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Simulink Basics
SIMULINK
Basics
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
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Simulink Basics
Content
• What’s SIMULINK?
• SIMULINK–Libraries Sources, Sinks und Math
• Simulation parameters
• Algorithm’s for numerical integration
• SIMULINK–Libraries Signals&Systems, Subsystems
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
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SIMULINK Basics
What’s Simulink?
• Graphical modelling of dynamic systems by signal flow
graphs
• Addition to MATLAB (Toolbox)
• Simulink–Additions: Blocksets (SimPower-Systems,
SimMechanics)
gedaempfteSinusschwingung
Sine Wave
Product3
Product2Product1
Mux
eu
MathFunction −1
Gain1
−1
Gain
80
Constant
Clock
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 1
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SIMULINK Basics
Starting SIMULINK
• Blocks are basic elements
• Blocks characterized by input, output, name, icon
• Double click opens
Block Parameters dialog
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 3
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SIMULINK Basics
SIMULINK block libraries Sources and Sinks
Block library Sources:
• Generation of signals
• Import data from MATLAB
workspace
• Import of data from files
StepSine WaveSignal
Generator
RepeatingSequence
Ramp PulseGenerator
untitled.mat
From File
simin
FromWorkspace
1
Constant
1In1
Block library Sinks:
• Graphical display of signals
• Write data to MATLAB
workspace
• Write data to files
1Out1
XY Graphsimout
To Workspace
untitled.mat
To File
Scope
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 4
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SIMULINK Basics
Example for Sources and Sinks
Signal 1
Signal 2
Signal Builder
Scope
1s
Integrator
Signal Builder : bsp sigbuild.mdl
Signal Builder Dialog box for group of three signals
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 5
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SIMULINK Basics
SIMULINK block library Math Opertions
Block library Math:
• Arithmetic, logical and relational operators
• Mathematical and trigonometric functions
sin
TrigonometricFunction
Sum
1
SliderGain <=
RelationalOperator
Product
K*u
MatrixGain
eu
MathFunction
AND
LogicalOperator
1
Gain
Dot Product
etc.
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 6
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SIMULINK Basics
Examples for Math Operations
Simulink model bspmath.mdl of equation
f(t) = 80 · e− 1
80t· sin (0.25t + π
3)
gedaempfteSinusschwingung
Sine Wave
Product3
Product2Product1
Mux
eu
MathFunction −1
Gain1
−1
Gain
80
Constant
Clock
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 7
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SIMULINK Basics
Simulation: parameters and solvers
Configuration
Parameters
dialog box
Solver pane:
• Specify start and stop time of simulation
• Solvers for numerical integration
• Output options
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 8
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SIMULINK Basics
Numerical integration of ODE
Inhomogeneous linear ordinary differential equation:
DGL y(t)u(t) y(t) = f(u(t), y(t))
Integration: yn+1 = yn +
tn+1∫
tn
f(u(t), y(t))dt
Numerous methods:
• Euler method• Heun’s method• Other Runge–Kutta–methods• Adams–Bashforth methods• · · ·
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 9
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SIMULINK Basics
Numerical integration of ODE
Euler method (explicit)
y0
y0
hy0y(t)
t0
h
t1t
y1
y
dyy(t1)
y1 = y0 + h · y0
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 10
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SIMULINK Basics
Numerical integration of ODE
Runge–Kutta method
y0
y0
y1 P3(t)
P3 2 2(t ) = yP
t0
h
t1 t2t
y1
y
y2 = y0 +2h
6· [y0 + 4y1 + f(u2, yP
2 )]
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 11
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SIMULINK Basics
Numerical integration of ODE
Adams–Bashforth method
yn-2
P2(t)
P2 n+1(t )
tn-2 tn-1 tn tn+1
t
yn-1
yn
y
h
yn+1 = yn +h
12· [23yn − 16yn−1 + 5yn−2]
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 12
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SIMULINK Basics
Solver: integration algorithms in MATLAB
Variable–step solver:
• use variable step size
• allow error control & detection of zero crossings
• for continuous-time, non-stiff systems:
⇒ ode45 (first try), ode23, ode113
• for continuous-time, stiff systems:
⇒ ode15s, ode23s, ode23t,ode23tb
• for discrete-time systems:
⇒ discrete (Variable–step)
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 13
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SIMULINK Basics
Solver: integration algorithms in MATLAB
Fixed–step solver:
• use fixed step size
• no error control
• no detection of zero crossings
• for continuous-time systems:
⇒ ode5, ode4, ode3, ode2, ode1
• for discrete-time systems:
⇒ discrete (Fixed–step)
Matlab/Simulink
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SIMULINK Basics
Simulation: parameters and solver methods
Configuration
Parameters
dialog box
Data Import/Export pane:
• Initialization
• Load data from Workspace
• Write data to Workspace
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 18
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SIMULINK Basics
Simulation: parameters and solver methods
Configuration
Parameters
dialog box
Diagnostics pane:
• Control of warning and error messages
• Set simulation options
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 19
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SIMULINK Basics
Simulation
Start and stop of simulation
• from SIMULINK window
• from MATLAB Command Window
– set_param(’sys’, ’SimulationCommand’, ’cmd’)
get_param(’sys’, ’SimulationStatus’)
– [t,x,y] = sim(’model’, timespan, options, ut)
options = simset(property, value, ...)
newopts = simset(oldopts, property, value, ...)
struct = simget(’model’)
Example:[t,x,y] = sim(’m1’,[],simset(simget(’m1’),’Solver’,’ode23’,’MaxStep’,0.01))
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 20
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SIMULINK Basics
Error handling
Simulation
Diagnostics
Viewer
• upper part: error information
• lower part: complete text of error message
Matlab/Simulink
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SIMULINK Basics
SIMULINK block library Signal Routing
Block library Signal Routing:
• Date saving
A
Data StoreWrite
A
Data StoreRead
A
Data StoreMemory
• Connect and selection of signals
SelectorMux
[1]
ICHit Crossing
[A]
Goto
[A]
From
Demux
Demux
BusSelector
etc.
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 24
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SIMULINK Basics
Subsystems
Subsystems:
• Structural order of complex models
• Combining blocks of similar function
• hierarchic structuring
• Creation by
1. menue item Edit/Create Subsystem
2. block library Subsystems
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 25
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SIMULINK Basics
SIMULINK block library Subsystems
Block library Subsystems:
while { ... }In1
ICOut1
While IteratorSubsystem
In1 Out1
TriggeredSubsystem
In1 Out1
Subsystem
ActionIn1 Out1
If ActionSubsystem
u1if(u1 > 0)
else
If
function()
In1 Out1
Function−CallSubsystem
In1 Out1
EnabledSubsystem
In1 Out1
Atomic Subsystem
etc.
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 26
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SIMULINK Basics
Conditionally executed subsystems / Masking
Conditionally Executed Subsystems
• Execution controlled by control signal
• comprise Enable or Trigger
Masking of subsystems
• building a new block from a subsystem
• easier parametrization of complex subsystems
• Setting up of user defined libraries
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 27
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SIMULINK Basics
Masking of subsystems
Example bspmask.mdl
b y−Achsenabschnitt
m
Steigung
yx
⇒y=mx+b
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth 28