Mathematical Modelling and Dynamic Simulation

7/30/2019 Mathematical Modelling and Dynamic Simulation

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2012 The MathWorks, Inc.

Mathematical Modelling and Dynamic

Simulation

By Coorous Mohtadi

Educational Technical Evangelist


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Key Points

Symbolic Mathematics allows deeper understanding

Integrated with MATLAB environment

Complement numerical modelling

Simulink supports

Modelling and Simulation

Implementation on targets

Integrated with MATLAB

Simscape is a natural tool for Physical Modelling


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Calvin & Hobbes, Bill Watterson 1990

Where do we start?


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So where do we really start?


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So, where do we really start?

Understand the underlying mathematics/physics of the problem

q

r

X

Y


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So, where do we really start?


*** Gain insight into the problem ***

q

r

X

Y

ZZ

mg

CM


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Now we need pen and paper


*** Gain insight into the problem ***

q

r

X

Y

ZZ

mg

mgcos(q)CM


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Or, we can use the Symbolic Math Toolbox

notebook interface

To help us derive the dynamic

equations analytically

To find analytic (when possible)

and/or numerical solutions to

the problem


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Of course, we could use MATLAB to solve the

differential equation

q

r

X

Y

ZZ

mg

mgcos(q)CM

Dynamic differential equation for an ideal single link


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Or, we can use Simulink to build a graphical

representation of the equation

q

r

X

Y

ZZ

mg

mgcos(q)CM

Dynamic differential equation for an ideal single link


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And use the s im command to control the

Simulink model from MATLAB scripts

q

r

X

Y

ZZ

mg

mgcos(q)CM

Dynamic differential equation for a single link with friction

b: viscous friction

coefficient


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Simulink model with Feedback Control

Adjust k1 & k2 to get

best performance


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Response Optimization

Optimize Controller gains using Simulink Design Optimization


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Computational Paradigms with MATLAB

MATLAB

Parallel Computing MATLAB Distributed Computing Server

Symbolic Math

Symbolic

SimMechanics

Simscape

Simulink

Modelling &

Simulation

Statistics

Optimization

Numeric

Simulink or Simscape Blocks

MATLAB Functions


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Data-Driven ModellingFirst Principles Modelling

Neural Networks

Physical NetworksSystem

Identification

Parameter Tuning

Programming

Block Diagram

Modelling Language

Symbolic Methods

Modelling Approaches

Modelling Physical Systems

With MathWorks Products

Statistical Methods

(MATLAB, C)

(Simulink)

(Simscape language)

(Symbolic MathToolbox)

(Simscape and other

Physical Modelling

products)

(Neural NetworkToolbox)

(Model BasedCalibration Toolbox)

(Simulink Design Optimization)

(System IdentificationToolbox)


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Key Points




Simulink supports






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Simulink

sldemo_tank penddemo


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Simulink Applications


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Simulink

Simulink is a software package for

modeling, simulating, and analyzing

dynamical systems

Block diagram editing

Nonlinear simulation

Hybrid (continuous and discrete) models

Asynchronous (non-uniform sampling) simulation

Fully integrated with MATLAB, MATLAB toolboxes

and blocksets.


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Simulink

Accurately design, implement, and test:

Control systems

Signal Processing systems

Communications systems

Embedded systems

Physical systems

other Dynamical systems


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Launching Simulink


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Simulink Library Browser


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Finding Blocks


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Getting Help

Context sensitive help

Simulink documentation


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Creating Subsystem

Context menu -> Create Subsystem

Subsystem ports

Inside a subsystem

How to undo Create Subsystem?


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Masking Subsystem

Mask- Encapsulation with a UI

Provides

Mask icon display

Block description

Parameter dialog prompt

Block help text


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Key Points




Simulink supports Modelling and Simulation





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Build Accurate Models Quickly

Requires less domain knowledge and

programming effort than traditional methods

Spend more time developing, less time modeling

Physical Modeling

MATLAB, Simulink

Domain Knowledge Programming Effort

Programming

Effort

Domain

Knowledge

Mechanical

Electronic

Multidomain

Hydraulic

Power Systems

Plant

Specification

Fortran, C++


Plant

Model


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Electrical Systems in Equations

DC MotorR

L

Kt,Ke

J,b

i

dt

diLRiKv

m

windwindme

dt

dJDiKT

mt


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Electrical Systems in Simscape

DC Motor

Simscape model advantages

Easier to read than equations

Quicker to create

More intuitive easier to explain to other engineers

R

L

Kt,Ke

J,b

i

dt

diLRiKv

m

windwindme

dt

dJDiKT

mt


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Mechanical Systems in Equations

Simple Pendulum

Tz = I1

-mgl*sin(1)= ml21

1 = - sin(1)..

