Notes, Professor Anand Vaz-Lectures on Modeling of Physical System Dynamics
Transcript of Notes, Professor Anand Vaz-Lectures on Modeling of Physical System Dynamics
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Modeling of Physical System Dynamics
Anand Vaz
Professor
Department of Mechanical EngineeringDr. B. R. Ambedkar National Institute of Technology
Jalandhar
Punjab 144011, India
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Outline of the presentation
Introduction Design
CAD
Modeling of Physical System Dynamics Bond graphs
Simulation using Bond graphs
Examples An electromechanical system
Suspension system
Summary
Questions?
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Design- the essence of engineering
Concept of a product Idea
Design Functionality and features
Drawings and material specifications
Processes planning
Estimation
Manufacture Machinery and processes
Inventory
Costing
Marketing
Enterprise management
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Computer Aided Design
Capability of the Computer Programmable
Rapid execution of repetitive tasks Interfaced with peripherals and machines
Affordable
CAD Commercially available software: AutoDesk, I-DEAS, CATIA,
Drawings and material specifications
Processes planning
Estimation
Integrated with Manufacturing
Automated Inventory monitoring and control Costing
Marketing
Enterprise management
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Modeling of Physical System Dynamics
Analysis of Dynamics is more important than Statics which may be misleading
Physical systems are those in whichPoweris transacted between its components
System: entity separable from the rest of the universe by means of a physical or conceptual boundary
Composed of interacting parts
Powercan have diverse forms Mechanical, Electrical, Electronic, Thermal, Chemical, Fluid,
Causality is an important aspect of Physical systems It is the cause and effect relationship between components of the physical system
Controlof Physical systems is an important objective in Engineering
Modelingof Physical systems is therefore an essential prerequisite for studying
response Bond graphs is a unified approach to the modeling ofPhysical system dynamics
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State determined systems
State variables
System equations Ordinary differential equations
Algebraic equations output
Linear systems
Well developed theory Nonlinear systems
Resort to simulation
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Uses of dynamic models
Analysis
Given input future history and initial conditions, determining theoutputs
Identification
Given input history and output history, determining the system
Synthesis
Given input future history and some desired output history,
determining the system so that the input to it will produce the
desired output
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Software
CAMP-G
20-SIM SYMBOLS
AMESim
MATLAB based coding
Easy to program
All control with the modeler
Easy to modify, append, etc.
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Bond graphs: A brief introduction
Henry Paynter (MIT, 1959): The inventor of Bond
graphs. Powerflow as aproductofeffortandflow variables
Power bond Elements
Pictorial grammar for Physical System Dynamics
Junctions, elements and connections
Cause and effect
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Henry Paynter:
The inventor of Bond Graphs
1959At the birth of Bond Graphs 1997Upon his election to the NAE
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Multiport systems
Port
Channel flow or transaction of power betweensubsystems
Multiport Physical systems with one or moreports
1-port: system with a single port
2-port: system with two ports
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Examples of multiports
Electric motor
Hydraulic pump Drive shaft
Spring-shock absorber unit
Transistor
Speaker
Crank and slider mechanism Wheel
Separately excited DC motor
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Power transaction through a bond
Power = e(t) f(t)effort = e(t) V I
F v
P Q
T
flow = f(t)
s&
Variables of power: e(t), f(t)
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Bond graph modelling of physical system
dynamics Bond graph modeling Why?
Pictorial representation of the dynamics of the system
Offers insight into physics of the system Applied uniformly to Multi-energy domains
Interaction of power between the elements of the system
Representation of Cause-effect relationships
Algorithmic derivation of System equations in I-order state space form Suitable for numerical Integration. e.g. Runge-Kutta,
Modify the BG, append or delete part of it easily
Helps in developing control strategies, e.g.
the impedance control strategy (Neville Hogan) ghost control strategy (Mukherjee, )
Structural control properties (Genevieve Dauphin-Tanguy, ChristopheSueur, ...)
Fault identification and diagnosis (Samantaray, Mukherjee, )
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Elements
Source of efforte
S
Source of flowf
S
Inertia I
Stiffness C
Dissipation R
Sources
Elements
Junctions
Transformer
Gyrator
junction0
junction1
Transformer TF
Gyrator GY
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Example: A simple mechanical system
( )tF
m
K R
x&
1
3
4
mI:
RR :
KC:
( ) SEtF :2
1
x&
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Example: A simple electrical system
1
1
3
4
LI:
RR :( ) SEtV : 2
i
C
1:C
i
C
1
R
LI:
( )tV
It is the same Bond graph!!!
Bond graphs model multi-energy domains dont they???
