Synchronous Position Control of Pneumatic Cylinder Driving Apparatus

ᙽី⻝ ⱬ⌸᳜ ᛴᵡ ㄭ㟠ム れ㟠 ᵡី ㆤ⼼

沫滆昷^†

Synchronous Position Control of Pneumatic Cylinder Driving Apparatus Ji-Seong Jang

Key Words : Nonlinear Characteristics(゚㍶䡫 䔏㎇), Pneumatic Cylinder Driving Apparatus(Ὃ₆㞫 㔺Ⰶ▪ ῂ☯ 㧻䂮), Synchronous Position Control(☯₆ 㥚䂮 㩲㠊)

Abstract

In this study, a position synchronous control algorithm being applied to two-axes pneumatic cylinder driving apparatus is proposed. The position synchronous control algorithm is composed of position controller and synchronous controller. The position controller is designed to minimize the effect of several nonlinear characteristics of the driving apparatus. The synchronous controller is designed to reduce the synchronous error. The effectiveness of the proposed controller is proved by simulation results.

1. ^{昢 嵦}

Ὃ₆㞫 㔺Ⰶ▪⯒ 㧊㣿䞲 ῂ☯ 㧻䂮⓪ Ὃ₆㦮 ゚

㍶䡫㎇㠦 ₆㧎䞮⓪ ┺㟧䞲 ゚㍶䡫 䔏㎇㧊 㫊㨂䞲

┺. ╖䚲㩗㧎 ゚㍶䡫 䔏㎇㦖 䞒㓺䏺㦮 㥚䂮 ⼖䢪, 㔺Ⰶ▪ 㔺 ⌊⿖ 㞫⩻ ⼖䢪 ⹥ 㡾☚ ⼖䢪㠦 㦮䞲 ἶ㥶 㰚☯㑮㦮 ⼖䢪⁽¹⁾, 㩲㠊 ⺎ぢ㦮 㞫⩻½㥶⨟ 䔏

㎇ ⹥ 㩲㠊 㧛⩻½㥶⨟ 䔏㎇㦮 ⼖䢪㠦 㦮䞲 㩲㠊Ἒ 㦮 㧊✳ ⼖䢪⁽²⁾, 㩫㰖 Ⱎ㺆⩻ὒ ゚ᾦ䞮㡂 ㌗╖㩗㦒

⪲ 㧧㦖 ῂ☯⩻㠦 㦮䞲 㓺䕇-㔂Ⱃ 䡚㌗⁽³⁾❇㧊 㧞

┺. ⁎⩂⸖⪲ Ὃ₆㞫 㔺Ⰶ▪⪲ ῂ㎇♲ ┺㿫 ῂ☯

㧻䂮㠦㍲ 㔺Ⰶ▪㦮 㥚䂮 ☯₆ 㩲㠊⯒ ╂㎇䞮₆ 㥚 䟊㍲⓪ 㤆㍶ ṗṗ㦮 㔺Ⰶ▪⯒ ☛Ⱃ㩗㦒⪲ 㩲㠊䞮

⓪ ἓ㤆㠦 ㌗₆䞲 ゚㍶䡫 䔏㎇㦮 㡗䟻㦚 㾲㏢䞲㦒

⪲ 㠋㩲䞶 㑮 㧞⓪ 㩲㠊₆Ṗ ㍺Ἒ♮㠊㟒 䞮ἶ, ┺ 㦢㦒⪲ 㔺Ⰶ▪Ṛ㦮 ☯₆ 㡺㹾⯒ 㠋㩲䞶 㑮 㧞⓪ 㩲㠊₆Ṗ ⿖Ṗ ♮㠊㟒 䞲┺. Maeda ❇⁽⁴⁾㦖 ㌗䞮⪲

