More Related Content Similar to A bond graph approach , simulation and modelling ( Mechatronics ), INDIA (20) A bond graph approach , simulation and modelling ( Mechatronics ), INDIA1. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
1
Introduction to physical systems, their
modeling and simulation: A Bond
Graph Approach
Anand Vaz
Professor
Department of Mechanical Engineering
Dr. B. R. Ambedkar National Institute of Technology
Jalandhar
Punjab 144011, India
2. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
2
Physical Systems
• What do we understand by physical systems?
• What is a system?
• entity separable from the rest of the universe by means of a
physical or conceptual boundary
• Composed of interacting parts
• Physical systems are those in which Energy or Power is transacted
between their components
• Power can have diverse forms
– Mechanical, Electrical, Electronic, Thermal, Chemical, Fluid,…
• What about cause and effect? Input and output?
• Causality is an important aspect of Physical systems
– It is the cause and effect relationship between components of the
physical system
3. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
3
Physical Systems
• Why are models needed?
– To study and understand the behaviour or response of a system
when it is subject to various conditions.
– To perform experiments or simulations and make measurements.
– For design and testing
– Control of physical systems is an important objective in
Engineering
– Systematic derivation of system equations and Computer coding
for simulation
• Modeling of Physical systems is an essential prerequisite for
studying response
4. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
4
Computer Aided Design
• Digital Computer: What are its major capabilities and features?
– Programmable
– Rapid execution of repetitive tasks
– Interface with peripherals and machines
– Affordable
• CAD
– Commercially available software: AutoDesk, I-DEAS, CATIA,…
• Drawings and material specifications
• Planning of processes
• Estimation
– Integration with Manufacturing
– Automated Inventory monitoring and control
– Costing
– Marketing
– Enterprise management
5. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
5
State determined systems
• State variables
– Minimum number of variables required to describe the behaviour
of a system completely
• System equations
– Ordinary differential equations – rates of change of states
– Algebraic equations – constraints
– outputs
• Linear systems
– Well developed theory
• Nonlinear systems
– Resort to simulation
6. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
6
Uses of dynamic models
• Analysis
– Given input future history and initial conditions, determining the
outputs
• 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
• Control
– Given the system, determining the inputs to it that will produce
desired output
7. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
7
Dynamics and CAD
• Analysis of Dynamics is more important than Statics which may be
misleading
• Pictures and graphs are easier to understand than equations
• Can mathematical features of dynamics be represented pictorially?
• Can this modeling methodology be applied to any energy domain?
• Can system equations be derived easily from this pictorial model?
• How to simulate this model of a dynamic system in an easy
manner?
• Can simulation code be derived automatically?
• Can a pictorial model offer insight into analysis for design and
control?
• Bond Graph is a unified approach to the modeling of Physical
system dynamics
8. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
8
Example of an electro-mechanical system
..Eb(t)
GY
m
V(t) 1ai
R: Ra
pw
R: Rb
I: La
( ) ( )at i tτ µ=
1ωSe:V(t)
ia
( )tτ
ia ( )tω
I: Jd
( ) ( )bE t tµ ω=
( )tω
V(t)
Ra
La
Jd
Rb
ia
9. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
9
Bond graphs: A brief introduction
• Henry Paynter (MIT, 1959): The inventor of
Bond graphs.
– Pictorial grammar for Physical System Dynamics
• Power bond
– Power transaction as a product of effort and flow variables
• Elements
– Junctions, elements and connections
• Cause and effect
10. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
10
Bond graph modelling of physical system
dynamics
• Bond graph modeling – Why?
• Graphical 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,…
– Basis for modern control theory
– Coding for simulation
• Modify the BG, append or delete part of it easily
• Helps in developing strategies for control and diagnosis, e.g.
– the impedance control strategy (Neville Hogan)
– Overwhelming or ghost control strategy (Mukherjee, …)
– Structural control properties (Genevieve Dauphin-Tanguy, Christophe Sueur, ...)
– Fault identification and diagnosis (Genevieve Dauphin-Tanguy, Bouamama,
Samantaray, Mukherjee, …)
11. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
11
Software
• CAMP-G
• 20-SIM
• SYMBOLS Shakti/Vista
• AMESim
• MATLAB/SCILAB based coding
– Easy to program
– All control with the modeler
– Easy to modify, append, etc.
12. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
12
Power transaction through a bond
effort = e(t)
flow = f(t)
Power = e(t) · f(t)
V I
F v
P Q
T
τ ω
… …
s
Variables of power: e(t), f(t)
13. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
13
• Sources
• Elements
• Junctions
• Transformer
• Gyrator
Elements
junction0
junction1
Source of effort e
S
Source of flow f
S
Inertia I
Stiffness C
Dissipation R
Transformer TF
Gyrator GY
14. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
14
Causality
effort = e(t)
flow = f(t)
cause – effect relationship
between elements/subsystems
A B
Input - Output relationship
e
f
15. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
15
Causal stroke
Effort receiving end
A B
e
f
Flow receiving end
Effort receiving end
A B
e
f
Flow receiving end
16. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
16
K·q2
Example: A simple mechanical system
K R
m
F(t)
v = x
C: K-1
R: R
( )1v t
I: m
Se: F(t)
p1
q2
1
24
3
1p v 1p
m
=
v
v
v
R·v
F
17. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
17
Example: A simple electrical system
It is the same Bond graph!!!
Bond graph can model in multi-energy domains – can’t it???
R: R
( )1i t
I: L
Se: V(t)
p1
q2
1
24
3
1p i 1p
L
=
i
i
i
R·i
V
RV(t)
L
C
i
i
2
1
q
C
C: C
18. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
18
Example: A simple mechanical system
K R
M
F(t)
v1 =x
v0 v1
F(t)
0 ( )1v t 0F
C: K-1
0 1
1 v
R: R
1 ( )1v t
I: M
Sf : v0(t) Se: F(t)
v1
p1
q2
1
2
3
4
5
8 6
7
v0 = 0x
19. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
19
Causality of Sources & Junctions
Output = effect
Se
Input = cause
Input = cause
Output = effect
Sf
Source of effort Source of flow
Junctions
1f 0e
e1
e2
e3
e4
f
f
f
f
e
e
e
e
f1
f4
f2
f3
e
f
e
f
e1 = e2 + e3 + e4 f1 = f2 + f3 + f4
20. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
20
Output = effect
Input = cause
Causality of I element
( )e t p=
I : M
( )f p= Ψ
p
Mass M
v
1 1
( ) ( ) ( )
i i
t t
t t
p
f t p pd e d
M M M
τ τ τ=Ψ = = =∫ ∫
(effect)
(cause)
d
function
dt
=( )effect cause
i
t
t
function dτ= ∫
Natural or Integral causality for I element
;
21. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
21
Input = cause
Output = effect
I element in Derivative Causality
( )e t p=
I : M
( )f p= Ψ
p
( )1
( ) ( ) ( )
dp d d
e t p f M f
dt dt dt
−
===Ψ = ⋅
( )effect (cause)
d
function
dt
=
Not natural causality for I element
Effect does not depend on past cause?
22. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
22
Input = cause
Output = effect
Causality of C element
( )e q= Φ 1
C: K−
f q=
q
( ) ( ) ( )
i i
t t
t t
e t q K q K qd K f dτ τ τ=Φ = ⋅ = =∫ ∫
(effect)
(cause)
d
function
dt
=
( )effect cause
i
t
t
function dτ
=
∫
Spring K
vA
A B
vB
A B
dq
q v v
dt
= = −
Natural or Integral causality for C element
23. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
23
Input = cause
Output = effect
C element in Derivative Causality
( )e q= Φ 1
C : K−
f q=
q
1 1
( ) ( ( )) ( )
dq d d
f t q e K e
dt dt dt
− −
== = Φ = ⋅
Spring K
vA
A B
vB
A B
dq
q v v
dt
= = −
( )effect (cause)
d
function
dt
=
Not natural causality for C element
Effect does not depend on past cause?
24. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
24
Input = cause
Output = effect
Causality of R element
e
R
( )f e= Φ
Resistance R
VA
A B
VB
( ) ( )A BV V e
f i e
R R
−
= = = = Φ
Input = cause
Output = effect
( )e f= Φ
R
f ( ) ( )A Be V V R i R f f= − = ⋅ = ⋅ = Φ
25. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
25
Transformer
Power conserving transformer
1e1 2 2e
1f 2f
2 1f fµ= ⋅
1 2e eµ⇒ = ⋅
TF
1 1 2 2e f e f⋅ = ⋅
( )2 1e fµ= ⋅ ⋅
( )2 1e fµ= ⋅ ⋅
1 2e eµ= ⋅
µ
1 1,ω τ
2 2,ω τ
1
2 1
2
N
N
ω ω= −
1
1 2
2
N
N
τ τ= −
1N
2N
Ex. Gears in mesh
26. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
26
..
