Modeling of a Pneumatic Cylinder Position Control system Considering Transfer Characteristics of a Transmission Line

ì͐ڗ یɆ ࢳԒڋ Ý̓ळ èİפ սΐɝ ٷߩ ۔؂Øڗ ϐɮΕ

沫滆昷^†

·

·

Modeling of a Pneumatic Cylinder Position Control system Considering Transfer Characteristics of a Transmission Line

Ji-Seong Jang, Bo-Sik Kang and Sang-Won Ji

Key Words : Pneumatic Cylinder(Ὃ₆㞫 㔺Ⰶ▪), Position Control System(㥚䂮 㩲㠊Ἒ), Transfer Characteristics(㩚╂ 䔏㎇), Transmission Line(㩚╂ ὖ⪲)

Abstract

In this study, a linearized model of pneumatic cylinder position control system including transmission line is proposed. The transmission line using compressible fluid has a nonlinear transfer characteristics because that the frequency response of it is changed by the flowing state of the fluid. But, when the pressure difference between both sides of transmission line is low, the effect of resonance characteristics of it under high frequency range can be neglected because of the friction force and low pass characteristics of the position control system. Therefore, the transmission line can be modeled by second order transfer function and the natural frequency, damping ratio and gain are changed by the diameter and length of it. The effectiveness of the proposed model is proved by comparison of simulation results using proposed model with experimental results and simulation results using conventional model.

1.

Ὃ₆㞫 㔺Ⰶ▪⯒ 㧊㣿䞲 㥚䂮 㩲㠊Ἒ⓪ Ὃ₆㦮 㥶⨟ ⡦⓪ 㞫⩻㦚 㩲㠊䞮⓪ 㩲㠊 ⺎ぢ, 㞫㿫 Ὃ

₆⪲ ῂ☯♮⓪ 㔺Ⰶ▪ ⹥ 㞫㿫 Ὃ₆⯒ 㩚╂䞮⓪ ὖ⪲⪲ ῂ㎇♲┺. ㌗₆䞲 ῂ㎇ 㣪㏢ 㭧㠦㍲ ὖ⪲

⓪ 㞫㿫 Ὃ₆⯒ 㔺Ⰶ▪⪲ Ὃ 䞮₆ 㥚䞲 䞚㑮 㣪

㏢⪲㖾 ἓ㤆㠦 ➆⧒㍲⓪ ┺㟧䞲 ₎㧊㦮 ὖ⪲Ṗ

㌂㣿♮㰖Ⱒ, Ὃ₆㞫 ὖ⪲㦮 㭒䕢㑮 㩚╂ 䔏㎇㦖 Ὃ₆㦮 㥶☯ ㌗䌲Ṗ ゚㞫㿫㎇ 㥶☯㧊Ⳋ ⶊ䞲Ἒ㦮 Ὃ㰚 㭒䕢㑮⯒ Ṭ⓪ Ἒ⪲ 䚲䡚♮ἶ,⁽¹⁾ 㞫㿫㎇ 㥶

☯㧊Ⳋ 1 Ṳ㦮 Ὃ㰚 ⳾✲⯒ Ṗ㰖⓪ 㧚Ἒ Ṧ㐶Ἒ

⡦⓪ ὒṦ㐶Ἒ⪲ 䚲䡚♮⸖⪲^(2~3) 㩲㠊Ἒ㦮 ㍶䡫

⳾◎㠦 ὖ⪲㦮 ⳾◎㦚 䙂䞾㔲䋺₆Ṗ 㣿㧊䞮㰖 㞠

┺. ⁎⩂⸖⪲ ₆㫊㦮 㡆ῂ㠦㍲⓪ ὖ⪲㦮 ₎㧊Ṗ 㰽㦖 ἓ㤆㠦⓪ ὖ⪲⯒ ┾㑲䞲 㣿㩗㦒⪲ Ṗ㩫䞮㡂 㩲㠊Ἒ⯒ 䚲䡚䞮ἶ 㧞ἶ,⁽⁴⁾ ὖ⪲Ṗ ₊ ἓ㤆㠦⓪ ὖ⪲⯒ 㣿㩗ὒ 㔲Ṛ 㰖㡆 㣪㏢⪲ Ṗ㩫䞮㡂 㩲㠊 Ἒ⯒ ₆㑶䞮㡖┺.⁽⁵⁾ ⁎⩂⋮,ὖ⪲㦮 ₎㧊Ṗ ⁏┾㩗 㦒⪲ 㰽㦖 ἓ㤆⯒ 㩲㣎䞮ἶ⓪ ὖ⪲⯒ ┾㑲䞲 㣿 㩗Ⱒ㦒⪲ 䚲䡚䞮₆⓪ Ἲ⧖䞮ἶ ⡦䞲, ὖ⪲⯒ 㣿 㩗ὒ 㔲Ṛ 㰖㡆 㣪㏢⪲ 䚲䡚䞮⓪ ἓ㤆㠦⓪ ὖ⪲

㦮 㧊✳ Ṧ㏢⯒ ἶ⩺䞮㰖 㞠㦒⸖⪲ 㥚䂮 㩲㠊Ἒ 㦮 ⳾◎㧊 䌖╏䞮Ợ 䚲䡚♮㠞┺ἶ 䘟Ṗ䞮₆⓪ Ἲ

⧖䞮┺.