ῂ☯䞮⓪ Ⰲ䝚䔎㠦 Ὃ₆㞫 㔺Ⰶ▪⯒ ⼧⪂⪲ 㡆ἆ 䞮㡂 Ⰲ䝚䔎Ṗ 㑮䘟㦒⪲ 㥶㰖♮Ⳋ㍲ ㌗䞮⪲ 㧊☯

䞮⓪ 㥚䂮 ☯₆ 㩲㠊 㧻䂮⯒ ῂ㎇䞮㡖㦒⋮, ㌗₆ 䞲 ゚㍶䡫 䔏㎇㦚 㩚⿖ 㣎⧖㦒⪲ 䀾 䞮㡂 㩲㠊Ἒ

⯒ ῂ㎇䞮㡖ἶ, ⡦䞲, ṗ 㔺Ⰶ▪Ṛ㦮 ☯₆ 㡺㹾⯒

㩲Ệ䞶 㑮 㧞⓪ 㩲㠊₆⯒ ⿖Ṗ䞮㰖 㞠㞮㦒⸖⪲ 㩫

㌗ ㌗䌲 ⹥ ὒ☚ ㌗䌲㠦㍲ 㟧䢎䞲 ☯₆ 㩲㠊⯒ ╂

㎇䞮㰖 ⴑ䞮㡖┺.

⽎ 㡆ῂ㠦㍲⓪ 2 㿫㦒⪲ ῂ㎇♲ Ὃ₆㞫 㔺Ⰶ▪

ῂ☯ 㧻䂮㦮 ゚㍶䡫 䔏㎇㦚 ☯㩗㧎 㣪㏢㢖 㩫㩗㧎 㣪㏢⪲ ⿚Ⰲ䞮㡂 ṗṗ㦮 ゚㍶䡫 䔏㎇㦚 ⽊㌗䞮₆ 㥚䞲 㥚䂮 㩲㠊₆⯒ ㍺Ἒ䞲 䤚, ṗ 㔺Ⰶ▪Ṛ㦮 ☯

₆ 㡺㹾⯒ 㠋㩲䞮₆ 㥚䞲 㩲㠊₆⯒ ⿖Ṗ䞾㦒⪲㖾 㥚䂮 ☯₆ 㡺㹾⯒ 㠋㩲䞶 㑮 㧞⓪ 㩲㠊₆⯒ ㍺Ἒ 䞲┺. ㌗₆䞲 ゚㍶䡫 䔏㎇ 㭧㠦㍲ ☯㩗㧎 㣪㏢⓪ ἶ㥶 㰚☯㑮⯒ ⼖䢪㔲䋺⓪ 䞒㓺䏺㦮 㥚䂮㢖 㔺Ⰶ

▪ 㔺 ⌊⿖ 㞫⩻㦮 ⼖䢪, 㩲㠊 ⺎ぢ㦮 㞫⩻ബ㥶⨟

䔏㎇㦚 ⼖䢪㔲䋺⓪ 㔺Ⰶ▪ 㔺 ⌊⿖ 㞫⩻ ⼖䢪⪲

㌳ṗ䞶 㑮 㧞ἶ, 䞒㓺䏺㦮 㥚䂮㢖 㔺Ⰶ▪ 㔺 ⌊⿖

㞫⩻㧊 ⼖䢪䞮㡂☚ 㩲㠊Ἒ㦮 䘦⬾䝚 㩚╂ 䞾㑮⯒

㧒㩫䞮Ợ 㥶㰖䞮₆ 㥚䞮㡂 ゚㍶䡫 ⽊㌗₆⁽¹⁾⯒ 㧊 㣿䞮㡖┺. 㩲㠊 ⺎ぢ㦮 㩲㠊 㧛⩻-㥶⨟ 䔏㎇㦮 ⼖ 䢪㢖 Ⱎ㺆⩻㠦 ₆㧎䞮⓪ 㩫㩗㧎 ゚㍶䡫 㣪㏢⓪ 㣎