Hydraulic Cylinder
F(t) Q
V(t)
P
A
F(t)
V(t)
P
Q
TF
A
27. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
27
Causality for the Transformer
1e1 2 2e
1f 2f
2 1f fµ= ⋅
TF
1 2e eµ= ⋅
µ
1e1 2 2e
1f 2f
1 2
1
f f
µ
= ⋅
TF
2 1
1
e e
µ
= ⋅
µ
28. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
28
Gyrator
Power conserving gyrator
1e1 2 2e
1f 2f
2 1e fµ= ⋅
1 2e fµ⇒ = ⋅
GY
1 1 2 2e f e f⋅ = ⋅
( )1 2f fµ= ⋅ ⋅
( )2 1f fµ= ⋅ ⋅
1 2e fµ= ⋅
µ
2 1F Vµ= ⋅
Ex. Mechanical gyrator
1 2F Vµ= ⋅
Y
Z
X
V2
F2
V1
F1
29. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
29
Causality for the Gyrator
1e1 2 2e
1f 2f
2 1e fµ= ⋅
GY
1 2e fµ= ⋅
µ
1e1 2 2e
1f 2f
1 2
1
f e
µ
= ⋅
GY
µ
2 1
1
f e
µ
= ⋅
30. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
30
What does causality tell us?
1
1: mI 2: mI
1FT ( ) SEtF :
1x 2x
1
2
l
l Differential
Causality
1x
()tF
1m 2m 2x
2l1l
rigid, massless
0
2: mI
1FT ( ) SEtF :
1: mI
1x 2x
1
2
l
l
1
stKC :
2m
1x
2x
1m
()tF
2l1l
Derivative causality! Salvaging causality by BG surgery
Interpretation of the modified system
31. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
31
Example of an electro-mechanical system
..Eb(t)
GY
m
V(t)
1ai
R: Ra
pw
R: Rb
I: La
( ) ( )at i tτ µ=
1ωSe:V(t) ia
( )tτ
ia ( )tω
I: Jd
( ) ( )bE t tµ ω=
( )tω
5
3
1
2
4
6 7
C: 1
8
p1
p2
q8
V(t)
Ra
La
Jd
Rb
ia
32. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
32
Electromechanical Actuator
( )v t x=
K
R
Head mass = M
( ) ( )F t i tµ= ⋅
( )V t
( )i t
33. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
33
Voice coil motor
VOICE COIL MOTOR
Spindle motor
Disk
Magnet Primary turns
Magnetic flux
Shorted turns
ae
be
+-
-
+
aR sRaL
sLasL
ai si
( ) ( )tiktF ai=
( )tF
( ) ( )tvKte bb =
e f
f
ai
Differential
Causalitysi
1
0
YG
kb
aLI :
TBR :
YG
ki
( ) SEtea :
aRR :
ILas :
1 1
TMI :
sLI :
sRR :
( )tv
ebe
34. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
34
A simple Machine Tool
Rθ
LSθ
TPm
x
Gear
reduction
1FT
N
( ) SEtV :
aLI :
i x
YG
µ
1 1
RJI : LSLI :
FT
P
π2
1
TPmI :
slideRR :aRR :
Differential
Causality
Rotor inertia Lead screw Tool post inertia
R
θ
LS
θ
35. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
35
Example: Cam follower mechanism
A
( )
θ
θ
θ
θ
θ
∂
∂=
⋅
∂
∂=
=
rx
dt
dr
dt
dx
rx
B
B
B
A Cam-Follower (Spring Loaded)
K
B
SR
m
J
r θ
θ
Ax1
0 1
Bx1
sRR :
KC :
A Simplification
mI :
Ax1FS
0
THE BONDGRAPH
RRs : 0 0
θ∂
∂r
TF :
θ
1
KC :
JI :
Bx1
( )
FS
t
θ
θ
1
Ax1
0 1
KC :
sRR :
1
ϑ∂
∂r
TF :
JI :
( )
FS
t
θ
THE SIMPLIFIED BONDGRAPH
FS
0
mI :
36. 36
VB VA
VA VE
KAB
RAB
MB MA ME
B A Engine
KAE
RAE
vB vA vE
VE
1 BV 0 ABF
RB
C: KAB
-1
FE
I: MB
1B AV
R: RAB
1 AV 0 AEF
RA
C: KAE
-1
I: MA
1A EV
R: RAE
1 EV
I: ME
RE
FRE
FRA
FRB
37. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
37
Deriving System Equations
Q.1. What do the elements give to the system? (Outputs of elements.)
