Efficient Modeling and Simulation of Multidisciplinary Systems

across the Internet

Heřman Mann

Computing and Information Centre

Czech Technical University in Prague

TUTORIAL

2

Tutorial objectives

After attending this tutorial you should be able to:• understand the difference between various approaches to

modeling and their suitability to different tasks• be able to apply the concepts of multipole modeling in

different physical domains • be motivated to try the simulation software system DYNAST

freely accessible across the Internet• be aware of the importance of physical-level simulation for

reliable control design• be prepared to introduce a unified approach to engineering

dynamics at you school (if you are a teacher)• interested in visiting the DynLAB web-based course on

modeling and simulation (to be fully completed soon)

3

Kernel engineering tools

Modeling = procedure to simplify investigation of their dynamic behavior

Simulation = imitation of dynamic behavior of real systems

Analysis = relating system behavior to a changing variable or parameter

Diagnostics = indicating the reason for a system failure

Why engineers need these tools?• to better understand behavior of existing dynamic systems• to predict, verify and optimize behavior of designed systems• to detect, localize and diagnose faults in engineering products

4

Multidisciplinary approach

Contemporary engineering crosses borders between traditional disciplines:

• different physical domains– electrical, magnetic, mechanical, fluid, thermal, ...

• different levels of modeling abstraction– conceptual, functional, physical, virtual prototyping, (digital) control,

diagnossis, ...

• different levels of modeling idealization– (non)linear, time (in)variable, parameter (in)dependent, …

• different model descriptions– equations, transfer functions, block diagrams, multipoles, ...

5

Efficiency of simulation

In the past:– efficiency of simulation was evaluated with regard to its demand of

computer time only

Nowadays:– the computer time is so inexpensive that the cost of simulation is

dominated by the cost of personnel qualified to be able • to prepare the input data• to supervise the computation• to interpret the results

Therefore: – efficient simulation software should provide

• automated equation formulation• robust computational algorithms• user-friendly interface

6

Design procedure

• Design proceeds through several levels of abstraction– conceptual– functional (e.g., control design)– physical (e.g., real or virtual prototyping)– technological

• Different system descriptions are used– geometric (blue – topological (geometric dimensions of subsystems are not shown, only

their interactions) – behavioral (internal interactions of subsystems are not shown, only

their external behavior)

• Design proceeds through several levels of granularity (perpendicular to the design-space diagram)

7

Design space

trajectory of ideal design procedure (real one in many loops)

blocks multipoles

design space

8

Modeling & simulation procedure

1. System definition• system separation from its surroundings• system decomposition into subsystems• identification of subsystem energy interactions

2. Model development• subsystem abstraction and idealization• identification of subsystem parameters

3. Formulation of• equations for subsystems • equations for subsystem interactions• combined and reduced equations

4. Equation solution 5. Interpretation of the solution

9

Simulation using Simulink

1. System definition• system separation from its surroundings• system decomposition into subsystems

2. Model development• subsystem abstraction and idealization• parameter identification

3. Formulation of• equations for subsystems • equations for subsystem interactions• combined and reduced equations

4. Composition of a block diagram 5. Block-diagram analysis 6. Interpretation of the solution

10

Block Diagram Algebra

11

Block diagram applications

Graphical representation of• causes-effects relations

– inputs: causes– outputs: effects

• explicit equations– inputs: independent variables– outputs: dependent variables

• control structures– inputs: excitations, disturbances– outputs: desired variables

12

Copying lathe (1)

Geometric description

13

Copying lathe (2)

Behavioral description (block diagram for control design)

master-shape waveform

workpiece-shape waveform

force exerted by cylinder

14

Copying lathe (3)

Topological description (multipole diagram for physical design)

source of pressure

source of master- shape waveform r

cylinder mass

model of workpiece resistance

slide-bed friction

F

15

Multipole diagrams

• can be set up based on mere inspection of the modeled real systems without any equation formulation or block-diagram construction

• equations underlying the system models can be not only solved, but also formed automatically by the computer

• they project geometric configuration of real dynamic systems onto their topological configuration

• they portray graphically energy interactions between subsystems in the systems

• they can be combined with block diagrams, which represent a special case of multipole diagrams)

16

Multipole modeling

• Principles of multipole modeling

• Concept of across and through variables

• Postulates of continuity and compatibility

• Advantages of multipole modeling

17

Investigation of dynamic behavior

Dynamic behavior of a dynamic system is governed • by the flow of energy and matter between subsystems of the

system and between the subsystems and the surroundings• by storing energy in the subsystems or releasing it later as

well as by changes from one form to another.