⧖ ⽊㌗₆⁽⁵⁾⯒ 㧊㣿䞮㡂 㠋㩲䞮㡖┺. 㔺Ⰶ▪Ṛ㦮

☯₆ 㡺㹾⯒ ⽊㌗䞮₆ 㥚䞲 㩲㠊₆⓪ ゚⪖ 㧊✳㦚

㌂㣿䞮㡂 㔺Ⰶ▪Ṛ㦮 㥚䂮 ☯₆ 㡺㹾⯒ ṗ 㔺Ⰶ▪

㩲㠊 ⬾䝚㠦 ⿖Ṗ䞮⓪ ῂ㫆⪲ ㍺Ἒ䞮㡖┺. ㍺Ἒ䞲 㩲㠊₆㦮 ㎇⓻㦖 㔲⸂⩞㧊㎮ὒ 㔺䠮㠦 㦮䞮㡂 Ỗ 㯳䞮㡖ἶ, ┺㟧䞲 ⳿䚲 㧛⩻㠦 ╖䞮㡂 㟧䢎䞲 㩲

† 㩫䣢㤦ڇٻ⿖ἓ╖䞯ᾦٻ₆ἚὋ䞯⿖ٻ

E-mail : [email protected]

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

ṗṗ㦮 ⪲✲Ⰲ㓺 㔺Ⰶ▪㠦⓪ ㌗䞮 ῂ☯㣿 䘎⪲✲

㔺Ⰶ▪Ṗ ㍺䂮♮㠊 㧞┺. ⁎Ⱂ㠦㍲ ㌂㣿♲ ₆䢎⓪

┺㦢ὒ ṯ┺.

G : 㔺Ⰶ▪⪲ Ὃ  ⡦⓪ 㔺Ⰶ▪⪲⿖䎆 㥶㿲♮⓪ 㰞⨟ 㥶⨟[kg/s], M : Ṗ☯⿖ 㰞⨟[kg], P : 㔺Ⰶ▪ 㔺

⌊⿖ 㞫⩻[Pa], Pa : ╖₆㞫[Pa], Ps : Ὃ 㞫[Pa], Se : 㩲㠊 ⺎ぢ 㥶䣾 ┾Ⳋ㩗[m²], V : 㔺Ⰶ▪ 㔺 ⌊⿖ 㼊 㩗[m³], x : 䞒㓺䏺 㥚䂮[m]

㔺Ⰶ▪ ⌊⿖ 㡾☚ ⼖䢪⯒ ┾㡊 ⼖䢪⪲ Ṗ㩫䞮ἶ 㩲㠊 ⺎ぢ㢖 㔺Ⰶ▪⯒ 㡆ἆ䞮⓪ 㩚╂ ὖ⪲⓪ ┾㑲 䞲 㼊㩗㦒⪲ Ṗ㩫䞮㡂 㩚╂ ὖ⪲ 㟧┾㠦㍲ ⹲㌳䞶 㑮 㧞⓪ 㞫⩻ 㦧╋㦮 㰖㡆 ⹥ 㩚╂ ὖ⪲ ⌊⿖㦮 Ⱎ㺆 ㏦㔺㦚 ⶊ㔲䞮Ⳋ 㔺Ⰶ▪ ⌊⿖㦮 㞫⩻ ⼖䢪⓪ 㔳 (1)ڇٻ(2)㢖 ṯ㧊 ₆㑶䞶 㑮 㧞┺.







 +

∆

= ∆

∆

∆ i i a

i i

i G RT

t A x V P

k t P

1 1 1

1 (1)







 +

∆

− ∆

∆ =

∆ i i a

i i

i G RT

t A x V P

k t P

2 2 2

2 (2) k : ゚㡊゚, A : 㑮㞫 Ⳋ㩗[m²], R : ₆㼊 ㌗㑮 [J/(kgബK)], Ta : ╖₆ 㡾☚ [K], 㻾㧦 i=1, 2

Fig. 1 Schematic diagram of the pneumatic cylinder G driving apparatus

㔺Ⰶ▪ 㔺⪲ Ὃ ♮⓪ 㥶⨟㦖 ┺㦢 㔳㦒⪲ ₆㑶 䞶 㑮 㧞┺.