2 2;e k q=
Q.2. What does the system give to elements with integral causality?
(Inputs to elements with integral causality.)
1 1e p=
2 2f q=
( )1 1
2 2
1 00
R
k
F tmp p
q q
m
− −
= +
They can be arranged in a matrix form
The I-order state-space form!
K R
m
F(t)
v = x
K·q2
C: K-1
R: R
( )1v t
I: m
Se: F(t)
p1
q2
1
24
3
1p v 1p
m
=
v
v
v
R·v
F
1
1 ;
p
f
m
= 3 3,e R f=
1,R f=
1
;
p
R
m
=
4 2 3e e e= − − ( ) 1
2 ;
p
F t k q R
m
= − −
1f= 1
;
p
m
=
4 ( );e F t=
38. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
38
Equivalence with the classical equation?
( )1 1 2
R
p F t p k q
m
= − −
( ) ( )2 2 2
R
m q F t m q k q
m
= − −
( )tFqkqRqm =++ 222
( )2 2 2,mq F t R q k q= − −
Free body diagram
Applying Newton’s II law From Bond graphs
They are equivalent!!!
1
2 2 1 ,
p
f q f
m
= = =
m
F(t)
v = 2q
2R q 2k q
39. 39
v0 v1
F(t)
0 ( )1v t 0 KRF
C: K-1
0 1
1 v
R: R
1 ( )1v t
I: M1
Sf : v0(t) Se: F(t)
v1
p1
q2
1
2
3
4
5
8 6
7
K R
F(t)
v1 =x
v0 = 0x
M1
Skate board system
40. 40
I. What do the elements give to the system?
v0 v1
F(t)
0 ( )1v t 0F
C: K-1
0 1
1 v
R: R
1 ( )1v t
I: M1
Sf : v0(t) Se: F(t)
v1
p1
q2
1
2
3
4
5
8 6
7
3 ( )e F t=
1
1
1
p
f
M
=
4 0 ( )f v t=
2 2e K q=
5 5e R f=
5 7f f=
7 6 8f f f= −
6 1f f=
1
0
1
( )
p
R v t
M
= −
1 1e p=
1 3 6e e e= −
6 7e e=
7 2 5e e e= +
( )F t= 2K q− 1
0
1
( )
p
R v t
M
− −
2 2f q=
2 7f f=
8 4f f=
1
0
1
( )
p
v t
M
= −
K R
F(t)
v1 =x
v0 = 0x
M1
II. What does the system give to elements
with integral causality?
Procedure for deriving System Equations
41. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
41
Simulation from Bond graphs
Using separation of variables,
f1
( )
( ) ( , , )
dx t
x t f x u t
dt
= =
1
1( , , )
dx
f x u t
dt
=
0; ( )ix t x=
1 1( , , )dx f x u dτ τ=
1
1
( )
1
( )
( , , )
i i
x t t
x t t
dx f x u dτ τ=∫ ∫
1 1 1( ) ( ) ( , , )
i
t
i
t
x t x t f x u dτ τ− =∫
1 1 1( ) ( ) ( , , )
i
t
i
t
x t x t f x u dτ τ= + ∫
x1(ti)
x1(t)
ti tft
1( )x t
42. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
42
Simulating Bond Graph models
&
More examples
Anand Vaz
Professor
Department of Mechanical Engineering
Dr. B. R. Ambedkar National Institute of Technology
Jalandhar
Punjab 144011, India
43. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
43
K·q2
Example: A simple mechanical system
K R
m
F(t)
v = x
C: K-1
R: R
( )1v t
I: m
Se: F(t)
p1
q2
1
24
3
1p v 1p
m
=
v
v
v
R·v
F
44. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
44
K·q2
Example: The Van der Pol Oscillator
system
K R
m
F(t)
v = x
C: K-1
R: R
( )1v t
I: m
Se: F(t)
p1
q2
1
24
3
1p v 1p
m
=
v
v
v
F
2
2( 1)R q v⋅ − ⋅
45. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
45
..
