Notes, Professor Anand Vaz-Lectures on Modeling of Physical System Dynamics

8/3/2019 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?


3/51

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


5/51

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


12/51

Examples of multiports

Electric motor

Hydraulic pump Drive shaft

Spring-shock absorber unit

Transistor

Speaker

Crank and slider mechanism Wheel

Separately excited DC motor


13/51

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)


14/51

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 =


20/51

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


25/51

Causality ofR element

Resistance

effortR

flowRvi 1==

flowReffortRiv == ve=

if=


26/51

Causality of Transformer & Gyrator

Transformer Gyrator

TF GY

GYTF


27/51

Causality of Sources & Junctions

eS S

Source of effort Source of flow

01

Junctions


28/51

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


30/51

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


31/51

Electromechanical Actuator

( )v t x= &K

R

Head mass = M

( ) ( )F t i t =

( )V t( )i t


32/51

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


34/51

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


35/51

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!!!


37/51

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


38/51

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


40/51

..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


41/51

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


42/51

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


43/51

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


44/51

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


45/51

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


46/51

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


47/51

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


48/51

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


49/51

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


50/51

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?

[email protected], or

[email protected]
mailto:[email protected]:[email protected]:[email protected]:[email protected]

Documents

Notes, Professor Anand Vaz-Lectures on Modeling of Physical System Dynamics