1= Gi

( ) 















 



−



 





> −

+ k k s k i s i s a

s ei

i P

P P

P k RT P k P S

P ₁ ² ₁ ¹

1 1

1 , 2

528 .

0 (4)

1 1

1 0.528, 1 2 ⁻

+



 



≤  ^k

k s a

s ei

i RT k

P k P S

P (5)

2= Gi

( ) 



















−









> −

+ k k i k a i

a i a

i ei

a P

P P

P k RT P k P S

P

1 2 2 2 2

2 0.528, 2 2 1 (6)

1 1 2

2 2

, 2 528 .

0 ⁻

+



 



≤  ^k

k i a

i ei

a RT k

P k P S

P (7) 㔺Ⰶ▪㦮 Ⱎ㺆 䔏㎇ ⹥ 㩲㠊 ⺎ぢ㦮 㧛⩻ὒ 㥶 䣾 ┾Ⳋ㩗ὒ㦮 ὖἚ⯒ Fig. 2ۙ4 㠦 ⋮䌖⌎┺.

Fig. 2 Measurement results of friction force of the upper side rodless cylinder

Fig. 3 Measurement results of friction force of the lower side rodless cylinder

Fig. 4 Measurement results of effective area of the control valve

Table 1 Physical parameters of the driving apparatus

A 0.1256 L 0.5

B₁ 31 M₁ 5

B₂ 32.4 M₂ 4

F_c1 58 P_s 591,600

F_c2 39 R 287

k 1.4 T_a 293

Table 1 㦖 ῂ☯Ἒ㦮 ⶒⰂ 䕢⧒⹎䎆⯒ ⋮䌖⌎┺.

3. 洢檺匶 昪凊

3.1 氊獞 洢檺匶 昪凊

゚㍶䡫 ⽊㌗₆⯒ 㩗㣿䞮㡂 㔺Ⰶ▪ 㔺⪲ Ὃ  ⡦

⓪ 㔺Ⰶ▪ 㔺⪲⿖䎆 ⹿㿲♮⓪ 㥶⨟㦚 ┺㦢 㔳ὒ ṯ㧊 ἆ㩫䞮Ⳋ d³xi/dt³=Φi㦮 ὖἚṖ ㎇Ⱃ䞮⸖⪲

Φi 㠦㍲ 䞒㓺䏺 㥚䂮 xi ₢㰖Ṗ ㍶䡫㩗㧎 ὖἚ⪲

♲┺. ⁽¹⁾

( )

{ , , , },

) (1

2 1 i i i i i i

i C x f x v P P

G = Φ −

( ) 1 2 2( 1 2)

2

1, ( )

,

, _{i i}

i i i i i i i

i i i i

i i

i P P

M v AB x LkP MA x v MA kP P

P v x

f − −

− −

−

=

²_{2 2} ci^, i i i i

i F

M v B M

B +

+

i i i i

i a i

i

i a G G G

x L M

kRT x

M x kRT

C =− =







 + −

= , _{1 2}

) ) (

( (8)

㧊⩂䞲 ㌗䌲㠦㍲ ㌗䌲 䞒✲⺇ 㩲㠊₆⯒ 㧊㣿䞮 Ⳋ Fig. 5 㢖 ṯ㦖 䘦⬾䝚Ἒ⯒ ῂ㎇䞶 㑮 㧞ἶ, 㩲 㠊₆ 㧊✳㦮 ㍺㩫㠦 㦮䞮㡂 䘦⬾䝚Ἒ㦮 ⁏㦚 㤦䞮