Example of an electro-mechanical system
Eb(t)
GY
m
V(t)
1ai
R: Ra R: Rb
I: La
( ) ( )at i tτ µ=
1ωSe:V(t) ia
( )tτ
ia ( )tω
I: Jd
( ) ( )bE t tµ ω=
( )tω
5
3
1
2
4
6 7
C: 1
8
p1
p2
q8
This image cannot currently be displayed.
V(t)
Ra
La
Jd
Rb
ia
46. 46
VB VA
VA VE
KAB
RAB
MB MA ME
B A Engine
KAE
RAE
vB vA vE
VE
1 BV 0 ABF
RB
C: KAB
-1
FE
I: MB
1B AV
R: RAB
1 AV 0 AEF
RA
C: KAE
-1
I: MA
1A EV
R: RAE
1 EV
I: ME
RE
FRE
FRA
FRB
47. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
47
V2 (t)
Bond Graph for the Fluid system
V1(t)
P
TF
A1..F1(t)
V1(t) 1
1V 0P
R1
P
Q2
C:?
I: M1
TF
1/A2..
2
1V
I: M2
F2 (t)
R2
Q1
1M
2M
1F
1x 2x
2F
Cross-sectional
area 1A
Cross-sectional
area 2A
Compressible fluid
48. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
48
..
Hydraulic Cylinder
F(t) Q
V(t)
P
A
F(t)
V(t)
P
Q
TF
A
49. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
49
.. with friction and leakage
V(t)
P
TF
A..F(t)
V(t)
1V 0P
Rfriction
P
Q
Rleakage
F(t) Q
V(t)
P
ARfriction
50. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
50
..adding piston inertia
V(t)
P
TF
A..F(t)
V(t)
1V 0P
Rfriction
P
Q
Rleakage
I: Mpiston
piston
( ) Me t p=
F(t) Q
V(t)
P
ARfriction
F(t) Q
V(t)
P
ARfriction
51. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
51
Fluid inertia
Q
v(t)
A
PA PB
Q
x∆
0
lim
t
x
v
t∆ →
∆
=
∆
0
lim
t
x
Q A v A
t∆ →
∆
= = ⋅
∆
( )0
lim A B
t
d x
A l P P A
dt t
ρ
∆ →
∆
⋅ ⋅ ⋅ = − ⋅ ∆
Q
1Q
PA PB
Q
l
A
ρ ⋅
I:
Pp Q
Applying Newton’s II Law,
[ ]P A B
d d l
p Q P P
dt dt A
ρ ⋅
= = −
l
52. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
52
Pump or motor
.. P
Q
TF
µτ (t)
ω(t)
1Q
PA
PB
τ (t), ω(t)
QPA
QPB
Pump
BG for Pump
.. P
Q
TF
τ (t)
ω(t)
1Q
PA
PB1
µ
BG for Motor
53. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
53
Fluid system
1M
2M
1F
1x 2x
2F
Cross-sectional
area 1A
Cross-sectional
area 2A
Compressible fluid
54. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
54
V2 (t)
Bond Graph for the Fluid system
V1(t)
P
TF
A1..F1(t)
V1(t) 1
1V 0P
R1
P
Q2
C:?
I: M1
TF
1/A2..
