يﺎﻫ ﻢﺘﺴﯿﺳ ﯽﺣاﺮﻃ و ﻞﯿﻠﺤﺗ هﺮﯿﻐﺘﻣﺪﻨﭼ لﺮﺘﻨﮐ
ﻖﯾﺪﺻ ﯽﮐﺎﺧ ﯽﻠﻋ لﺮﺘﻨﮐ هوﺮﮔ -
ﺮﻬﻣ 1400
ﻢﯿﺣّﺮﻟا ﻦﻤﺣّﺮﻟا ﻪّﻠﻟا ﻢﺴﺑ
2
هﺮﯿﻐﺘﻣﺪﻨﭼ لﺮﺘﻨﮐ يﺎﻫ ﻢﺘﺴﯿﺳ • :
ﻪﻟﺎﺴﻣ حﺮﻃ
يﺎﻫ ﻢﺘﺴﯿﺳ ﯽﺣاﺮﻃ و ﻞﯿﻠﺤﺗ
ﮏﯿﺳﻼﮐ لﺮﺘﻨﮐ ﻞﯿﻠﺤﺗ :ﻢﺘﺴﯿﺳزا ﯽﻠﺧاد هﺎﮔﺪﯾد ﺖﻟﺎﺣ يﺎﻀﻓ ﯽﺣاﺮﻃ و
ﻢﺘﺴﯿﺳ رد ﯽﻄﺧﺮﯿﻏ ﺮﺻﺎﻨﻋ ﯽﻄﺧ ﺮﯿﻏ لﺮﺘﻨﮐ يﺎﻫ ﻢﺘﺴﯿﺳ : ﻢﺘﺴﯿﺳ رد ﯽﮕﻨﯿﻬﺑ
ﻪﻨﯿﻬﺑ لﺮﺘﻨﮐ يﺎﻫ ﻢﺘﺴﯿﺳ : ﺎﺑ ﺮﯿﻐﺘﻣ ،ﻦﯿﻌﻣﺎﻧ يﺎﻫﺮﺘﻣارﺎﭘ
مﻮﻠﻌﻣﺎﻧ يﺎﻫ ﻢﺘﺴﯿﺳ و نﺎﻣز : موﺎﻘﻣ لﺮﺘﻨﮐ
ﯽﻘﯿﺒﻄﺗ لﺮﺘﻨﮐ ﺪﻨﻤﺷﻮﻫ لﺮﺘﻨﮐ
يدورو ﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ -
ﯽﺟوﺮﺧ ﺪﻨﭼ
: هﺮﯿﻐﺘﻣﺪﻨﭼ لﺮﺘﻨﮐ يﺎﻫ ﻢﺘﺴﯿﺳ
ﯽﺟوﺮﺧ ﺪﻨﭼ و يدورو ﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ رد يﺪﯿﻠﮐ ﻪﻟﺎﺴﻣ ود • :
ﻢﺘﺴﯿﺳ رد ﯽﻟﺮﺘﻨﮐ ﻞﺧاﺪﺘﻣ يﺎﻫ ﻪﻘﻠﺣ
ﺗ ﻪﻟﺎﺴﻣ :
ﻞﺧاﺪ
ﯽﻟﺮﺘﻨﮐ يﺎﻫرﺎﮑﻫار
ﻞﺧاﺪﺗ ﻪﻟﺎﺴﻣ •
(The Interaction Problem) The SISO Plant:
c( )
g s g s( )
r + y
−
e u
4
• A General Multivariable Plant ( ) ( ) ( ) Y s = G s U s
1 2
( ) ( ) ( )
l ( ) y s Y s y s
y s
=
1 2
( ) ( ) ( )
m ( ) u s U s u s
u s
=
11 12 1
21 22 2
1 2
( ) ( ) ( )
( ) ( ) ( )
( )
( ) ( ) ( )
m m
l l lm
g s g s g s g s g s g s G s
g s g s g s
=
• Square and Nonsquare Multivariable Plants
11( )
g s y s1( )
1( ) u s
21( ) g s
12( ) g s
22( ) g s
2( )
2( ) y s u s
11 12
21 22
( ) ( )
( ) ( ) ( )
g s g s
G s g s g s
=
• Case Study: A Two-Input Two-Output Multivariable Plant
1 11 1 12 2
2 21 1 22 2
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) y s g s u s g s u s y s g s u s g s u s
= +
= +
Or in block diagram representation:
• INTERACTIONS
6
[ ]
[ ]
1 1 1 1
2 2 2 2
1 2
( ) ( ) ( )
( ) ( ) ( )
where ( ), ( ) are the reference inputs or the set points.
c c
u s g r s y s u s g r s y s
r s r s
= −
= −
• Interactions Analysis: Design two SISO dynamical controllers to control the outputs.