⓪ 㥚䂮⪲ ⺆䂮䞶 㑮 㧞㦒⸖⪲ 㔺Ⰶ▪ 㔺 ⌊⿖ 㞫

⩻ ⹥ 䞒㓺䏺㦮 㥚䂮 ⼖䢪㠦 㦮䞲 ῂ☯Ἒ㦮 ☯㩗 㧎 ゚㍶䡫 䔏㎇㦚 ⽊㌗䞶 㑮 㧞┺. 㔳 (9)⓪ Fig. 5

Fig. 5 Closed loop system with nonlinear compensator and state feedback controller

Fig. 6 block diagram of the position control system 㦮 xr⿖䎆 xi₢㰖㦮 㩚╂ 䞾㑮ἶ, ゚㍶䡫 ⽊㌗₆㢖

㌗䌲 䞒✲⺇ 㩲㠊₆⯒ 㧊㣿䞲 㥚䂮 㩲㠊Ἒ㦮 䘦⬾

䝚 㩚╂ 䞾㑮⯒ ⋮䌖⌎┺. ͑ )

2 (

3 H s

K s K s K s

K x

x

p v a

p r

i =

+ +

= + (9)

㔳 (8)ὒ (9)⯒ 㧊㣿䞮㡂 㩲㠊₆⯒ ῂ㎇䞲 䤚, 㥚䂮 㩲㠊⯒ 㑮䟟䞮Ⳋ 㩲㠊Ἒ㦮 㩫㩗㧎 ⳾◎Ⱇ 㡺 㹾㠦 㦮䞮㡂 㥚䂮 㩲㠊 㡺㹾Ṗ ⹲㌳ 䞶 㑮 㧞┺.

㧊⩂䞲 㥚䂮 㩲㠊 㡺㹾⯒ ⽊㌗䞮㡂 ṗ 㔺Ⰶ▪Ṗ 㩲㠊Ἒ㦮 㩫㩗㧎 ⳾◎Ⱇ 㡺㹾㠦 ὖἚ㠜㧊 ⳿䚲䂮

⯒ 㿪㫛䞶 㑮 㧞☚⪳ 䞮₆ 㥚䞮㡂 㔳 (8)ὒ (9)⪲

㍺Ἒ䞲 㩲㠊Ἒ⯒ ⌊⿖ ⳾◎⪲ 㧊㣿䞮⓪ 㣎⧖ ὖ䁷

₆⯒ 㩗㣿䞮㡖┺. 㣎⧖ ὖ䁷₆⯒ 㩗㣿䞮Ⳋ 㞞㩫䢪 䞚䎆㦮 㧊✳㧊 1 㧊 ♮⓪ 㭒䕢㑮 ╖㡃㠦㍲⓪ 㡺㹾 Ṗ 0 㧊 ♮⸖⪲ 㩲㠊 ⺎ぢ㦮 㩲㠊 㧛⩻ബ㥶⨟ 䔏

㎇㦮 ⼖䢪㢖 Ⱎ㺆⩻ ⼖䢪㠦 ₆㧎䞮⓪ 㩫㩗㧎 ゚㍶

䡫 䔏㎇㠦 㦮䞲 㥚䂮 㩲㠊 㡺㹾⯒ 㠋㩲䞶 㑮 㧞┺.

㔳 (8)ὒ (9) ⹥ 㣎⧖ ὖ䁷₆⯒ 㧊㣿䞲 㥚䂮 㩲 㠊Ἒ㦮 な⪳ ㍶☚⯒ Fig. 6 㠦 ⋮䌖⌎┺. Fig. 6 㠦㍲

di(s)⓪ 㣎⧖, Hn(s)⓪ 㥚䂮 㩲㠊Ἒ㦮 Ὃ䃃 㩚╂ 䞾 㑮, Q(s)⓪ 㞞㩫䢪 䞚䎆⯒ ⋮䌖⌎┺.

3.2 壟匶 洢檺匶 昪凊

Fig. 7 㦖 ☯₆ 㩲㠊₆⯒ 䙂䞾䞲 㩲㠊Ἒ㦮 な⪳

㍶☚⯒ ⋮䌖⌎┺.