⽎ ⏒ⶎ㠦㍲⓪ ὖ⪲⯒ 䙂䞾䞲 Ὃ₆㞫 㔺Ⰶ▪

㥚䂮 㩲㠊Ἒ㦮 ㍶䡫 ⳾◎㦚 㥶☚䞮₆ 㥚䞮㡂 ὖ

⪲㦮 㩚╂ 䔏㎇㦚 ἶ⩺䞲 㥚䂮 㩲㠊Ἒ ⳾◎㦚 㩲 㞞䞲┺. 㩚㑶䞲 Ὃ₆㞫 ὖ⪲ ⳾◎ 㭧㠦㍲ Ὃ₆㦮 㥶☯㧊 ゚㞫㿫㎇ 㥶☯㧎 ἓ㤆⓪ ὖ⪲ 㟧┾㦮 㞫

⩻㹾Ṗ 㧧㦒⸖⪲ ὖ⪲㦮 Ὃ㰚 䔏㎇㠦 㦮䞲 㞫⩻

ⰻ☯㧊 ⹲㌳䞮㡂☚ 㔺Ⰶ▪ ῂ☯⿖㦮 Ⱎ㺆⩻㧊 㞫

⩻ ⰻ☯㠦 㦮䞲 ῂ☯⩻⽊┺ 䋂ἶ, ⁎ ἆὒ 1 㹾Ὃ 㰚 㭒䕢㑮⯒ 㩲㣎䞲 ὖ⪲㦮 ἶ㭒䕢 Ὃ㰚 䔏㎇㧊 G†G⿖ἓ╖䞯ᾦٻ₆ἚὋ䞯⿖

E-mail : [email protected]

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

*ٻ䞲ῃ₆Ἒ㡆ῂ㤦ٻ㥶Ὃ㞫㡆ῂ⁎⭏

** ⿖ἓ╖䞯ᾦٻ㩲㠊₆ἚὋ䞯ὒ

㩲㠊Ἒ㦮 㿲⩻㠦 ⹎䂮⓪ 㡗䟻㦖 ⶊ㔲䞶 㑮 㧞┺.

⁎⩂⸖⪲, ⽎ ⏒ⶎ㠦㍲⓪ ゚㞫㿫㎇ 㥶☯ ⳾◎㠦

㍲ ☚㿲♲ 1 㹾 Ὃ㰚 㭒䕢㑮⯒ 㧊㣿䞮㡂 ὖ⪲㦮 㩚╂ 䔏㎇㦚 2 㹾Ἒ⪲ ₆㑶䞮ἶ Ṧ㐶゚ ⹥ 㧊✳

㦖 㰗ἓὒ ₎㧊㠦 ➆⧒㍲ ⼖䢪䞲┺ἶ Ṗ㩫䞮㡂 㥚䂮 㩲㠊Ἒ ⳾◎㦚 ῂ㎇䞮㡖┺. 㩲㞞䞲 ⳾◎㦮 䌖╏㎇㦖 㩲㞞䞲 ⳾◎㦮 㔲⸂⩞㧊㎮ ἆὒ㢖 㔺䠮 ἆὒ ⹥ ὖ⪲⯒ 㣿㩗ὒ 㔲Ṛ 㰖㡆 㣪㏢⪲ Ṗ㩫䞲

₆㫊 ⳾◎㦮 㔲⸂⩞㧊㎮ ἆὒ㢖㦮 ゚ᾦ⯒ 䐋䞮㡂 Ỗ㯳䞮㡖┺.

2.

Fig. 1 㦖 㥚䂮 㩲㠊 㧻䂮㦮 ῂ㎇㦚 ⋮䌖⌎┺.

㔺Ⰶ▪⓪ ⌊ἓ 25[mmڸڇٻ䟟㩫₎㧊ٻڐڋڋڶۈۈڸ㧎ٻ⪲

✲⩞㓺 㔺Ⰶ▪(MY H25-500H, SMC Co.)⯒ 㧊㣿䞮 㡖┺. 䞒㓺䏺㦮 㥚䂮⓪ 䙂䎦㎪Ⲫ䎆(Novotechnik Co, TLH500)⯒ 㡆ἆ䞮㡂 Ỗ㿲䞮㡖┺. 㞫⩻㦖 㞫

⩻㎒㍲(Sensys Co., PS HK001 0KCAG)⯒ 㔺Ⰶ▪ 㧛 ῂ⿖㠦 ㍺䂮䞮㡂 Ỗ㿲䞮㡖┺. 㩲㠊 ⺎ぢ⓪ 㾲╖

㥶䣾 ┾Ⳋ㩗㧊 18.2[mm²]㧎 㥶⨟ ゚⪖ 㩲㠊 ⺎ぢ (FESTO Co., MPYE-5-1/4-010B)⯒ 㧊㣿䞮㡖┺.

