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Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System Notes | EduRev

: Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System Notes | EduRev

 Page 1


NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
State Space Approach in Modelling State Space Approach in Modelling
D Bi h kh Bh tt h Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur
Joint Initiative of IITs and IISc - Funded by MHRD
Page 2


NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
State Space Approach in Modelling State Space Approach in Modelling
D Bi h kh Bh tt h Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
Answer of the Last Assignment g
Following Mason’s law, there are two forward paths in the SFG:
T
1  
=  G
1 
G
2 
G
3 
and 
T
2 
=  G
4
There are four loops:
L
1
= -G
1 
H
1
L
2 
=  -G
3 
H
2 
L
3
= -G
1
G
2
G
3
H
3
L
3 
   G
1 
G
2 
G
3 
H
3 
L
4 
=  -G
4 
H
3 
?= 1 –(L
1  
+  L
2  
+ L
3 
+ L
4 
) + L
1 
L
2 
?
1  
= 1
?
2  
=  1
h ffi ldb d ( )/
2
Hence, the transfer function could be expressed as (T
1
+ T
2 
)/ ?
Joint Initiative of IITs and IISc -Funded by MHRD
Page 3


NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
State Space Approach in Modelling State Space Approach in Modelling
D Bi h kh Bh tt h Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
Answer of the Last Assignment g
Following Mason’s law, there are two forward paths in the SFG:
T
1  
=  G
1 
G
2 
G
3 
and 
T
2 
=  G
4
There are four loops:
L
1
= -G
1 
H
1
L
2 
=  -G
3 
H
2 
L
3
= -G
1
G
2
G
3
H
3
L
3 
   G
1 
G
2 
G
3 
H
3 
L
4 
=  -G
4 
H
3 
?= 1 –(L
1  
+  L
2  
+ L
3 
+ L
4 
) + L
1 
L
2 
?
1  
= 1
?
2  
=  1
h ffi ldb d ( )/
2
Hence, the transfer function could be expressed as (T
1
+ T
2 
)/ ?
Joint Initiative of IITs and IISc -Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
The Lecture Contains
? State Space Modeling
?EOM of a SDOF system in State Space Form
?Response of a State Space System
?Examples to Solve
Joint Initiative of IITs and IISc - Funded by MHRD
Page 4


NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
State Space Approach in Modelling State Space Approach in Modelling
D Bi h kh Bh tt h Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
Answer of the Last Assignment g
Following Mason’s law, there are two forward paths in the SFG:
T
1  
=  G
1 
G
2 
G
3 
and 
T
2 
=  G
4
There are four loops:
L
1
= -G
1 
H
1
L
2 
=  -G
3 
H
2 
L
3
= -G
1
G
2
G
3
H
3
L
3 
   G
1 
G
2 
G
3 
H
3 
L
4 
=  -G
4 
H
3 
?= 1 –(L
1  
+  L
2  
+ L
3 
+ L
4 
) + L
1 
L
2 
?
1  
= 1
?
2  
=  1
h ffi ldb d ( )/
2
Hence, the transfer function could be expressed as (T
1
+ T
2 
)/ ?
Joint Initiative of IITs and IISc -Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
The Lecture Contains
? State Space Modeling
?EOM of a SDOF system in State Space Form
?Response of a State Space System
?Examples to Solve
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
State-Space Modelling
The stateof a model of a dynamic system is a set of 
independent physical quantities, the specification of which (in 
the absence of excitation) completely determines the future 
positions of the system 
Dynamics describes how the state evolves. The dynamicsof a 
model is an update rule for the system state that describes 
howthestateevolves asafunctiononthecurrentstateand how the state evolves, as a function on the current state and 
any external inputs 
.
.
1
x
?
?
?
?
?
?
) ( ) (
.
.
2 .
t U B t X A
x
X ? ?
?
?
?
?
?
?
?
?
?
?
?
Joint Initiative of IITs and IISc -Funded by MHRD
.
x
n
?
?
?
?
?
?
Page 5


NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
State Space Approach in Modelling State Space Approach in Modelling
D Bi h kh Bh tt h Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
Answer of the Last Assignment g
Following Mason’s law, there are two forward paths in the SFG:
T
1  
=  G
1 
G
2 
G
3 
and 
T
2 
=  G
4
There are four loops:
L
1
= -G
1 
H
1
L
2 
=  -G
3 
H
2 
L
3
= -G
1
G
2
G
3
H
3
L
3 
   G
1 
G
2 
G
3 
H
3 
L
4 
=  -G
4 
H
3 
?= 1 –(L
1  
+  L
2  
+ L
3 
+ L
4 
) + L
1 
L
2 
?
1  
= 1
?
2  
=  1
h ffi ldb d ( )/
2
Hence, the transfer function could be expressed as (T
1
+ T
2 
)/ ?
Joint Initiative of IITs and IISc -Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
The Lecture Contains
? State Space Modeling
?EOM of a SDOF system in State Space Form
?Response of a State Space System
?Examples to Solve
Joint Initiative of IITs and IISc - Funded by MHRD
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
State-Space Modelling
The stateof a model of a dynamic system is a set of 
independent physical quantities, the specification of which (in 
the absence of excitation) completely determines the future 
positions of the system 
Dynamics describes how the state evolves. The dynamicsof a 
model is an update rule for the system state that describes 
howthestateevolves asafunctiononthecurrentstateand how the state evolves, as a function on the current state and 
any external inputs 
.
.
1
x
?
?
?
?
?
?
) ( ) (
.
.
2 .
t U B t X A
x
X ? ?
?
?
?
?
?
?
?
?
?
?
?
Joint Initiative of IITs and IISc -Funded by MHRD
.
x
n
?
?
?
?
?
?
NPTEL >> Mechanical Engineering >>  Modeling and Control of Dynamic electro-Mechanical System Module 1- Lecture 4
Wh tlkbt lt hi l t dldb diff ti l When we talk about electro-mechanical systems modeled by differential 
equations, such as masses and springs, electric circuits or satellites (rigid 
bodies) rotating in space, we can attach some additional intuition: the 
variables inthestate shouldbeadequate tospecifytheenergyofthe variables in the state should be adequate to specify the energyof the 
system. 
For example, take a ball free-falling to earth: we can specify the position 
of the ball by specifying the height (h) above the ground, but we also 
need to include the velocity of the ball (dh/dt) to specify the total energy 
(E = 1/2*m*(dh/dt)^2 + mgh). Therefore, the state of the ball is (h,dh/dt). 
Joint Initiative of IITs and IISc -Funded by MHRD
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