Fig. 7 㦮 㩲㠊Ἒ㠦㍲ ☯₆ 㩲㠊₆ Ks(s)⯒ 䙂䞾 䞮㰖 㞠㦖 ἓ㤆㦮 㥚䂮 ☯₆ 㡺㹾 e3(s)⓪ ┺㦢 㔳 㦒⪲ ⋮䌖⌒ 㑮 㧞┺. 㧊䞮㦮 㔳㠦㍲⓪ ⧒䝢⧒㓺 㡆㌆㧦 s ⯒ ㌳⨋䞲┺.

Fig. 7 Block diagram of the synchronous position control system

n i n r

i d

Q Q HH

Q x H

Q Q HH x H

− +

+ −

−

= + _{−1 −1}

1

) 1 ( 1

) 1 (

) 1

( 1 2 1

3 2

1 d d

Q Q HH

Q e H

e e

n

− − +

= −

=

− ₋ (10)

㔳(10)㦚 ㌊䘊⽊Ⳋ 䞒㓺䏺㦮 㥚䂮Ṗ 㩫㌗ ㌗䌲 㠦 ☚╂䞮₆ 㧊㩚㠦⓪ 㣎⧖㦮 㡗䟻㠦 㦮䞮㡂 ☯₆ 㡺㹾Ṗ ⹲㌳䞾㦚 㞢 㑮 㧞┺.

┺㦢㦒⪲ ☯₆ 㩲㠊₆ Ks(s)⯒ 䙂䞾䞲 ἓ㤆㦮 㥚 䂮 ☯₆ 㡺㹾⓪ ┺㦢 㔳㦒⪲ ⋮䌖⌒ 㑮 㧞┺.

1 1 1 1

1

) 1 (

1 d

Q Q HH

Q x H

Q Q HH x H

r n

n + −

+ −

−

= + _{− −}

1 ^{1 1 2},

1 x

QK HH Q Q HH

QK HH

s n n

s n

−

−

−

+

− + +

1 2

2 1 1

) 1 (

1 d

Q Q HH

Q x H

Q Q HH x H

r n

n + −

+ −

−

= + _{− −}

1 ^{1 1 1},

1 x

QK HH Q Q HH

QK HH

s n n

s n

−

−

−

+

− + +

=

=

− _{2 3}

1 e e

e

( )

1

) 1 ( )

2 1 ( 1

) 1 (

1 1 1 2 1

1 d d

QK HH

Q H Q K Q HH

Q K Q HH

s n s

n

s

n −

+

−

− + +

− + +

−

−

− (11)

㔳 (11)㦚 ㌊䘊⽊Ⳋ ☯₆ 㩲㠊₆㦮 ㌓㧛㠦 㦮䞮 㡂 ☯₆ 㡺㹾㦮 㾲╖ 㧊✳㧊 Ṧ㏢䞮⸖⪲, ☯₆ 㩲 㠊₆⯒ ㌓㧛䞮㰖 㞠㦖 ἓ㤆㢖 ゚ᾦ䞮㡂 ☯₆ 㡺㹾 Ṗ 㭚㠊✺Ợ ♾㦚 㞢 㑮 㧞┺.

3.3 ☯₆ 㡺㹾㦮 㭒䕢㑮 䔏㎇ ⿚㍳

㭒䕢㑮 䔏㎇ ⿚㍳㠦 ㌂㣿䞲 㩲㠊₆㦮 䕢⧒⹎䎆

⯒ Table 2 㠦 ⋮䌖⌎┺. Fig. 8 㦖 Table 2 㠦 ₆㑶䞲 㩲㠊₆ 䕢⧒⹎䎆⯒ 㧊㣿䞮㡂 㥚䂮 ☯₆ 㡺㹾㦮 㭒 䕢㑮 䔏㎇㦚 ⿚㍳䞲 ἆὒ㧊┺.