ཛControl Valve, ཛྷཝPressure Sensor, ཞCylinder, ཟPotentiometer, འTransmission Line

Fig. 1 Schematic diagram of position control apparatus

Fig. 2 Schematic diagram of cylinder driving system

3.

㔺Ⰶ▪ ῂ☯Ἒ 㩲㠊Ἒ㦮 Ṳ⨋☚⯒ Fig. 2 㠦 ⋮䌖

⌎┺. Fig. 2 㠦㍲ ㌂㣿♲ ₆䢎⓪ ┺㦢ὒ ṯ┺.

d : ὖ⪲ 㰗ἓ[m], G : 㔺Ⰶ▪⪲ Ὃ  ⡦⓪ 㔺Ⰶ

▪⪲⿖䎆 㥶㿲♮⓪ 㰞⨟ 㥶⨟[kg/s], L : ὖ⪲ ₎㧊 [m], M : Ṗ☯⿖ 㰞⨟[kg], P : 㔺Ⰶ▪ ⌊ ⿖ 㞫⩻

[Pa], Pa : ╖₆㞫[Pa], Ps : Ὃ 㞫[Pa], Se : 㩲㠊 ⺎ぢ 㥶䣾 ┾Ⳋ㩗[mm²], T : Ὃ₆ 㡾☚[K], Ta : ╖₆ 㡾☚

[K], Ts : Ὃ  Ὃ₆ 㡾☚[K], V : 㔺Ⰶ▪ 㔺 ⌊⿖ 㼊 㩗[m³], x : 䞒㓺䏺 㥚䂮[m]

Ὃ₆㦮 㥶☯ ㌗䌲Ṗ ゚㞫㿫㎇ 㥶☯㧊ἶ ὖ⪲ 㿲 ῂṖ 㹾┾♮㠊 㧞┺ἶ Ṗ㩫䞮Ⳋ ὖ⪲ 㧛ῂ 㞫⩻ὒ 㿲ῂ 㞫⩻㦮 㩚╂ 䞾㑮⓪ ┺㦢 㔳㦒⪲ ₆㑶䞶 㑮 㧞┺.⁽⁶⁾

1 2 2

2 2

( ) ( )

( ) ( ) 2 ^l

nl T s

in out l nl nl

P s P s

P s P s s s e

ω

ς ω ω

= = −

+ +

2 2

2 , 16 2,

4 ^a

nl l l

nl a

RT L

L d T RT

π κ ν

ω ς

ω κ

= = = (1)

㔳 (1)㠦㍲ e^-Tls⓪ 㞫⩻ 㦧╋ 㰖㡆 㔲Ṛ[s], ച ⓪

゚㡊゚, R 㦖 ₆㼊 ㌗㑮[J/(kgബK)], ഝ⓪ Ὃ₆㦮 ☯ 㩦㎇ Ἒ㑮[m2/s], ω_nl 㦖 1 㹾 ἶ㥶 㰚☯㑮[rad/s],

ςl㦖 Ṧ㐶゚, Pin㦖 P1䁷 ὖ⪲㦮 㩲㠊 ⺎ぢ 㿲ῂ 㞫⩻[Pa], Pout㦖 P2䁷 ὖ⪲㦮 㩲㠊 ⺎ぢ 㧛ῂ 㞫⩻

[Pa]㦚 ⋮䌖⌎┺. 㔳 (1)㦖 Ὃ₆㦮 㥶☯ ㌗䌲⯒ ゚ 㞫㿫㎇ 㥶☯㦒⪲ Ṗ㩫䞲 ἓ㤆㧊⸖⪲ 㔺Ⰶ▪⯒ 㧊 㣿䞲 㥚䂮 㩲㠊Ἒ㠦 ⁎╖⪲ 㩗㣿䞶 㑮 㠜┺. 㥚䂮 㩲㠊Ἒ㦮 ☯ 䔏㎇㠦 㡗䟻㦚 ⹎䂮⓪ ὒ☚ ㌗䌲㠦㍲

⓪ Ὃ₆㦮 㥶☯ ㌗䌲Ṗ 㞫㿫㎇ 㥶☯㧊ἶ, 㞫㿫㎇

㥶☯㧎 ἓ㤆㠦⓪ ὖ⪲ 㿲ῂ㠦㍲ ⰻ☯㧊 ⹲㌳䞮㰖 㞠⓪┺⓪ ㌂㔺㠦 㹿㞞䞮㡂 ⽎ ⏒ⶎ㠦㍲⓪ 㔳 (1) 㦚 ┺㦢ὒ ṯ㧊 㑮㩫䞮㡖┺.