Therefore, before starting any dynamic investigation of a system we should clearly

• separate the system from its surroundings• decompose the system into its disjoint subsystems

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Multidisciplinary system (1)

Tachom eter

Busline

E lectronicam plifier

H ydraulicm otor

O utputsynchro

Inputsynchro

Compensatingnetwork

H ydraulicvalve

Load

D em odulator

G ear

C ontro l

Source ofpressure

Shaft

19

Multipole models

Multipole model approximates subsystem mutual energy interactions assuming that

• the interactions take place just in a limited number of interaction sites formed by adjacent energy entries into the subsystems

• the energy flow through each such entry can be expressed by a product of two complementary power variables

20

Tachom eter

Busline

E lectronicam plifier

H ydraulicm otor

O utputsynchro

Inputsynchro

Compensatingnetwork

H ydraulicvalve

Load

D em odulator

G ear

C ontro l

Source ofpressure

Shaft

Multidisciplinary system (2)

Subsystems are separated by energy boundaries, sites of energy interactions are denoted by small circles

21

Multidisciplinary system (3)

Tachom eter

Bus

line

E lectron icam plifier

H ydraulicm otor

O utputsynchro

Inputsynchro

Compensatingnetwork

Hyd

raul

icva

lve

Load

D em odulatorG

ear

Source of

pressure

Shaft

Energy interactions between subsystems are characterized exclusively by energy flows through the sites of interactions at the energy boundaries

22

Multidisciplinary system (4)

Tachom eter

Bus

line

E lectron icam plifier

H ydraulicm otor

O utputsynchro

Inputsynchro

Compensatingnetwork

Hyd

raul

icva

lve

Load

D em odulatorG

ear

Source of

pressure

Shaft

The energy boundaries are detached and the energy interactions areinterconnected with the energy entries of subsystems by ideal links

23

Multipole constitutive relation

vB vC

vD

vE

A D

CB

EvA

iB iC

iD

iE

A D

CB

EiA

( )c( )b

A D

CB

E

( )a

5 - pole across variables through variables

Each multipole can be characterized by a constitutive relation between its across and through variables expressed by means of a combination of

• physical elements• blocks• equations• look-up tables

24

Power variables

25

Measurement of variables

Direct measurement of through variables requires including the measuring instrument between disconnected adjacent energy entries

Across variables are measured between distant energy entries without disconnecting them

26

Postulate of Continuity

a

b

c

Through variables a, b, c :

a + b + c = 0

27

Postulate of Compatibility

a

b

c

Across variables a, b, c :

a + b + c = 0

28

Reference across-variables

Measurement of reference across variables

29

Non-mechanical elements

30

Simple electrical system

31

Simple hydraulic system

32

Mechanical elements

33

Simple translational system

34

Simple rotational system

35

Cold rolling mill

36

Unified approach to modeling

37

Other approaches (1)

38

Other approaches (2)

39

Additional advantages

• multipole models can be developed once for the individual subsystems and stored to be used any time later

• this job can be done for different types of subsystems by specialists in the field

• submodels can be represented by different descriptions suiting best to the related engineering discipline or application

• submodel refinement or subsystem replacement can be taken into account without interfering with the rest of the system model

• mixed-level modeling is allowed

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Mechanical systems

• Translational systems

• Rotational systems

• Coupled mechanical systems– Rotary-to-rotary couplings– Rotary-to-linear couplings– Linear-to-linear couplings

• Planar systems

41

Jumping ball

42

Translatory systems

y

k dmg

yAAy

yd

yS yA

mA

( )a ( )b

yS

mg

yd

k

m

d

m2 m1FdF

v2 v1

l l

F

kR

kB0 l0

d2 d1

Fd

CAR 2CAR 1

m1 m2

lF

v1 v2( )c( )b( )a

43

Quarter-car model

44

Motor on vibration isolator

stop characteristic

45

Impact of a long spring

46

Torsional pendulums

47

Weight-lifting mechanism

48

Rotary-to-rotary coupling

B

A

A

B

n

Pure transformer

Coupling ratio:

Power consumption:

0 BBAA P

49

Coupled gears

B

A

A

B

n

Coupling ratio:

Power consumption:

0 BBAA P

Pure transformer

50

Gear trains (part 1)