Consider the following two separate cases:
• One loop closed
• Both loops closed
• Only first loop closed: Second loop open and its input kept constant, i.e. zero
11 1
1 1
11 1
1
2 1
1 1
1 2
1
Then,
( ) ( )
( ) (
( )
1 ( ) ( ) )
( ) ( ) ( )
1 ( ) ( )
c c c
c
g s g s
y s r s
g s g s g
g s
y s r s
g s g s s
= +
= +
1( )
gc s y s1( )
1( ) r s
2( ) y s
1( ) u s
2( ) 0 u s =
Loop 1
PLANT
Any Change in the first set point will affect both the outputs under control (first output) and the output under no control (second output).
8
• Both loop closed:
Assume that the plant is under tight control. A change is made in the first set point. The following key observations are made:
1( )
gc s y s1( )
1( ) r s
2( ) y s
1( ) u s
2( ) u s
Loop 1
PLANT
2( ) gc s
2( ) r s
Loop 2
DIRECT EFFECT
INDIRECT EFFECT
• The Direct Effect: The first controller will get the first output to the desired set point.
• The Indirect Effect: The first controller will disturb the second output and the second controller attempts to reject its effects. But changes in the second controller effects the first loop performance.
INTERACTION BETWEEN TWO CONTROL LOOPS!
1 11 1 12 2
2 21 1 22 2
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) and, y s g s u s g s u s
y s g s u s g s u s
= +
= +
[ ]
[ ]
1 1 1 1
2 2 2 2
( ) ( ) ( )
( ) ( ) ( )
c
c
u s g r s y s u s g r s y s
= −
= −
And finally, the closed loop transfer function matrix is ( ) ( ) ( ), That is
Y s = T s R s
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
11 1 1 12 2 2 11 1 1 12 2 2
21 1 1 22 2 2 21 1 1 22 2 2
Gives,
1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
c c c c
c c c c
g s g s y s g s g s y s g s g s r s g s g s r s g s g s y s g s g s y s g s g s r s g s g s r s
+ + = +
+ + = +
10
( )
1 11 1 12 2
2 21 1 22 2
11 1 1 2 11 22
11
2 12
1 21
22 2 1 2
2
12 2
12
2
1
21
( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Where,
( ) ( ) ( ) ( ) ( ) ( )
( ) ( )
( ) ( )
( ) ( ) ( )
( )
( ) ( ) (
( ) ( )
( ) (
( )
)
)
c c c
c
c
c c c
y s t s r s t s r s y s t s r s t s r s
g s g s g s g s g s g s g s g s
t s
q s g s
t s
q s
g s t s
q s
g s g s g
g s g s
s
g s
t
= +
= +
+ −
=
=
=
= +
( )
( )( )
11 22
11 1 22 2 1
12 21
2
12 21
( ) ( ) ( ) ( )
( ) 1 ( ) ( ) 1 ( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
c c c c
s g s g s q s
q s g s g s
g s g s
g
g s g s s g s g s g s
−
= + + −
• Key observations:
12 21
11 1 22 2
1 1 2 2
11 1 22 2
No Interactions, i.e. g ( ) ( ) 0, implies
( ) ( ) ( ) ( )
( ) ( ), and ( ) ( )
1 ( ) ( ) 1 ( )
Closed Loop Stability Conditi
( ) on!
c c
c c
s g s
g s g s g s g s
y s r s y s r s
g s g s g s g s
= =
= =
+ +
of the Interacting Plant is D
Closed Loop Stability etermined by q s( ) = 0
Hence, separate loop tuning does not ensure the overall closed loop stability of the multivariable plant.
Tune the controllers to ensure the overall closed loop stability of the multivariable plant and the stability of the separate designs. Failure tolerant multivariable plants.
Interactions effect the closed loop stability and performance of the multivariable plant.