1 2 2

2 2

( )( ) ( )( ) 2 ^l ( ) ^l

T s T s

nl nl

in out l nl nl l

k P s P s

e H s e

P s P s s s

ω ς ω ω

− −

= = =

+ +

^{2 2} ₂ , 0.7, , 1.0

4 ^a

nl l l nl

a

RT L

T k

L RT

ω π κ ς

= ≥ = κ ≤ (2)

┺㦢㦒⪲, Ὃ₆㦮 㥶☯ ㌗䌲⯒ ┾㡊 ⼖䢪, 䘟䡫

㌗䌲㠦㍲ P1=P2=P0, V1=V2=V0, T1=T2=Ta⪲ 㩫㦮䞮ἶ, ὖ⪲⯒ ┾㑲䞲 㣿⨟㦒⪲ 䀾 䞮㡂 㥶㧛 㥶⨟ G1, 㥶㿲 㥶⨟ G2㢖 㔺Ⰶ▪ ⌊⿖ 㞫⩻ὒ㦮 ὖἚ⯒ ₆ 㑶䞮Ⳋ 㔳 (3)㦒⪲ ⋮䌖⌒ 㑮 㧞┺.

㔳 (3)㠦㍲ Vd ⓪ ὖ⪲㦮 㣿㩗[m³], v ⓪ 䞒㓺䏺 㧊☯ ㏣☚[m/s], A ⓪ 㔺Ⰶ▪ 㑮㞫 Ⳋ㩗 [m²]㦚 ⋮ 䌖⌎┺.

22

{ }

1 0 1

0 ^a

d

dP P Av G RT

dt =V κV − +

+

{ }

2 0 2

0 a

d

dP P Av G RT

dt V V

= κ +

+ (3)

㔳 (3)㠦㍲ G1, G2⓪ Ps, Pa, Se, P1 ⹥ P2㠦 㦮䞮㡂 ἆ㩫♮㰖Ⱒ ὖ⪲㦮 㡗䟻㠦 㦮䞮㡂 P1, P2 㢖 Pin, P_out㧊 㧒䂮䞮㰖 㞠㦒⸖⪲ G1, G2 Ṗ 㔳 (2)㠦㍲ ₆ 㑶䞲 㩚╂ 䞾㑮㠦 㦮䞮㡂 㡗䟻㦚 ⹱ἶ, ⡦䞲 ⺎ぢ

⯒ 䐋ὒ䞮⓪ Ὃ₆㦮 㥶㏣㦚 㦢㏣㦒⪲ Ṗ㩫䞮Ⳋ, 㔳 (3)⯒ ┺㦢 㔳㦒⪲ ₆㑶䞶 㑮 㧞┺.

{ }

1 0

0 _{q a l}( ) ^{T sl}

d

P s P Axs k uRT H s e

V V

κ ₋

= − +

+

{ }

2 0

0 _{q a l}( ) ^{T sl}

d

P s P Axs k uRT H s e

V κV −

= + − (4)

㔳 (4)⯒ 㥶☚䞮⓪ ὒ㩫㠦㍲ G1=-G2=G0=kqബu ⪲ 㩫㦮䞮㡖ἶ kq[kg/(sബV)]⓪ ⺎ぢ⪲㦮 㩲㠊 㧛⩻

u[V]㢖 㩲㠊 ⺎ぢ⯒ 䐋ὒ䞮⓪ 㰞⨟ 㥶⨟ὒ㦮 ὖἚ

⯒ ⋮䌖⌊⓪ Ἒ㑮㧊┺.

䞒㓺䏺㦮 㤊☯ ⹿㩫㔳㦖 㔳 (5)⪲ ₆㑶䞶 㑮 㧞

┺.

( )

2

1 2

2 _csgn

d x dx dx

M A dP dP B F

dt dt

dt

 

= − − −   (5) 㔳 (5)㠦㍲ B [N/(m/s)]⓪ 㩦㎇ Ⱎ㺆 Ἒ㑮, Fc [N]

⓪ 㩫㰖 Ⱎ㺆⩻㦚 ⋮䌖⌎┺. 㩫㰖 Ⱎ㺆⩻㦚 ⶊ㔲 䞮ἶ 㔳 (4)㢖 (5)⯒ 㧊㣿䞮㡂 㥚䂮 㩲㠊Ἒ㦮 㩚╂

䞾㑮⯒ ῂ䞮Ⳋ 㔳 (6)㦒⪲ ⋮䌖⌒ 㑮 㧞┺.

( ) ( ) ( )

( ) ^{l cyl v}

T s T s T s

l cyl

x s H s H s e e e u s

− − −

=

( )

2

2 2 0

( ) , ,2 ,

2

q a

cyl n n n n n

n n n

k k RT B

H s k

AP M

s s s

ω ς ω

ς ω ω

= = =

+ +

( )

2 0 2

0 n 2

d

P A M V V ω = κ

+ (6)

㔳 (6)㠦㍲ e^-Tcyls ⓪ ὖ㎇㠦 㦮䞲 䞒㓺䏺㦮 㥚䂮 㦧╋ 㰖㡆 㔲Ṛ[s], e^-Tvs⓪ 㩲㠊 ⺎ぢ㦮 㦧╋ 㰖㡆 㔲Ṛ[s]㦚 ⋮䌖⌎┺.

㔳 (6)㦚 㧊㣿䞮㡂 㩲㠊Ἒ⯒ ῂ㎇䞮⓪ ἓ㤆㠦⓪

┺㦢ὒ ṯ㧊 Ṗ㩫䞲┺.