Gear train Configuration n

External

spur gears

Internal

spur gears

Beveled

gear pair

b

a

r

r

b

a

r

r

b

a

r

r

Model

51

Gear trains (part 2)

Gear train Configuration n

Planetgear

Skewgear pair

b

a

r

r

b

a

r

r

Model

52

Belt-and-pulley or chain-and sprocket

ba rrn / barrn

53

Gear train with backlash

Backlash characteristics

54

Rotary-to-linear couplings

B

A

A

B

F

xn

Coupling ratio:

Power consumption:

0 BBAA xFP Pure transformer

55

Rotary-to-linear convertion

mg

y

Ar

m, J

A

mgm

Ay An J

n r

( )a ( )b

n = - 1/r

56

Rack-and-pinion gear-train

rn /1

57

Movable rack-and-pinion assembly

rn /1

58

Pulley or sprocket assembly

rn

59

Lead screw assembly

Pn P … screw pitch

60

Slider crank

20

2

0

)sin(

)sincos(sin

1

yrl

yrrr

x

n

A

AA

A

BA

61

Linear-to-linear coupling

B

A

A

B

F

F

x

xn

Coupling ratio:

Power consumption:

0 BBAA xFxFP Pure transformer

62

Levers and pulleys

63

Lever systems

k

k

mg

m

CB

A

l

ymg

By

CyAy

mk

( )a ( )b

n kl

k

mg

m

A B C

D

B'

l1 l2

l3v t( )

y

Ayna Cy

By B'ym mg

( )a ( )b

nal /l1 2

nb

nb l /l2 3

64

Planar oblique throw

65

Central star and planet

66

Math pendulums

n

m mmg

Ax

xAB yAB

Ay

Bx Byx

y mA

B

mg( )a ( )b

n yABxAB

xy

A

B

C

xB xC0

C2

n1

m1

m1

m2

m2m2g

m1g

n2

CxxC

xB

yB

yC

By

Cy

n 1 yBxB

n 2

y y BC x x BC

( )b( )a

67

Planar systems

x

y

mC

mA

B

mg BxdC

xB

mC

( )a ( )b

n

mmg

Ax

xAB yAB

Ay

By

m n yABxAB

mg

m

AB

k

n yABxAB

( )a ( )b

m mg

yAB

xABnBxAy

kyAB

xAB

68

Translatory joint fixed to frame

Multipole model

69

Translatory joint between bodies

70

Revolute joints

71

Body with revolute joints

72

Two-link planar robot

73

Physical 2-pendulum with friction

74

Truck with active damping

75

Truck model

76

Electrical & electronic systems

CMOS inverter

77

Pulse-width modulator

78

Astable multivibrator

79

Three-phase thyristor rectifier

80

Electro-mechanical systems

Conductor moving in a magnetic field

81

Coils in a magnetic field

82

ac rotational transducer

83

Movable-core solenoid

84

Permanent magnet DC machine

85

Chopper-driven dc motor

86

Movable-plate condenser

87

Reluctance machine

88

Three-phase stepping motor

89

Electromagnetic relay

90

Magnetic levitation of a ball

91

Chopper-driven dc motor

92

Fluid-power systems

Q

( ) ( )a b

Gf

Q

pB

Cf1 Cf2

Lf

93

Valve for flow control

94

Fluid-mechanical transducers

95

Fluid-damped car suspension

96

Two-stage relief valve

97

Relief valve in a system

98

Spool valves

99

FPN simulation benchmark

100

DYNAST software system

for efficient simulation of multidisciplinary engineering systems

freely accessible across the Internet at

http://virtual.cvut.cz/dyn/

DYNAST has been designed • for practicing engineers to enhance efficiency and quality of

their work• for engineering students to accelerate and deepen their

understanding of system dynamics• for remote engineering teams to support their collaboration

101

DYNAST distributed simulation environment

Web browser

DYNAST Shellfor submitting diagrams or equations and for plotting

CORTONAfor 3D animation

of simulated systems

MATLABfor design of control for

simulated systems

Learning mng. systemfor course delivery

DYNAST Solverfor forming and solving

equations

DYNAST Publisherfor documenting simulation experiments & submodels

DYNAST Monitorfor assisting learners in

modelling and simulation

Internet

Client Server

102

DYNAST Solver

provides the computation power for the DYNAST system.