12
• Issues in the Analysis and Design of Multivariable Control Systems:
Multivariable system representation
Multivariable Poles and Zeros
Controllability and Observability
State space realizations
Multivariable system stability
Multivariable system robustness analysis
Control structure selection: Input-output selection and Input-output pairing
Control system design strategies:
Diagonal or Decentralized Block Diagonal
Fully Centralized
Control design methodology
• Multivariable Design Methodologies:
State space methods
Multivariable root loci approach
Rosenbrock frequency response approach
Pole placement methods
Eigenstructure assignment
Multivariable PI(D) controllers
Multivariable system robustness analysis
The classical robust control methods
QFT
Soft computing approaches
14
ﺪﻨﭼ • لﺎﺜﻣ
ﯽﻠﻤﻋ زا
ﻢﺘﺴﯿﺳ يﺎﻫ
هﺮﯿﻐﺘﻣﺪﻨﭼ
ﻪﻧﺎﮔرﺎﻬﭼ نﺰﺨﻣ ﺪﻨﯾآﺮﻓ •
ن ﺰ ﺨ ﭗ ﻣ 1
ﻤﭘ 1
ن ﺰ ﺨ
ﻣ 3 ﻣ 4ﺨﺰن
ن ﺰ ﺨ
ﻣ 2 ﻤﭘ 2 ﭗ
1 2
y y
v v
1 2
ﻞﯾﺪﺒﺗ ﻊﺑﺎﺗ ﺲﯾﺮﺗﺎﻣ ترﻮﺻ ﻪﺑ ﺎﯾ و :
16
• An Example: The Stirred Tank Heater
• The Control Objectives:
- Level Control (Loop 1)
- Temperature Control (Loop 2)
• Control actions: Effluent flow rate and Steam flow rate.
• Changes in liquid level: Loop 1 compensate for the regulation error, which disturbs the temperature. Loop 2 to compensate for disturbance.