Fig. 8 Frequency response of the synchronous error Fig. 8 㠦㍲ 㔺㍶㦖 Q 㦮 㭒䕢㑮 㩚╂ 䔏㎇㦚 ⋮ 䌖⌊ἶ, 㩦㍶ ⹥ 㧒㩦 㐶㍶㦖 ṗṗ ☯₆ 㩲㠊₆⯒

㌂㣿䞲 ἓ㤆㢖 ㌂㣿䞮㰖 㞠㦖 ἓ㤆㦮 ☯₆ 㡺㹾㦮 㭒䕢㑮 㩚╂ 䔏㎇㦚 ⋮䌖⌎┺. ⁎Ⱂ㠦㍲ 㞢 㑮 㧞

⓪ ⹪㢖 ṯ㧊 Q 㦮 㧊✳㧊 Ệ㦮 1 㧊 ♮⓪ ἶ 㭒 䕢㑮 ╖㡃㠦㍲⓪ 㭒䕢㑮 㩚╂ 䔏㎇㧊 㧒䂮䞮㰖Ⱒ, Q 㧊 㧊✳㧊 1 㧊䞮㧎 㭒䕢㑮 ╖㡃㠦㍲⓪ ☯₆ 㡺 㹾㦮 㧊✳㧊 㟓 5[dB]㩫☚ Ṧ㏢䞮ἶ 㧞㦢㦚 㞢 㑮 㧞┺.

4. 柪竞 冶刂 愕 処然

Fig. 9ۙ12 ⓪ ☯₆ 㩲㠊₆⯒ ㌂㣿䞮㰖 㞠㦖 ἓ㤆 㢖 ㌂㣿䞲 ἓ㤆㦮 㔺䠮 ἆὒ㧊ἶ, (a)⓪ 䞒㓺䏺㦮

⼖㥚, (b)⓪ ☯₆ 㡺㹾 e3⯒ ⋮䌖⌎┺.

Fig. 9 㢖 10 㦖 㽞₆ 㥚䂮⯒ 0.3 [m]⪲ ㍺㩫䞮ἶ 㾲㫛 㥚䂮Ṗ ṗṗ 0.1 [m], 0.2 [m]㧎 㓺䝢⧒㧎 䡫㌗

㦮 ⳿䚲 Ὼ㩗㦚 㿪㫛䞮☚⪳ 㥚䂮 㩲㠊⯒ 㑮䟟䞲 ἆὒ㧊┺. 㧊 ἆὒ⪲⿖䎆 ☯₆ 㩲㠊₆⯒ ㌂㣿䞮Ⳋ ὒ☚ ㌗䌲㠦㍲㦮 ☯₆ 㡺㹾Ṗ Ṧ㏢䞮ἶ, ⳿䚲 㥚 䂮㠦 ▪㤇 ゾⰂ 㑮⪊䞾㦚 㞢 㑮 㧞┺.

Fig. 11 ὒ 12 ⓪ 㽞₆ 㥚䂮⯒ ṗṗ 0.3 [m], 0.1 [m]⪲ ㍺㩫䞮ἶ 㓺䎳 䙃㧊 ധ0.2 [m]㧎 㓺䝢⧒㧎 䡫㌗㦮 ⳿䚲 Ὼ㩗㦚 㰖㩫䞮㡂 㥚䂮 㩲㠊⯒ 㑮䟟䞮 Ⳋ㍲ 㥚䂮 㩲㠊 㔲㧧 3 㽞 䤚㠦 ധ0.05 [m]㦮 㣎⧖

㦚 ㏢䝚䔎㤾㠊㠦 㦮䞮㡂 㧎Ṗ䞲 ἆὒ㧊┺. 㧊 ἆ ὒ⪲⿖䎆 ☯₆ 㩲㠊₆⯒ ㌂㣿䞮Ⳋ 㾲╖ ☯₆ 㡺㹾 Ṗ Ṧ㏢䞮ἶ 㣎⧖㦮 㡗䟻㦚 㔶㏣䞮Ợ 㩲Ệ䞾㦚 㞢 㑮 㧞┺. ὒ☚ ㌗䌲㠦㍲㦮 ☯₆ 㡺㹾Ṗ Ṧ㏢䞮ἶ,

⳿䚲 㥚䂮㠦 ▪㤇 ゾⰂ 㑮⪊䞾㦚 㞢 㑮 㧞┺.

