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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?
Understand the underlying mathematics/physics of the problem
*** Gain insight into the problem ***
q
r
X
Y
ZZ
mg
CM
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Now we need pen and paper
Understand the underlying mathematics/physics of the problem
*** 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
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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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
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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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++
Domain Knowledge Programming Effort
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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Mechanical Systems in SimMechanics
1
x
y
z
mg
1'' = gl sin
1
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Mechanical Systems in SimMechanics
2
m2g
1
x
y
z
m1g
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Mechanical Systems in SimMechanics
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++
Domain Knowledge Programming Effort
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
Modelling and Simulation
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
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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