• Changes in temperature: Loop 2 compensate for temperature tracking error.
Loop 1 not effected.
• One way or single direction interaction.
• Transfer function matrix:
11
21 22
( ) 0
( ) ( ) ( )
=
g s
G s g s g s
ﻪﺳ ترﺪﻗ ﻢﺘﺴﯿﺳ ﮏﯾ • -
ﻪﻨﯿﺷﺎﻣ
18
ﻞﯾﺪﺒﺗ ﻊﺑﺎﺗ ﺲﯾﺮﺗﺎﻣ لﺪﻣ و :
ﺪﻨﯾآﺮﻓ لﺮﺘﻨﮐ ﻢﺘﺴﯿﺳ • pH
pH ﺖﺳا ﯽﺑآ لﻮﻠﺤﻣ ندﻮﺑ يزﺎﺑ ﺎﯾ يﺪﯿﺳا ناﺰﯿﻣ ﺶﺠﻨﺳ ياﺮﺑ يرﺎﯿﻌﻣ
. :دراد دﺮﺑرﺎﮐ ﺖﻌﻨﺻ رد ﯽﻔﻠﺘﺨﻣ يﺎﻫ ﺶﺨﺑ رد pHﺪﻨﯾآﺮﻓ ﻗ زا ﯽﯾﺎﯿﻤﯿﺷ يﺎﻫﺪﻨﯾآﺮﻓ
ﻞﯿﺒ نﻮﯿﺳاﺪﯿﺴﮐا و بﺮﭼ يﺎﻫﺪﯿﺳا ﺎﯾ ﺎﻫ نﻮﺑﺎﺻ ﺪﯿﻟﻮﺗ ،ﺮﯿﻤﺨﺗ ،بﺂﺴﭘ يزﺎﺳ ﯽﺜﻨﺧ
ﺪﻨﯾآﺮﻓ ﯽﻠﮐ يﺎﻤﺷ : pH
20
ﯽﻄﺧ ﺎﺑ ﻪﮐ ﺖﺳا ﯽﻄﺧﺮﯿﻏ ﻢﺘﺴﯿﺳ ﯽﮑﯿﻣﺎﻨﯾد تﻻدﺎﻌﻣ رﺎﮐ ﻪﻄﻘﻧ لﻮﺣ يزﺎﺳ
8/7
=
،pH
) ﯽﺘﻧﺎﺳ ﺮﺘﻣ
( 16 = ار ﺮﯾز ﻞﯾﺪﺒﺗ ﻊﺑﺎﺗ ﺲﯾﺮﺗﺎﻣ ﺖﺑﺎﺛ ﯽﺑد ﺎﺑ ﺮﻓﺎﺑ شﺎﺸﺘﻏا رﻮﻀﺣ رد و عﺎﻔﺗرا
ﺪﻫد ﯽﻣ :
يﺎﻫ هﺪﻨﻨﮐ لﺮﺘﻨﮐ ﺎﺑ ﻪﺘﺴﺑ ﻪﻘﻠﺣ ﻢﺘﺴﯿﺳ يﺎﻫ ﺦﺳﺎﭘ • ﺮﯿﻏ ترﻮﺻ ﻪﺑ لﺮﺘﻨﮐ يﺎﻫ ﻪﻘﻠﺣ رداﺰﺠﻣ PI
ﺎﻫﺮﺘﻣارﺎﭘ ﺐﺳﺎﻨﻣ ﻢﯿﻈﻨﺗ ﺎﺑ ﺰﮐﺮﻤﺘﻣ :
0 0.5 1 1.5
y1
0 500 1000 1500
-0.5 0 0.5 1 1.5
y2
Time (sec)
22
ﻞﺼﻓ 1:
ﻪﻣﺪﻘﻣ
ﻪﻟﺎﺴﻣ • ﻞﺧاﺪﺗ
و تﻼﮑﺸﻣ
نآﻢﺘﺴﯿﺳ ﯽﺣاﺮﻃ و ﻞﯿﻠﺤﺗ • يﺎﻫ
لﺮﺘﻨﮐ هﺮﯿﻐﺘﻣﺪﻨﭼ
ﮏﯾ • ﻪﻌﻟﺎﻄﻣ يدرﻮﻣ
: يﺎﻫزﺎﯿﻧ ﺖﻌﻨﺻ
و ﺦﺳﺎﭘ يﺎﻫ
ﯽﺳﺪﻨﻬﻣ لﺮﺘﻨﮐ
لﺎﺜﻣ • يﺎﻫ
ﯽﻠﻤﻋ زا
ﻢﺘﺴﯿﺳ يﺎﻫ
هﺮﯿﻐﺘﻣﺪﻨﭼ
ﻊﺟاﺮﻣ • ﻞﺼﻓ 2
: ﻢﺘﺴﯿﺳ ﺶﯾﺎﻤﻧ هﺮﯿﻐﺘﻣﺪﻨﭼ ﯽﻄﺧ يﺎﻫ
ﻢﺘﺴﯿﺳ ﺲﯾﺮﺗﺎﻣ ﻒﯿﺻﻮﺗ • ﻢﺘﺴﯿﺳ ﻪﺒﺗﺮﻣ • كاﺮﺒﻧزر ﻢﺘﺴﯿﺳ ﺲﯾﺮﺗﺎﻣ • ﺮﺴﮐ ﻒﯿﺻﻮﺗ • -
ﺮﺴﮐ ﻒﯿﺻﻮﺗ و ﯽﺴﯾﺮﺗﺎﻣ -
ﺶﻫﺎﮐ ﯽﺴﯾﺮﺗﺎﻣ ﺮﯾﺬﭘﺎﻧ
ﺐﻟﺎﻄﻣ ﺖﺳﺮﻬﻓ
ﻞﺼﻓ 3
: ﺐﻄﻗ ﻢﺘﺴﯿﺳ رد ﺎﻫﺮﻔﺻ و ﺎﻫ
هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ
ﺐﻄﻗ • هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ يﺎﻫ