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Transformer
1N
2N
11 , 22,
FT&&
1 21e
1f
2e
2f
12 ff =
Power conserving transformer1
2
12
N
N=
2211
fefe =
11 2
2
N
N =
21
2
12 ,1
eee
e
f
f ===
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Gyrator
YG &&1 21e
1f
2e
2f
Y
Z
X
2V
2F
1V
1F
12 fe =
2211 fefe =
2
1
1
2
f
e
f
e==
21 fe =
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Causality of Storage elements
K
Spring
qke=
qf&
=
KC:
q
( )effort flowi
t
t
k q k q dt f d = = =
&
pe &= mI:
m
p
mass
( )1flow efforti
t
t
p p dt f d
m m= = = &
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Output = effect
Causality of I element
Input = cause
( )e t p= &I :( )f p=
p
Mass M
v
1 1( ) ( ) ( )
i i
t t
t t
p f t p pd e d
M M M = = = = &
(effect)(cause)
dfunction
dt=effect ( cause )
i
t
t
function d = ;
Natural causality for I element
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I element in Derivative Causality
Input = cause
Output = effect
( )e t p= & I :( )f p=
p
( )1( ) ( ) ( )dp d d
e t p f M f dt dt dt
= = = = &
( )effect (cause)d
functiondt
=
Not natural causality for I element
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Input = cause
Output = effect
Causality of C element
( )e q= C :f q= &
q
( ) ( ) ( )
i i
t t
t t
e t q K q Kqd K f d = = = = &
(effect) (cause)d functiondt
=
effect (cause)
i
t
t
function d =
Spring KvA
A B
vB
A B
dqq v v
dt
= = &
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Input = cause
Output = effect
C element in Derivative Causality
( )e q= C :f q= &
q
1 1( ) ( ( )) ( )dq d d
f t q e K edt dt dt
= = = = &
Spring KvA
A B
vB
A B
dqq v v
dt
= = &
( )effect (cause)d
functiondt
=
Not natural causality for C element
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Causality ofR element
Resistance
effortR
flowRvi 1==
flowReffortRiv == ve=
if=
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Causality of Transformer & Gyrator
Transformer Gyrator
TF GY
GYTF
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Causality of Sources & Junctions
eS S
Source of effort Source of flow
01
Junctions
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What does causality tell us?
1x&
( )tF
1m 2m 2x&
2l1l
rigid, massless2m
1x&
2x&
1m
()tF
2l1l
Interpretation of the modified system
0
2: mI
1FT&&( ) SEtF :
1: mI
1x& 2x&
1
2
ll
1
stKC:
1
1: mI 2: mI
1FT&& ( ) SEtF :
1x& 2x&
1
2
ll
Differential
Causality
Salvaging causality by BG surgeryDerivative causality!
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Example of an electro-mechanical system
i11
bRR :
aRR : dJI:
aLI:
( ) SEtV : i
i=
YG &&()tVbR
aR i
dJ
Disk
aL
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Voice coil motor
( ) ( )tiktF ai=
( )tF
( ) ( )tvKte bb =
e f
f
ai
Differential
Causalitysi
1
0
YG
kb&&a
LI:T
BR :
YG
ki&&( ) SEtea :
aRR :
ILas :
1 1
TMI:
sLI:
sLI:
sRR :
( )tv
ebe
VOICE COIL MOTOR
Spindle motor
Disk
Magnet Primary turns
Magnetic fluxShorted turns
ae
be
+ -
-
+
aR sR aL
sLasL ai si
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Electromechanical Actuator
( )v t x= &K
R
Head mass = M
( ) ( )F t i t =
( )V t( )i t
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A simple Machine Tool
R
LS
TPm
x&
Gear
reduction
1FTN
&&( ) SEtV :
aLI:
i x&YG&&
1 1
RJI: LSLI:
FT
P
&&
2 1
TPmI:
slideRR :aRR :Differential
Causality
Rotor inertia Lead screw Tool post inertia
R&
LS&
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Example: Cam follower mechanism
A
( )
&&=
=
=
rx
dtdr
dtdx
rx
B
B
B
A Cam-Follower (Spring Loaded)
K
B
SRm
Jr &
mI:
Ax&1FS&&
0
THE BONDGRAPH
RRs :0 0
r
TF:
&1
KC:
JI:
Bx&1
( )FS
t&&
&
&1
Ax&1
0 1
KC:
sRR :
1
r
TF:
JI:( )FS
t&&
&
THE SIMPLIFIED BONDGRAPH
FS&&
0
mI:
Ax&1
0 1
Bx&1
sRR :
KC:
A Simplification
vB vA vE
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vB
KAB
RAB
B A EngineKAE
RAE
vA vE
MB MA ME
VB VA VA VE VE1
BV0
B
RB
C:KAB
FE
1I: MB B AV
R:RAB
1V 0AE
RA
C:KAE
I: MA 1A EV
R:RAE
1EV
I: ME
FREFRAFRB
RE
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Deriving System Equations
Q.1. What do the elements give to the system?