2
1V
I: M2
F2 (t)
R2
Q1
1M
2M
1F
1x 2x
2F
Cross-sectional
area 1A
Cross-sectional
area 2A
Compressible fluid
55. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
55
Hydraulic Cylinder driven Tool post
PA QA
FR
MT
( )Tv t
FRs
Area = AA
Area = AB
PB QB
56. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
56
Hydraulic Cylinder driven Tool post
PA(t)
MT
( )V t x=
FS
PRV
PB(t)
PD
C
E
A
τ (t)
ω(t)
QB(t)
QA(t)
Area = AA
Area = AB
QE(t)
57. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
57
BG for Mechanical-Fluid system
Q
TF
µτ (t)
ω(t)
1 CQ
PD
PC
DPC
, ,
0 C A EP
0 DP
1 EQ
TF 1V
TF:R:RPRV
I: MT
R:RS
1/AA
Se:PD
AB
58. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
58
BG for Mechanical-Fluid system
Q
TF
µτ (t)
ω(t)
1 CQ
PD
PC
DPC
, ,
0 C A EP
0 DP
1 EQ
TF 1V
TF:R:RPRV
I: MT
R:RS
1/AA
Se:PD
AB
PA(t)
MT
( )V t x=
FS
PRV
PB(t)
PD
C
E
A
τ (t)
ω(t)
QB(t)
QA(t)
Area = AA
Area = AB
QE(t)
59. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
59
String based actuation
L R 0X
0Y
1RX
1RY
1LX
1A2A1P
2P
1Rθ
1Lθ
Active finger link
Thumb link (passive)
1m (opening)
2
m (closing)
String 1
String 2
60. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
60
Bond graph for the system with
differential causality
Effective during closing
1F
0
1Rθ1 A
J:I
1:C
1R
:τe
S
1Lθ1P
J:I
1:C TF TF
TF TF
Ls1
1
Ls2
1
Rs1
1
Rs2
12F
0
1Lr-
2R
r-2L
r
1Rr
Effective during opening
12
3
8
9101213
14
15
1617192021
24 e25e
Differential
causality
61. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
61
Bond graph for the string based prosthesis
Effective during opening
Effective during closing
12
3
4 5
6 7
8
910
11
1213
14
15
1617
18
1920
21
2223
24 e25e
62. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
62
Developments in Bond graph theory
• Structural controllability and observability
• Bicausality
• Differential bond graphs
• Multibond graphs
• Fault diagnosis
• Control strategies
63. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
63
Developments at NITJ
• Multibond graph modeling of Rigid body
mechanics
• Mechanisms and machines
– Robotic systems, Crankshaft-connecting-rod-piston-cylinder, Universal joint,
Quick return mechanism, Pantograph, Power hacksaw, Epicyclic gear trains,
Differential gear mechanism, …
• Soft contact dynamics
– Rigid objects interacting with soft material
• Biomechanics
– Development of hand prosthetic systems
– Extensor mechanism of the hand, the Winslow tendon network, …
64. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
• Control systems
• Coding in MATLAB
• Learning and teaching
64
Developments at NITJ …
65. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
65
Rufus Oldenburger Award
Conferral at the Dynamic Systems and
Control Luncheon, Thursday, December 6,
1979, during the Winter Annual Meeting in
New York, N. Y. Presentation by Donald N.
Zwiep, ASME President, 1979-1980,
PROFESSOR HENRY M. PAYNTER,
Professor of Mechanical Engineering,
Massachusetts Institute of Technology,
Cambridge, Massachusetts
66. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
66
Henry Paynter:
The inventor of Bond Graphs
1959
At the birth of Bond Graphs
1997
Upon his election to the NAE
67. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
67
68. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
68
Summary
• Modeling of Physical System Dynamics
– Bond graphs
– Causality
– Derivation of system equations
– Simulation using Bond graphs
• Examples
• Resources:
– Books
• Karnopp, Margolis and Rosenberg
• Amalendu Mukherjee, Ranjit Karmakar and Arun Samantaray
• Jean Thoma
• F T Brown
• Wolfgang Borutzky
– Journals
• ASME JDSM&C, IEEE SMC
• Journal of the Franklin Institute - Elsevier
• Simpra – Elsevier
• Simulation - SCS
– Other
• Lecture notes: Anand Vaz, ‘Lecture notes on Introduction to physical systems, their modeling and
simulation: A Bond Graph Approach’, October 2016, DOI: 10.13140/RG.2.2.19231.56487
• P. J. Gawthrop and G. P. Bevan, "Bond-graph modeling," in IEEE Control Systems, vol. 27, no. 2, pp.
24-45, April 2007. DOI: 10.1109/MCS.2007.338279
69. Lectures on Bond Graph Modeling of Mechatronic Systems, July – December 2016
©JosephAnandVaz,DepartmentofMechanicalEngineering,DrBRAmbedkarNIT,Jalandhar144011,India
69
Thank you!
Questions?
anandvaz@ieee.org, or
anandvaz@nitj.ac.in