ﺐﻄﻗ • ﻢﺘﺴﯿﺳ ﺲﯾﺮﺗﺎﻣ و ﺖﻟﺎﺣ يﺎﻀﻓ رد هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ يﺎﻫ
ﺐﻄﻗ • ﻞﯾﺪﺒﺗ ﻊﺑﺎﺗ ﺲﯾﺮﺗﺎﻣ رد هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ يﺎﻫ
ﺚﯿﻤﺳا ترﻮﺻ • -
ﻞﯾﺪﺒﺗ ﻊﺑﺎﺗ ﺲﯾﺮﺗﺎﻣ ﮏﯾ نﻼﯿﻣ ﮏﻣ
ﯽﻄﺧ هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ ِعﻮﻧ • هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ يﺎﻫﺮﻔﺻ • -
لﺎﻘﺘﻧا يﺎﻫﺮﻔﺻ و ﺮﺼﻨﻋ يﺎﻫﺮﻔﺻ
ﺖﻬﺟ • هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ رد لﺎﻘﺘﻧا ﺮﻔﺻ يﺎﻫ
ﻢﻤﯿﻧ ﯽﻣ ﺮﯿﻏ يﺎﻫ ﻢﺘﺴﯿﺳ رد ﯽﺟوﺮﺧ ﺮﻔﺻ ﺖﻬﺟ دﺮﺑرﺎﮐ ﮏﯾ • زﺎﻓ
لﺎﻘﺘﻧا يﺎﻫﺮﻔﺻ داﺪﻌﺗ • لﺎﻘﺘﻧا يﺎﻫﺮﻔﺻ ﯽﺑﺎﯾﺎﺟ •
24
ﻞﺼﻓ 4
: ﻢﺘﺴﯿﺳ ﯽﺣاﺮﻃ و ﻞﯿﻠﺤﺗ ﺖﻟﺎﺣ يﺎﻀﻓ هزﻮﺣ رد هﺮﯿﻐﺘﻣﺪﻨﭼ لﺮﺘﻨﮐ يﺎﻫ
لﺮﺘﻨﮐ • ﺖﯾؤر و يﺮﯾﺬﭘ
ﯽﻄﺧ يﺎﻫ ﻢﺘﺴﯿﺳ يﺮﯾﺬﭘ
لﺮﺘﻨﮐ • ﺖﯾؤر ،يﺮﯾﺬﭘ
ﻢﺘﺴﯿﺳ ﺲﯾﺮﺗﺎﻣ ﻒﯿﺻﻮﺗ رد يﺮﯾﺬﭘ
لﺮﺘﻨﮐ • لﺮﺘﻨﮐ و ﯽﺟوﺮﺧ يﺮﯾﺬﭘ
ﯽﻌﺑﺎﺗ يﺮﯾﺬﭘ
هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ رد ﻖﻘﺤﺗ ﻪﯾﺮﻈﻧ • :
و لﺎﻤﯿﻧ ﯽﻣ ﺮﯿﻏ يﺎﻫ ﻖﻘﺤﺗ ﯿﮔ ﻖﻘﺤﺗ
تﺮﺒﻠ
ﺖﻟﺎﺣ يﺎﻀﻓ تﻻدﺎﻌﻣ ﻪﺒﺗﺮﻣ ﺶﻫﺎﮐ • لﺎﻤﯿﻧ ﯽﻣ ﺮﯿﻏ ﺖﻟﺎﺣ يﺎﻀﻓ تﻻدﺎﻌﻣ ﻪﺒﺗﺮﻣ ﺶﻫﺎﮐ • ﯽﻣ ﺖﻟﺎﺣ يﺎﻀﻓ تﻻدﺎﻌﻣ ﻪﺒﺗﺮﻣ ﺶﻫﺎﮐ • لﺎﻤﯿﻧ
: هﺪﻧﺎﻣ شور و شِﺮُﺑ شور يراﺬﮔ
ﻪﺘﻓﺎﯾ ﺶﻫﺎﮐ ﯽﮑﯿﻣﺎﻨﯾد لﺪﻣ ﻪﺒﺗﺮﻣ بﺎﺨﺘﻧا • ﻪﻠﭘﻮﮐد • ﻢﺘﺴﯿﺳ يزﺎﺳ
ﺖﻟﺎﺣ ﮏﺑﺪﯿﻓ ﺎﺑ هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ
ﻞﺼﻓ 5
: ﺖﯾدوﺪﺤﻣ و يراﺪﯾﺎﭘ ﻢﺘﺴﯿﺳ رد يدﺮﮑﻠﻤﻋ يﺎﻫ
هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ
هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ ﯽﻣﺎﻧ يراﺪﯾﺎﭘ ﻞﯿﻠﺤﺗ • ﻪﺘﻓﺎﯾ ﻢﯿﻤﻌﺗ ﺖﺴﯿﺋﻮﮑﯾﺎﻧ يراﺪﯾﺎﭘ رﺎﯿﻌﻣ • ﺖﯾدوﺪﺤﻣ • ﺲﻧﺎﮐﺮﻓ هزﻮﺣ رد و نﺎﻣز هزﻮﺣ رد يدﺮﮑﻠﻤﻋ يﺎﻫ
ﻞﺼﻓ 6
: ﻢﺘﺴﯿﺳ دﺮﮑﻠﻤﻋ و يراﺪﯾﺎﭘ ﻞﯿﻠﺤﺗ ﻦﯿﻌﻣﺎﻧ هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ
لﺎﺜﻣ • ﯽﻔﯿﺻﻮﺗ يﺎﻫ
لﺪﻣ • هﺮﯿﻐﺘﻣﺪﻨﭼ ﻦﯿﻌﻣﺎﻧ يﺎﻫ ﻢﺘﺴﯿﺳ يزﺎﺳ :
ﯽﻨﯿﻌﻣﺎﻧ ﯽﺑ يﺎﻫ
يﺮﺘﻣارﺎﭘ و رﺎﺘﺧﺎﺳ
ﺑ ﯽﻨﯿﻌﻣﺎﻧ ياﺮﺑ موﺎﻘﻣ يراﺪﯾﺎﭘ و ﻦﯿﻌﻣﺎﻧ هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ موﺎﻘﻣ يراﺪﯾﺎﭘ ﻞﯿﻠﺤﺗ • ﯽ
رﺎﺘﺧﺎﺳ
ﺖﺴﯿﺋﻮﮑﯾﺎﻧ ﻪﯾﺮﻈﻧ سﺎﺳا ﺮﺑ موﺎﻘﻣ يراﺪﯾﺎﭘ ﻪﯿﺷﺎﺣ • هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ دﺮﮑﻠﻤﻋ ﻞﯿﻠﺤﺗ • :
ﺛا ﻒﯿﻌﻀﺗ و ﯽﺑﺎﯾدر ،شﺎﺸﺘﻏا ﺮﺛا ﻒﯿﻌﻀﺗ يﺎﻫﺎﻄﺧ ﺮ
هزاﺪﻧا ﻪﺘﺴﺑ ﻪﻘﻠﺣ ﺦﺳﺎﭘ ﺮﺑ يﺮﯿﮔ
موﺎﻘﻣ دﺮﮑﻠﻤﻋ •
26
ﻞﺼﻓ 7
: ﻢﺘﺴﯿﺳ ﯽﺣاﺮﻃ رد ﮏﯿﺳﻼﮐ ﺚﺣﺎﺒﻣ ﯿﻐﺘﻣﺪﻨﭼ لﺮﺘﻨﮐ يﺎﻫ
هﺮ
ﯽﺣاﺮﻃ ﺮﺑ يا ﻪﻣﺪﻘﻣ • ﯽﺟوﺮﺧ و يدورو بﺎﺨﺘﻧا • ﯽﺟوﺮﺧ و يدورو بﺎﺨﺘﻧا ﯽﺑﺎﯾزرا يﺎﻫرﺎﯿﻌﻣ • ﯽﻠﻤﻋ لﺎﺜﻣ ﮏﯾ • :
يزﺎﮔ ﻦﯿﺑرﻮﺗ
لﺮﺘﻨﮐ يﺪﻨﺑﺮﮑﯿﭘ بﺎﺨﺘﻧا • :
لﻮﺻا
RGA •
ﺘﻣﺮﯿﻏ لﺮﺘﻨﮐ يﺎﻫ ﻢﺘﺴﯿﺳ ﯽﺣاﺮﻃ رد لﺮﺘﻨﮐ يﺪﻨﺑﺮﮑﯿﭘ تﺎﻈﺣﻼﻣ ﺰﮐﺮﻤﯽﺒﯿﺗﺮﺗ ﻦﺘﺴﺑ ﻪﻘﻠﺣ شور ﻪﺑ هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ هﺪﻨﻨﮐ لﺮﺘﻨﮐ ﯽﺣاﺮﻃ •
ﺲﯾﺮﺗﺎﻣ ﯽﺣاﺮﻃ • ناﺮﺒﺟ ﺶﯿﭘ يﺎﻫ
لﺮﺘﻨﮐ يراﻮﺷد ﻞﺣ ياﺮﺑ زﺎﺳ
ﻞﺼﻓ 8
: لﺮﺘﻨﮐ ﻢﺘﺴﯿﺳ PI
هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ
ﻪﻣﺪﻘﻣ • ﻪﻠﭘ ﺦﺳﺎﭘ ﺲﯾﺮﺗﺎﻣ ﺮﺑ ﯽﻨﺘﺒﻣ يﺎﻫ ﯽﺣاﺮﻃ • ﻢﺘﺴﯿﺳ ي
ﻪﻟﺎﺴﻣ تﺎﯿﺿﺮﻓ و ﯽﺗﺎﻣﺪﻘﻣ ﺐﻟﺎﻄﻣ • ﯽﺣاﺮﻃ لوا رﺎﮑﻫار • ﯽﺣاﺮﻃ مود رﺎﮑﻫار • يﺎﻫ هﺪﻨﻨﮐ لﺮﺘﻨﮐ • ﻻﺎﺑ هﺮﻬﺑ هﺮﯿﻐﺘﻣﺪﻨﭼPI