ཛ 㔺Ⰶ▪ ῂ☯Ἒ ⹥ ὖ⪲Ṗ 㩲㠊Ἒ㦮 㞞㩫㎇㠦

⋒䂮⓪ 㡗䟻㦖 㔳 (6)㠦㍲ ₆㑶䞲 㩚╂ 䞾㑮 㭧 Hcyl(s), Hl(s)㠦 㦮䞮㡂 䘟Ṗ♲┺.

ཛྷ 㔲Ṛ 㰖㡆 㣪㏢ 㭧 㔺Ⰶ▪ ῂ☯Ἒ㦮 ὖ㎇ 㰖 㡆 ⹥ ὖ⪲㦮 㞫⩻ 㦧╋ 㰖㡆 㔲Ṛ㦖 㩲㠊Ἒ㦮 㞞 㩫㎇㠦⓪ 㡗䟻㦚 ⹎䂮㰖 㞠ἶ ┾㑲䞲 㔲Ṛ 㰖㡆 Ⱒ㦚 ⋮䌖⌎┺.

ཝ 㩲㠊 ⺎ぢ㦮 ☯ 䔏㎇㦖 㥚䂮 㩲㠊Ἒ㦮 ☯ 䔏

㎇ὒ ゚ᾦ䞮㡂 䡚㩖䧞 ザ⯊⸖⪲ 㩲㠊 ⺎ぢ⓪ 㔲Ṛ 㰖㡆 㣪㏢ Ⱒ㦒⪲ Ṗ㩫䞮Ⳇ 㩲㠊 ⺎ぢ㦮 㔲Ṛ 㰖 㡆 䔏㎇㦖 㩲㠊Ἒ㦮 㞞㩫㎇㠦 㡗䟻㦚 ⋒䂲┺.

㔳 (6)ὒ Ṗ㩫 ཛ~ཝ㦚 㧊㣿䞮㡂 㩲㠊Ἒ⯒ ῂ㎇

䞮Ⳋ Fig. 3 㦒⪲ ⋮䌖⌒ 㑮 㧞┺.

⽎ ⏒ⶎ㠦㍲ 㩲㞞䞮⓪ ⳾◎㧎 Fig. 3 ὒ㦮 ゚ᾦ

⯒ 㥚䞮㡂 ₆㫊 ⏒ⶎ㠦㍲ ㌂㣿䞲 㩲㠊Ἒ ⳾◎㦚 Fig. 4 㠦 ⋮䌖⌎┺. Fig. 4 㦮 e^-TCs㠦㍲ 㰖㡆 㔲Ṛ TC

⓪ (6)㠦㍲ ₆㑶䞲 㰖㡆 㔲Ṛ㦮 㽳 䞿㧎 Tl+ Tcyl+Tv

⯒ ⋮䌖⌎┺.

Fig. 3 ὒ Fig. 4 ⯒ ゚ᾦ䞮Ⳋ ┺㦢ὒ ṯ㦖 㹾㧊⯒

䢫㧎䞶 㑮 㧞┺.

㤆㍶, 䞒✲⺇ 㩲㠊⯒ 䞮㰖 㞠⓪ ἓ㤆㠦 ₆㫊 ⳾

◎㠦㍲⓪ ὖ⪲㦮 㩚╂ 䔏㎇㦚 ┾㑲䞲 㔲Ṛ 㰖㡆㦒

⪲ Ṗ㩫䞮ἶ 㧞ἶ, 㩲㞞䞮⓪ ⳾◎㠦㍲⓪ ὖ⪲㦮 㩚╂ 䔏㎇㦚 㔲Ṛ 㰖㡆 䔏㎇ὒ 㞚㤎⩂ 㭒䕢㑮 ╖ 㡃㠦 ➆⧒㍲ 㧊✳㧊 ⼖䢪䞮⓪ ⳾◎⪲ Ṗ㩫䞮ἶ 㧞

┺. ⁎⩂⸖⪲ 㥚䂮 㩲㠊Ἒ㦮 ☯䔏㎇ὒ ゚ᾦ䞮㡂 ὖ⪲㦮 ╖㡃䙃㧊 㿿⿚䧞 䋆 ἓ㤆㠦⓪ 㟧 ⳾◎㦮 㹾㧊Ṗ 㠜㰖Ⱒ ὖ⪲㦮 ₎㧊Ṗ ₎㠊㰖Ⳋ 㔳 (2)㠦 㦮䞮㡂 ὖ⪲㦮 ╖㡃䙃㧊 㧧㞚㰖⸖⪲ ὖ⪲㦮 㡗䟻 㠦 㦮䞮㡂 㩲㠊Ἒ㦮 㞞㩫㎇㧊 ⼖䢪䞶 㑮 㧞ἶ, 㧊

⩂䞲 䔏㎇㦖 ₆㫊 ⳾◎㦚 㧊㣿䞲 ἓ㤆㠦⓪ 䕢㞛䞶 㑮 㠜㦒⸖⪲ ⽎ ⏒ⶎ㠦㍲ 㩲㞞䞮⓪ ⳾◎㧊 ₆㫊

⳾◎⽊┺ 䌖╏䞲 ⳾◎㧚㦚 㞢 㑮 㧞┺.

