜ嵦

⽎ ⏒ⶎ㠦㍲⓪ 㩖 ⿖䞮㣿 Ṗ㰚 㧻䂮 㩲㧧㦚 ⳿ 㩗㦒⪲ ⚦ Ṳ㦮 Ὃ₆㞫 㔺Ⰶ▪⯒ 㰗⪂⪲ 㡆ἆ䞲 ῂ☯㧻䂮⯒ ῂ㎇䞮ἶ 㔺Ⰶ▪ ㌗䢎Ṛ㦮 Ṛ㎃㦚 ἶ

⩺䞲 ㍶䡫 ⳾◎㦚 㥶☚䞲 䤚 㥚䂮㢖 䧮㦚 ☯㔲㠦 㩲㠊䞮⓪ 㩲㠊₆⯒ ㍺Ἒ䞮㡖┺. 㩲㞞䞲 㩲㠊₆⓪ 㩲㠊Ἒ㦮 ㍶䡫 ⳾◎㦚 㧊㣿䞮㡂 㥚䂮 㩲㠊Ἒ㢖 䧮 㩲㠊Ἒ ㌗䢎 Ṛ㦮 ☯㩗㧎 Ṛ㎃ 㠋㩲⯒ ⳿㩗㦒⪲

㍺Ἒ䞲 ゚ Ṛ㎃ 㩲㠊₆㢖 ゚ Ṛ㎃ 㩲㠊₆㠦㍲ ⽊

㌗䞶 㑮 㠜⓪ ⳾◎Ⱇ 㡺㹾⯒ ⽊㌗䞮ἶ Ὼ㩗 㿪㩗

㎇⓻㦚 䟻㌗㔲䋺₆ 㥚䞮㡂 ㍺Ἒ䞲 㣎⧖ ὖ䁷₆⯒

⼧㣿䞮⓪ ῂ㫆⪲ ῂ㎇䞮㡖㦒Ⳇ ゚ Ṛ㎃ 㩲㠊₆㢖 㣎⧖ ὖ䁷₆⓪ 㩲㠊Ἒ㦮 㞞㩫㎇㦚 ⽊㧻䞮₆ 㥚䞮 㡂 Youla parametrization 㦚 㧊㣿䞮㡂 㥶☚䞮㡖┺.

Ṗ㰚 㧻䂮㦮 ㎇⓻㦖 ┺㟧䞲 ⳿䚲 Ὼ㩗㦚 㧊㣿䞲 㔺䠮㦚 䐋䞮㡂 Ỗ㯳䞮㡖ἶ, ⳿䚲 Ὼ㩗㦮 䡫㌗ ⹥

⹿䟻㧊 ⼖䢪䞮㡂☚ 㟧䢎䞲 Ὼ㩗 㿪㩗 ㎇⓻㦚 㠑㦚 㑮 㧞㠞┺.

7. 焾処怾竒

(1) Johira, I. T., 1997, "Pneumatic Servo System," The Japan Hydraulics & Pneumatics Society, Vol. 28, No.

7, pp. 748૫752.

(2) McGuirk, D. P., Pingdong, W.Gand Xiao, X., 1998,

“Fluid Power in the World,” The Japan Hydraulics &

Pneumatics Society, Vol. 29, No. 3, pp. 212૫243.

(3) Yamafuji, K.G and Fukushima, T., 1988, "Simulta- neous Control of Vertical Position and Force of a Pneumatic Cylinder," The Japan Hydraulics &

Pneumatics Society, Vol. 19, No. 3, pp. 226૫233.

(4) Jin, S. H., Watanabe, K. and Lee, S. G., 1995, “A Study on Position and Force Control of A Robot Manipulator with Artificial Rubber Muscle,” Journal of the Korean Society of Precision Engineering, Vol.

12, No. 1, pp. 97૫103.

(5) Desoer, C. A.,G1980, "Feedback system design; The fractional representation approach to analysis and synthesis," IEEE Trans. Automat. Control, AC-25, No.

3, pp. 399૫412.

(6) Jang, J. S., Lee, K. K. and Choi, M. S., 2003,

“Pressure Control of a Pneumatic Control System with a Long Transmission Line,” Transactions of the KSME, A, Vol. 27, No. 4, pp. 567૫576.