ﻢﻈﻨﻣ هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ ياﺮﺑ ﯽﺣاﺮﻃ • ﻢﺘﺴﯿﺳ ياﺮﺑ ﯽﺣاﺮﻃ • ﻢﻈﻨﻣﺎﻧ هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ
28
ﻞﺼﻓ 9
: ﯽﻌﺑﺮﻣﺎﻧ هﺮﯿﻐﺘﻣﺪﻨﭼ يﺎﻫ ﻢﺘﺴﯿﺳ :
ﻢﺘﺴﯿﺳ ﻓا ﺎﺑ لﺮﺘﻨﮐ يﺎﻫ
ﯽﮕﻧوﺰ
ﺎﻫ كﺮﺤﻣ رد نآ يﺎﻫدﺮﺑرﺎﮐ و ﺎﻫ كﺮﺤﻣ رد ﯽﮕﻧوﺰﻓا • نآ ﻞﺣ يﺎﻫ شور و لﺮﺘﻨﮐ ﺺﯿﺼﺨﺗ ﻪﻟﺎﺴﻣ • لﺮﺘﻨﮐ ﺺﯿﺼﺨﺗ رد يزﺎﺠﻣ سﻮﮑﻌﻣ دﺮﮑﯾور دﺮﺑرﺎﮐ • يدﺮﺑرﺎﮐ يﺎﻫ لﺎﺜﻣ •
ﯽﺑﺎﯾزرا - هرود
،تﺎﻨﯾﺮﻤﺗ و
ﻪﯿﺒﺷ يزﺎﺳ
: 10
هﺮﻤﻧ 5 : مﺮﺗ رد يﺎﻫﺰﯿﯾﻮﮐ و ﺎﻫ ﺖﯿﻟﺎﻌﻓ -
هﺮﻤﻧ هﺮﻤﻧ 5 : مﺮﺗ نﺎﯾﺎﭘ نﺎﺤﺘﻣا -
30
ﻊﺟاﺮﻣ
1.
ﻞﯿﻠﺤﺗ و
ﯽﺣاﺮﻃ ﻢﺘﺴﯿﺳ
يﺎﻫ لﺮﺘﻨﮐ
ﺪﻨﭼ
،هﺮﯿﻐﺘﻣ ﯽﻠﻋ
ﯽﮐﺎﺧ
،ﻖﯾﺪﺻ ﺘﻧا
تارﺎﺸ
هﺎﮕﺸﻧاد ﯽﺘﻌﻨﺻ
ﻪﺟاﻮﺧ ﻦﯾﺪﻟاﺮﯿﺼﻧ
،ﯽﺳﻮﻃ پﺎﭼ
مرﺎﻬﭼ 1393
.
1. Multivariable Feedback Control, S. Skogestad, I. Postlethwaite, Wiley, 2005.
2. Linear Robust Control, M. Green, D J N Limebeer, Prentice-Hall, 1995.
3. Multivariable Control System Design Techniques, G. F. Bryant, L.
F. Yeung, Wiley 1996.
4. Linear Control System Analysis and Design, J J Dazzo, C H Houpis, McGraw-Hill, 1988.
5. Multivariable System Theory and Design, R V Patel, N Munro, Pergammon Press, 1982.
6. Multivariable Feedback Design, J M Maciejowski, Wesley,1989.
7. Control Configuration Selection in Multivariable Plants, A. Khaki- Sedigh, B. Moaveni, Springer Verlag, 2009.
سرد ﺖﯾﺎﺳ بو • :
http://saba.kntu.ac.ir/eecd/khakisedigh/Courses/mv/
ﺖﯿﻘﻓﻮﻣ يوزرآ ﺪﯿﻣا ﺎﺑ