RK
( )tF
x&m m
pf 11 = 22 qke =
mpRe
fR
fRe
13
1
33
=
=
=
Q.2. What does the system give to elements with integral causality?
( )m
pRqktFeeepe 1232411 === &
m
pfqf 1122 === &
They can be arranged in a matrix form mI:
( ) SEtF : 1 KC:
RR :
1
24
3
( )
+
=
o
tF
q
p
m
km
R
q
p
2
1
2
1
01&
&
The I-order state-space form!
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Equivalence with the classical equation?
( )tF2q
t
2qk2qR&
m
Free body diagram
From Bond graphsApplying Newtons II law
m
pfqf 1122 === &( ) 222 qkqRtFqm = &
t
( ) 121 pmRqktFp =&
( ) ( )222 qm
m
RqktFqm &&& =
( )tFqkqRqm =++ 222 &&&
They are equivalent!!!
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Hydraulic and acoustic systems
Q1
2P
1P
3P
Q Q
Q
R
F(t) Q
V(t)
P
A
V(t)
A
PA PB
QQ
x
(t), (t)
QPA
QPB
Pump
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Hydraulic Cylinder
..
F(t) Q
V(t)
P
A
F(t)
V(t)
P
QTFA
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.. with friction and leakage
F(t) Q
V(t)
P
ARfriction
V(t)PTF
A..F(t)V(t) 1
V 0P PQ
Rfriction Rleakage
ddi i i i
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..adding piston inertia
F(t) Q
V(t)
P
ARfriction
F(t) Q
V(t)
P
ARfriction
V(t)
PTF
A..F(t)
V(t)
1V
Rfriction
0PP
Q
Rleakage
I: Mpistonpiston
( ) Me t p= &
Fl id i i
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Fluid inertiaV(t)
0lim
t
xV
t =
0limt
xQ A V At
= =
PA PB
AQQ
x
l
Applying Newtons II Law,
Q 1QPA PB
Q
lI:
Pp&( )0
limA Bt
d xl P P A
dt t
=
Q
[ ] P A Bd d l
p Q P P
dt dt A
= =
P
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Pump or motor
..PQ
TF
(t)
(t)1Q
PA
PB
(t), (t)
QPA
QPB
Pump
..PQ
TF(t)
(t)1Q
PA
PB1
BG for Pump BG for Motor
Fl id
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Fluid system
12
1F1x& 2x&
2F
Cross-sectional
area 1
Cross-sectional
area 2
Compressible fluid
B d G h f th Fl id t
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Bond Graph for the Fluid system
12
11x& 2x&
2
Cross-sectional
area 1
Cross-sectional
area 2
Compressible fluid
R1 R2C:?
V1(t)
PTF
A1..F1(t)
V1(t) 11V V2 (t)
0P
Q2
I: M1
TF
A2..
21V
I: M2
F2 (t)
Q1
H d li C li d d i T l t
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Hydraulic Cylinder driven Tool post
MT
Pc(t) Q
FRc
( )V t x= &
FRs
H d li C li d d i T l t
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Hydraulic Cylinder driven Tool post
PA(t)
MT( )V t x= &
FS
PRV
PB(t)
PD
C
E
A
(t)
(t)
QB(t)
QA(t)
Area =AA
Area =AB
QE(t)
BG f M h i l Fl id t
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BG for Mechanical-Fluid system
.
.Q
TF(t)(t)
1CQ
PD
DPC
, ,0
C A EP
0DP
1EQ
TF 1V
TF: ?
I: MT
PC
R:RPRV R:RS
?
Se:PD
String based actuation
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String based actuation
R 0
X
0Y
1RX
1RY
1LX
1A2A1P
2P
1R
1L
Active finger linkThumb link (passive)
1m (opening)
2m (closing)
String 1String 2
Bond graph for the system with
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g p y
differential causality
Effective during closing
1F0
1R&
1 AJ:I
1:C
1R:
eS
1L&
1P
J:I
1:C TFTF
TF TF
Ls1&1
Ls2&1
Rs1&1
Rs2&1
2F0
1Lr-
2Rr-
2Lr
1Rr
Effective during opening
12
3
8
9101213
14
15
1617192021
24 e25e
Differentialcausality
Bond graph for the string based prosthesis
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Bond graph for the string based prosthesis
1F0
1
:s
RR
RbrgR:R
1R&1 AJ:I
1:C
1R:
eS
1L&1 PJ:I
1:C
Lbrg
R:R
1
:s
KC
2
:s
KC2
:s
RR
TF TF
TF TF
Ls1&1
Ls2&1
Rs1&1
Rs2&1
2F0
1
1
1Lr-
2Rr-
2Lr
1Rr
Effective during opening
Effective during closing
12
3
4 5
6 7
8
910
11
1213
14
15
1617
18
192021
2223
24 e25e
Th k !
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Thank you!
Questions?
mailto:[email protected]:[email protected]:[email protected]:[email protected]