(a) Step response

(b) Synchronous error

Fig. 9 Synchronous control results ช

(a) Step response

(b) Synchronous error

Fig. 10 Synchronous control results ซ

(a) Step response

(b) Synchronous error

Fig. 11 Synchronous control results under step type disturbance ช

(a) Step response

(b) Synchronous error

Fig. 12 Synchronous control results under step type disturbance ซ

䞶 㑮 㧞⓪ 㩲㠊₆⯒ ㍺Ἒ䞮㡖┺. ☯㩗㧎 ゚㍶䡫 㣪㏢㦮 㡗䟻㦚 㠋㩲䞮₆ 㥚䞲 㩲㠊₆⪲⓪ ゚㍶䡫

⽊㌗₆⯒ 㧊㣿䞮㡂 䞒㓺䏺㦮 㥚䂮㢖 㔺Ⰶ▪ 㔺 ⌊

⿖ 㞫⩻㧊 ⼖䢪䞮㡂☚ 㩲㠊Ἒ㦮 䘦⬾䝚 㩚╂ 䞾㑮

⯒ 㧒㩫䞮Ợ 㥶㰖䞶 㑮 㧞☚⪳ 䞮㡖ἶ, 㩲㠊 ⺎ぢ 㦮 㩲㠊 㧛⩻ബ㥶⨟ 䔏㎇㦮 ⼖䢪㢖 Ⱎ㺆⩻㠦 ₆㧎 䞮⓪ 㩫㩗㧎 ゚㍶䡫 㣪㏢⓪ 㣎⧖ ⽊㌗₆⯒ 㧊㣿䞮 㡂 㠋㩲䞮㡖┺. 㔺Ⰶ▪Ṛ㦮 ☯₆ 㡺㹾⯒ ⽊㌗䞮₆ 㥚䞲 㩲㠊₆⓪ ゚⪖ 㧊✳㦚 ㌂㣿䞮㡂 㔺Ⰶ▪Ṛ㦮 㥚䂮 ☯₆ 㡺㹾⯒ ṗ 㔺Ⰶ▪ 㩲㠊 ⬾䝚㠦 ⿖Ṗ䞮

⓪ ῂ㫆⪲ ㍺Ἒ䞮㡖┺. ㍺Ἒ䞲 㩲㠊₆㦮 ㎇⓻㦖 㑮䂮 㔲⸂⩞㧊㎮㠦 㦮䞮㡂 Ỗ㯳䞮㡖ἶ, ⳿䚲 㧛⩻

㠦 ╖䞮㡂 㟧䢎䞲 㩲㠊 ㎇⓻㧊 㠑㠊㰦㦚 䢫㧎䞮㡖

┺.

Speedy Positioning with Externally Pressurized Air Bearings,” Proceedings of the SICE Symposium on Fluid Control and Measurement, pp. 101ۙ106.

(3) Yang, Q. H., Kawakaki, Y. and Kawai, S., 1997,

“Position Control of a Pneumatic Cylinder with Friction Compensation,” Journal of The Japan Hydraulics & Pneumatics Society, Vol. 28, No. 2, pp.

115ۙ121.

(4) Maeda, S., Kawakami, Y. and Nakano, K., 1999,

“Position Control of Pneumatic Lifters,” Trans. of the Japan Hydraulics & Pneumatics Society, Vol. 30, No.

4, pp. 1ۙ7.

(5) Noritsugu, T. and Takaiwa, M., 1995, “Positioning Control of Pneumatic Servo System with Pressure Control Loop Using Disturbance Observer,” Trans. of the Society of Instrument and Control Engineers, Vol.

31, No. 12, pp. 1970~1977.