All Courses
Get the App Signup / Login
Sign in Open App
Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System

Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System

Download, print and study this document offline 
 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
Read More
About this Document

Document Description: Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System for 2023 is part of for preparation. The notes and questions for Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System have been prepared according to the exam syllabus. Information about Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System covers topics like and Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System Example, for 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System.

Introduction of Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System in English is available as part of our for & Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System in Hindi for course. Download more important topics related with , notes, lectures and mock test series for Exam by signing up for free. : Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System
Description
Full syllabus notes, lecture & questions for Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System | Plus excerises question with solution to help you revise complete syllabus | Best notes, free PDF download
Information about Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System
In this doc you can find the meaning of Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System defined & explained in the simplest way possible. Besides explaining types of Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System theory, EduRev gives you an ample number of questions to practice Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System tests, examples and also practice tests.
Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System is the part of for 2023 exam preparation. The content of Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System has been prepared for learning according to the exam syllabus. Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System covers topics like for 2023 Exam. Find important questions, notes, tests & features of Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System in this document.
How EduRev helps you in preparation?
EduRev provides you with complete coverage and for 2023 Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System as a part of our plan for syllabus to prepare for exam. Our subject experts have curated special courses, tests & mock test series. All previous year questions (PYQs) & topic wise tests like tests for Mechanical Engineering Modeling and Control of Dynamic electro Mechanical System are provided with detailed solutions. Download more important topics, notes, lectures and mock test series for Exam by signing up for free
Download as PDF

Download free EduRev App

Track your progress, build streaks, highlight & save important lessons and more!
(Scan QR code)
© EduRev
Education Revolution
Follow Us