It can• compute transient and steady-state (static) solution of

systems of nonlinear algebro-differential equations • formulate these equations for multipole diagrams that may be

combined with block diagrams and/or equations• compute Fourrier analysis of the periodic steady-state solution• linearize nonlinear system models and provide system

transfer functions and responses in a semisymbolic form• compute frequency-domain characteristics in different forms

103

DYNAST Solver

104

Semisymbolic analysis

105

DYNAST Shell

provides a user-friendly working environment for DYNAST Solver.

Thanks to its wizard dialogs, users do not need to learn a simulation language.

DYNAST Shell allows for • submitting equations in textual and diagrams in graphical form• syntax analysis of the submitted problem for errors • processing the submitted problem by DYNAST Solver• plotting the resulting data in different graphical forms• creating graphical symbols and models for new components• processing of reports on simulation experiments and models• communication with the clients’ Matlab control-design toolset

106

Submitting a component model

107

DYNAST Shell -- symbol editor

108

DYNAST Publisher

is a LaTeX-based documentation system installed on the server for automated publishing of – reports on simulation experiments and – descriptions of library submodels

Publisher extracts automatically the relevant parts of the input data and captures the submitted multipole or block diagrams as well as the resulting output plots and includes them into the documents.

The documents can be converted by the server into PostScript, PDF and HTML formats.

109

DYNAST Monitor

allows design managers or tutors to observe from any site on the Internet the data files and diagrams the users are submitting to DYNAST Solver from their client computers.

The supervisor can communicate with the users across the Internet and assist them in solving their problems.

110

DYNAST in control design

functional level

physical level

Control synthesis

Control designverification

Controlledsystem

Controlobjectives

Plant to be controlled

Model reduction

Real-partsimplementation

MATLAB domain

DYNAST domain

111

Modeling using MATLABExample of the paper-and-pencil procedure necessary for the equation formulation and their transformation before MATLAB can be used to compute the open-loop response:

D. Tilbury, B. Messner: Control Tutorials for Matlab at http://www.engin.umich.edu/group/ctm/

112

Inverse pendulum experiment

Multipole model of the open loop in DYNAST working environment

pendulum model

sensor of d/dt

cart inertia

source of force F

cart friction

sensor of dx/dt integration of dx/dt sensor of x

113

DYNAST as modelling toolbox for Matlab

Validation of the open-loop model in DYNAST

Export of open-loop transfer functions to MATLAB environment in M-file

114

Analog PID control of inverse pendulum

Closed-loop model in DYNAST based on control design in MATLAB

Closed-loop verification in

DYNAST

115

DYNAST & MATLAB

116

Current control curriculum criticised

for

• exposing students to rigor math before motivating them by practical engineering issues

• presenting ‚textbook‘ problems carefully engineered to fit the ‚underlying‘ theory

• using computers to carry old exercises without exploiting them efficiently

Future Directions in Control Education, IEEE Control Systems, October 1999

117

Considerations for control education

1. Automatic control education currently has a very narrow approach ...

2. It is necessary to attach greater importance to all the design cycle of a control system

3. Modelling and identification ... are a key factor for achieving a good design ...

S. Dormido Bencomo: Control Learning: Present and Future, IFAC Congress, Barcelona 2002

118

DynLAB web-based courseon modeling and simulation

Geez, Joe, – now I wish I took that DynLAB course !

119

EU project DynLAB

The goal of the project within the Leonardo da Vinci EU program

is to develop the

Course on modeling and simulation of controlled multidisciplinary systems

in a virtual lab

Project consortium:– Czech Technical University in Prague– Ruhr-Universität, Bochum– Institute of Technology Tallaght, Dublin– EAS, Fraunhofer Institut, Dresden – University of Sussex, Brighton

Project website: http://virtual.cvut.cz/dynlab/

120

Innovative style of the course

• introducing learners to dynamics through simple examples to stimulate their interest before exposing them to rigor math

• exposing learners to a unified, systematic and efficient methodology for realistic modelling of multidisciplinary systems

• giving learners access to a powerful tutor-monitored simulation system across the Internet

• exploiting computers not only for equation solving, but also for their formulation to minimise learners’ distraction from dynamics

• giving learners a better ‘feel’ for the topic by problem graphical visualisation and interactive virtual experiments

• allowing different target groups to select an individual paths through the course both for self-study and remote tutoring

121

Visualization of system dynamics

3D movable model multipole diagram robot-arm trajectoryvisualized by CORTONA set-up in DYNAST Shell simulated by DYNAST

122

Learning modes in DynLAB

123

Ball-and-beam virtual experiment