┺㦢㦒⪲ 䞒✲⺇ 㩲㠊⯒ 䞮⓪ ἓ㤆㠦 ₆㫊 ⳾◎

㠦㍲⓪ 㩲㠊Ἒ㦮 㦧╋ 㰖㡆 㔲Ṛ㧊 㩚⿖ 㩲㠊Ἒ㦮 㞞㩫㎇㠦 㡗䟻㦚 ⹎䂮⓪ ộ㦒⪲ Ṗ㩫䞮㰖Ⱒ ⽎ ⏒ ⶎ㠦㍲⓪ 㩚╂ 䞾㑮 䡫䌲⪲ ₆㑶䞲 ὖ⪲ ⹥ 㔺Ⰶ

▪ ῂ☯Ἒ㦮 㦧╋ 㰖㡆 㔲Ṛ㦖 㩲㠊Ἒ㦮 㦧╋ 㰖 㡆㠦Ⱒ 㡗䟻㦚 ⹎䂮ἶ 㩲㠊Ἒ㦮 㞞㩫㎇㠦⓪ 㡗䟻 㦚 ⹎䂮㰖 㞠⓪ ộ㦒⪲ Ṗ㩫䞲┺.

Fig. 3 Proposed model of a position control system considering transmission line

Fig. 4 Conventional model of a position control system considering transmission line

4.

4.1 洢檺匶 昪凊

㔺䠮 㧻䂮㦮 ⶒⰂ 䕢⧒⹎䎆⯒ Table 1 㠦 ⋮䌖⌎

┺.

㔺䠮㠦 ㌂㣿䞲 㩲㠊₆⪲⓪ Fig. 3 㠦 ⋮䌖⌎ ゚⪖

㩲㠊₆ Kp[V/m]⯒ ㌂㣿䞮㡖┺. ゚⪖ 㩲㠊₆㦮 㧊

✳㦖 㔳 (6)㠦㍲ ⋮䌖⌎ 㩚╂ 䞾㑮 㭧㠦㍲ ὖ⪲⯒

㣿㩗 㣪㏢⪲ Ṗ㩫䞲 Hcyl(s)⯒ 㧊㣿䞮㡂 㩲㠊Ἒ㦮 Ṧ㐶゚Ṗ 0.3 㧊 ♮☚⪳ ㍺㩫䞮㡖┺. 㔺䠮㠦 ㌂㣿 䞲 㩲㠊₆ 㧊✳㦚 Table 2 㠦 ⋮䌖⌎┺.

4.2 滆櫶 柢儊 斶犢

㔳 (6)㠦 ⋮䌖⌎ 㰖㡆 㔲Ṛ 㭧㠦㍲ 㞫⩻ 㦧╋

㰖㡆 㔲Ṛ Tlὒ 㩲㠊 ⺎ぢ㦮 㦧╋ 㰖㡆 㔲Ṛ Tv㦮 䞿㦖 㩲㠊 ⺎ぢ⪲ 㩲㠊 㔶䢎Ṗ 㧎Ṗ ♲ 䤚 㔺Ⰶ▪

⌊⿖㦮 㞫⩻㧊 ⼖䢪䞮⓪ 㔲Ṛ㦒⪲ ㌳ṗ䞶 㑮 㧞㦒

⸖⪲ Fig. 4 㠦 ⋮䌖⌎ 㔺Ⰶ▪ ⌊⿖ 㞫⩻ 㦧╋㦒⪲

⿖䎆 㿪㩫䞶 㑮 㧞┺. Fig. 4 ⓪ Table 2 㠦㍲ d ⯒ 0.004[m], L 㦚 1[m]⪲ ㍺㩫䞲 ἓ㤆㧊ἶ, 㞫⩻㧊 6[ms]㠦㍲ ⼖䢪䞮₆ 㔲㧧䞮⸖⪲ 㔳 (2)㢖 (6)㦚 ㌂ 㣿䞮㡂 Tlὒ Tv⯒ ☚㿲䞮Ⳋ ṗṗ 3[ms]Ṗ ♾㦚 㞢 㑮 㧞┺. ⁎Ⰲἶ, 䞒㓺䏺㦮 㥚䂮Ṗ ⼖䢪䞮₆ 㔲㧧 䞮⓪ 㔲Ṛ㧊 Tl+ Tcyl+Tv㧚㦚 ㌳ṗ䞲┺Ⳋ Fig. 5 㢖 Fig. 4 ⯒ 㧊㣿䞮㡂 ὖ㎇㠦 㦮䞲 䞒㓺䏺㦮 㥚䂮 㦧

╋ 㰖㡆 㔲Ṛ Tcyl⯒ 15[ms]⪲ 㿪㩫䞶 㑮 㧞┺.

Table 2 㠦 ⋮䌖⌎ ṗṗ㦮 ὖ⪲⯒ ㌂㣿䞮⓪ 㩲㠊 Ἒ㠦 ╖䞮㡂 ㌗₆䞲 ⹿㔳㦚 㧊㣿䞮㡂 ㌆㿲䞲 㰖㡆 㔲Ṛ㦚 Table 3 㠦 ⋮䌖⌎┺.

