Simulink Basics
SIMULINK
Basics
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
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
SIMULINK Basics
What’s Simulink?
• Graphical modelling of dynamic systems by signal flow
graphs
• Addition to MATLAB (Toolbox)
• Simulink–Additions: Blocksets (SimPower-Systems,
SimMechanics)
Sine Wave
−1
Clock
Product1
80
Gain
Product3
eu
Math
Function
Product2
−1
Mux
gedaempfte
Sinusschwingung
Gain1
Constant
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
1
SIMULINK Basics
Starting SIMULINK
• Blocks are basic elements
• Blocks characterized by input, output, name, icon
• Double click opens
Block P arameters dialog
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
3
SIMULINK Basics
SIMULINK block libraries Sources and Sinks
Block library Sources:
• Generation of signals
• Import data from MATLAB
workspace
• Import of data from files
untitled.mat
1
Step
Signal Sine Wave
Generator
From File
1
In1
Constant
simin
Ramp
Repeating
Pulse
Generator Sequence
From
Workspace
Block library Sinks:
• Graphical display of signals
• Write data to MATLAB
workspace
• Write data to files
untitled.mat
To File
Scope XY Graph
simout
1
Out1
To Workspace
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
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SIMULINK Basics
Example for Sources and Sinks
Signal 1
Signal 2
1
s
Integrator
Scope
Signal Builder
Signal Builder : bsp sigbuild.mdl
Signal Builder Dialog box for group of three signals
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
5
SIMULINK Basics
SIMULINK block library Math Opertions
Block library Math:
• Arithmetic, logical and relational operators
• Mathematical and trigonometric functions
etc.
1
eu
Product
Math
Function
Sum
Gain
AND
1
Logical
Operator
Slider
Gain
<=
sin
Dot Product
Trigonometric
Function
K*u
Relational
Operator
Matrix
Gain
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
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SIMULINK Basics
Examples for Math Operations
Simulink model bspmath.mdl of equation
1
− t
f (t) = 80 · e 80 · sin (0.25t + π )
3
Sine Wave
−1
Clock
Product1
80
Gain
Product3
eu
Math
Function
Product2
−1
Mux
gedaempfte
Sinusschwingung
Gain1
Constant
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
7
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
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SIMULINK Basics
Numerical integration of ODE
Inhomogeneous linear ordinary differential equation:
u(t)
DGL
y(t)
ẏ(t) = f (u(t), y(t))
tn+1
Z
Integration:
yn+1 = yn +
f (u(t), y(t))dt
tn
Numerous methods:
•
•
•
•
•
Euler method
Heun’s method
Other Runge–Kutta–methods
Adams–Bashforth methods
···
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
9
SIMULINK Basics
Numerical integration of ODE
Euler method (explicit)
y
y1
dy
y(t1)
y0
hy0
y(t)
y0
h
t0
t1
t
y1 = y0 + h · ẏ0
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
10
SIMULINK Basics
Numerical integration of ODE
Runge–Kutta method
y
P
P3(t2) = y2
y1
y1
y0
P3(t)
y0
h
t0
t1
t2
t
2h
y2 = y0 +
· [ẏ0 + 4ẏ1 + f (u2, y2P )]
6
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
11
SIMULINK Basics
Numerical integration of ODE
Adams–Bashforth method
y
yn
P2(tn+1)
yn-1
P2(t)
yn-2
h
tn-2
tn-1
tn
tn+1
t
h
yn+1 = yn +
· [23ẏn − 16ẏn−1 + 5ẏn−2]
12
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
12
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
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
Dipl.-Ing. U. Wohlfarth
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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
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
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
SIMULINK Basics
Error handling
Simulation
Diagnostics
Viewer
• upper part: error information
• lower part: complete text of error message
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
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SIMULINK Basics
SIMULINK block library Signal Routing
Block library Signal Routing:
• Date saving
A
A
A
Data Store
Memory
Data Store
Read
Data Store
Write
• Connect and selection of signals
etc.
[A]
Mux
Demux
Bus
Selector
Demux
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
Selector
Hit
Crossing
[1]
From
IC
[A]
Goto
24
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
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SIMULINK Basics
SIMULINK block library Subsystems
Block library Subsystems:
In1
Out1
Subsystem
In1
Out1
In1
Atomic Subsystem
Triggered
Subsystem
In1
while { ... } Out1
IC
Out1
Function−Call
Subsystem
In1
Out1
Out1
If Action
Subsystem
In1
function()
In1
Action
Out1
if(u1 > 0)
While Iterator
Subsystem
u1
else
If
Enabled
Subsystem
etc.
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
26
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
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SIMULINK Basics
Masking of subsystems
Example bspmask.mdl
x
y
m
Steigung
⇒
b
Matlab/Simulink
Dipl.-Ing. U. Wohlfarth
y−Achsenabschnitt
y=mx+b
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