..

1

x

y

z

mg

l

..

gl


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Mechanical Systems in SimMechanics

Simple Pendulum

SimMechanics model advantages Easier to read than equations

Quicker to create

More intuitive easier to explain to other engineers

Tz = I1

-mgl*sin(1)= ml21

1 = - sin(1)..

..

1

x

y

z

mg

l

..

gl


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1

x

y

z

mg

1'' = gl sin

1


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2

m2g

1

x

y

z

m1g


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2m2g

1

x

y

z

m1g

3m3g

m4g

m5g5

4


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Create Reusable System-Level Models

Physical Modeling

MATLAB, Simulink

Models are easier to understand, reuse,and share with others

Domain Knowledge ProgrammingEffort

Programming

Effort

Domain

Knowledge

Mechanical

Electronic

Multidomain

Hydraulic

Power Systems

SimscapeFortran, C++


Plant

Model

Plant

Specification


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Optimize Your Entire Engineering System

Mechanical

Electronic

Multidomain

Hydraulic

Simulate the entire system in a single environment Does not require learning multiple tools or co-simulation

Programming

Effort

Power Systems

SimscapeDomain

Knowledge

SimMechanicsProgramming

Effort

Domain

Knowledge

SimDrivelineProgramming

Effort

Domain

Knowledge

SimHydraulicsProgramming

Effort

Domain

Knowledge

SimElectronicsProgramming

Effort

Domain

Knowledge

Programming

EffortSimPowerSystems Domain

Knowledge

Plant

Model


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Physical Systems in Simulink

Multibody mechanics (3-D) Mechanical systems (1-D)

Fluid power and controlMultidomain physical systems

Electrical power systems

Electromechanical and

electronic systems

SimMechanics

SimDriveline

SimHydraulics

SimElectronics

Si

mPowerSystems

Simscape

MATLAB, Simulink

SimMechanics

SimDriveline

SimHyd

raulics

SimElectronics

SimPower

Systems

SimscapeMechanical Hydraulic Electrical

Thermal

Custom Domains via

Simscape Language

Pneumatic Magnetic

N S


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MathWorks Investment in

Physical Modeling

Responding to customer demand,

MathWorks will continue

to invest heavily in tools

and capabilities for

physical modeling.

Magnetics Added

To Simscape

Pneumatics Added

To Simscape

Simscape Language

Introduced

SimElectronics

Introduced

Code Generation

Advances

SimHydraulics

Introduced

3-D Visualization

Improvements

AutodeskTranslator

Ideal Switching

Algorithm Introduced

Electric Drives

Library Introduced

ProEngineer

Translator

SolidWorks

Translator

SimDriveline

Introduced

Simscape-Based

Library Introduced

SimMechanics

Introduced

Simscape

Introduced

SimPowerSystems

Introduced

Simscape

Diagnostics

Improvements

Thermal effects

optional ports

Second Generation

Technology

Intf. Elements

Editing Modes

1998 2000 2002 2004 2006 2008 2010 2012 2014


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Summary

Optimize system performance

Develop in a single environment

No cosimulation

Find problems before buildinghardware using HIL

Discover integration problems

using simulation No cosimulation

Create accurate, reusable

plant models quickly and easily


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Enhance Learning Using


PREPARE

Experience

ENABLE

Optimize

Test

Understand

Connect

Communicate

Incorporate

Collaborate

UsePrototype

Expand


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Physical Modeling

Key Messages For Academia

Understand

1. Incorporate realistic and engaging examples

2. Communicate concepts using best available method

3. Connect theory to real systems

Explore

4. Expand learning to adjacent disciplines

5. Prototype new designs rapidly

6. Test designs completely

7. Optimize designs

Prepare

8. Use industry-standard tools

9. Collaborate with other levels

10. Experience Model-Based Design


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Key Points




Simulink supports Modelling and Simulation




Documents

Mathematical Modelling and Dynamic Simulation