Table 1 Physical parameters of the driving apparatus A 4.90625ബ10^-4 P0 420,000

B 50.3 R 287

d 0.0065, 0.005, 0.004 Se Max. 18.2

kq 5.06ബ10^-3 Ta 293

L 0.5, 1.0, 2.0, 10.0 x0 0.25

M 0.5 ച 1.4

Table 2 Controller gains used in the experiments

d L Kp

0.5 18.24

1.0 20.41

0.0065

2.0 24.76

0.5 16.89

1.0 17.71

2.0 19.36

0.004

10.0 32.52

0.005 10.0 41.78

Fig. 5 Pressure response in the cylinder chamber

Fig. 6 Position response of cylinder piston

Table 3 Estimated delay times of position control systems

d L Tv Tl Tcyl TC

0.5 0.003 0.0015 0.015 0.0195 1.0 0.003 0.003 0.015 0.021 0.0065

2.0 0.003 0.006 0.015 0.024 0.5 0.003 0.0015 0.015 0.0195 1.0 0.003 0.003 0.015 0.021 2.0 0.003 0.006 0.015 0.024 0.004

10.0 0.003 0.03 0.015 0.048 0.005 10.0 0.003 0.03 0.015 0.048 4.3 柪竞 冶刂歆 柢悲崎決晞 冶刂歆汞 捊剖 Fig. 7~14⓪ Table 2 㦮 㩲㠊₆⯒ 㧊㣿䞲 㔺䠮 ἆ ὒ㢖 Fig. 3, 4 㠦 ⋮䌖⌎ な⪳ ㍶☚⯒ 㧊㣿䞲 㔲⸂

⩞㧊㎮ ἆὒ⯒ ゚ᾦ䞲 ἆὒ⯒ ⋮䌖⌎┺. Fig. 7~14 㠦㍲ 㔺㍶㦖 㔺䠮 ἆὒ, 㩦㍶ὒ 㧒㩦 㐶㍶㦖 ṗṗ 㩲㞞䞲 ⳾◎ὒ ₆㫊 ⳾◎㦚 㧊㣿䞲 㔲⸂⩞㧊㎮ ἆ ὒ⯒ ⋮䌖⌊ἶ, 䞒㓺䏺㦮 㽞₆ 㥚䂮⯒ 0.25[m], ⳿ 䚲 㓺䎳㦚 0.1[m]⪲ ㍺㩫䞮㡂 㔺䠮 ⹥ 㔲⸂⩞㧊㎮

㦚 㑮䟟䞮㡖┺.

22

Fig. 7 Comparison of experimental result with simulation results(d : 0.0065[m], L : 0.5[m])

Fig. 8 Comparison of experimental result with simulation results(d : 0.004[m], L : 0.5[m])

Fig. 9 Comparison of experimental result with simulation results(d : 0.0065[m], L : 1.0[m])

Fig. 10 Comparison of experimental result with simulation results(d : 0.004[m], L : 1.0[m])

Fig. 11 Comparison of experimental result with simulation results(d : 0.0065[m], L : 2.0[m])

Fig. 12 Comparison of experimental result with simulation results(d : 0.004[m], L : 2.0[m])

Fig. 13 Comparison of experimental result with simulation results(d : 0.004[m], L : 10.0[m])

Fig. 14 Comparison of experimental result with simulation results(d : 0.005[m], L : 10.0[m])

Table 4 Estimated parameters of transmission lines used in the simulation

d L knl ςnl

0.5 1.0 0.7

1.0 0.8 0.7

0.0065

2.0 0.7 0.7

0.5 0.7 0.7

1.0 0.7 0.7

2.0 0.6 0.7

0.004

10.0 0.25 1.7

0.005 10.0 0.27 1.2 Fig. 7~14 ⯒ ㌊䘊⽊Ⳋ ☯㧒䞲 ゚⪖ 㧊✳㦚 ㌂㣿 䞮㡂☚ ₆㫊 ⳾◎ὒ 㩲㞞䞲 ⳾◎㦮 㦧╋ ἆὒṖ

㌗㧊䞾㦚 㞢 㑮 㧞┺. ₆㫊 ⳾◎㦚 㧊㣿䞲 ἓ㤆㠦

⓪ 㔺䠮ὒ ☯㧒䞲 㧊✳㦚 ㌂㣿䞮㡂☚ 㥚䂮 㦧╋㧊

⿞㞞㩫䟊㰖⓪ ἓ㤆Ṗ ⋮䌖⋮ἶ(Fig. 7, 11, 14) ⡦䞲, 䞒㓺䏺㦮 㦧╋ 㰖㡆 㔲Ṛ㧊 ㌗㧊䞮Ợ ⋮䌖⋮⓪ ἓ 㤆Ṗ 㧞㦢㦚 㞢 㑮 㧞┺.(Fig. 13, 14) ⁎⩂⋮, 㩲㞞 䞲 ⳾◎㦚 㧊㣿䞲 ἓ㤆㠦⓪ 䞒㓺䏺㦮 㦧╋ 㰖㡆 㔲Ṛ ⹥ 㼁 ⻞㱎⪲ ⹲㌳䞮⓪ 㰚☯ 㭒₆Ṗ 㧮 㧒䂮 䞮ἶ(Fig. 7, 9, 11, 13, 14), ⡦䞲 䞒㓺䏺㦮 㽞₆ 㦧╋

㟧㌗㧊 㔺䠮 ἆὒ㢖 㥶㌂䞾㦚 㞢 㑮 㧞┺.(Fig. 8, 10, 12). 㩲㞞䞲 ⳾◎ὒ 㔺䠮 ἆὒṖ 㩫䢫䞮Ợ 㧒 䂮䞮㰖 㞠⓪ ộ㦖 ⳾◎Ⱇ ὒ㩫㠦㍲ 㔺Ⰶ▪㦮 Ⱎ㺆 䔏㎇ὒ 㩲㠊 ⺎ぢ㦮 ⿞Ṧ╖⯒ ἶ⩺䞮㰖 㞠㞮₆ ➢ ⶎ㦒⪲ ㌳ṗ♲┺.

Table 4 ⓪ Fig. 7~14㠦㍲ ㌂㣿䞲 ⳾◎ 㭧㠦㍲ 㩲 㞞䞲 ⳾◎㦮 ὖ⪲ 䕢⧒⹎䎆 㿪㩫䂮⯒ ⋮䌖⌎┺.

5. 冶 嵦

ὖ⪲⓪ 㞫㿫 Ὃ₆⯒ 㔺Ⰶ▪⪲ Ὃ 䞮₆ 㥚䞲 䞚 㑮 㣪㏢㧊㰖Ⱒ ⳾◎Ⱇ㧊 㣿㧊䞮㰖 㞠₆ ➢ⶎ㠦 䡚 㨂₢㰖㦮 㡆ῂ㠦㍲⓪ ┾㑲䞲 㔲Ṛ 㰖㡆 㣪㏢⪲ Ṗ 㩫䞮㡖┺. ⽎ ⏒ⶎ㠦㍲⓪ ὖ⪲⯒ 䙂䞾䞲 Ὃ₆㞫 㔺Ⰶ▪ 㥚䂮 㩲㠊Ἒ㦮 ㍶䡫 ⳾◎㦚 㥶☚䞮₆ 㥚䞮 㡂 ὖ⪲㦮 ☯ 䔏㎇㦚 ἶ⩺䞲 㥚䂮 㩲㠊Ἒ ⳾◎㦚 㩲㞞䞮㡖┺. ⽎ ⏒ⶎ㠦㍲ 㩲㞞䞲 ὖ⪲ ⳾◎㦖 㔲 Ṛ 㰖㡆 㣪㏢㢖 ὖ⪲ 㟧┾ 㞫⩻㦮 㩚╂ 䔏㎇㦚 ἶ

⩺䞲 ⳾◎㧊ἶ ὖ⪲㦮 ₎㧊㢖 㰗ἓ㠦 ➆⧒㍲ ⼖䢪 䞮⓪ ㍶䡫 㩚╂ 䞾㑮㦮 䡫䌲㧊⸖⪲ ὖ⪲ ⳾◎㦚 䙂䞾䞲 㩲㠊₆⯒ 㣿㧊䞮Ợ ㍺Ἒ䞶 㑮 㧞┺. ⽎ ⏒ ⶎ㠦㍲ 㩲㞞䞲 ⳾◎㦮 䌖╏㎇㦖 㔺䠮 ἆὒ㢖㦮 ゚ ᾦ⯒ 䐋䞮㡂 Ỗ㯳䞮㡖ἶ, ₆㫊 ⳾◎ὒ ゚ᾦ䞮㡂 㩲㞞䞲 ⳾◎㧊 㔺䠮 ἆὒ㢖 㥶㌂䞲 ἆὒ⯒ ⽊㧚㦚 䢫㧎䞮㡖┺.

焾処怾竒

(1) Rohmann, C. P. and Grogan, E. C., 1957, ‘On the Dynamics of Pneumatic Transmission Lines,”

Transactions of the ASME, Vol. 97, pp. 853~874.

(2) Yoshioka, M. and Morikawa, Y., 1981, “Transient Response of Volume-Terminated Pneumatic Trans- mission Lines,” Transactions of the Society of Instrument and Control Engineers, Vol. 17, No. 9, pp.

920~926.

(3) 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. 567~576.

(4) TUKAMOTO, N., KAWAKAMI, Y. and NAKANO, K., 2002, “An Application of Gain-scheduling Control to a Pneumatic Servo System,” Transactions of the Japan Fluid Power Systems Society, Vol. 33, No. 1, pp.

15~20.

(5) Noritugu, T. and Takaiwa, M., 1995, “Design of Pneumatic Servo System Using Disturbance Observer,” Transactions of the Society of Instrument and Control Engineers, Vol. 31, No. 1, pp. 82~88.

(6) Mccloy, D. and Martin, H. R., 1980, “Control of Fluid Power,” JOHN WILEY & SONS INC., pp.

255~258.