An Interpretation of How
Simulation Software,
like LabVIEW’s®
Control Design & Simulation module,
might Work
(Work in Progress)
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http://twilight-pc-help.com/InterpretationOfHowSimulationSoftware,LikeLabVIEWsCDandSim,MightWork.pdf
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http://twilight-pc-help.com/InterpretationOfHowSimulationSoftware,LikeLabVIEWsCDandSim,MightWork_without_notes.pdf
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An Interpretation of How Simulation Software might Work
2
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
3
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
4
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
the Integrator block
5
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
the Integrator block
It somehow turns parameters, like:
Acceleration ...into Velocity and Velocity ...into Position
6
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
the Integrator block
It somehow turns parameters, like:
Acceleration ...into Velocity and Velocity ...into Position
7
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
the Integrator block
It somehow turns parameters, like:
Acceleration ...into Velocity and Velocity ...into Position
8
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
the Integrator block
It somehow turns parameters, like:
Acceleration ...into Velocity and Velocity ...into Position
9
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
the Integrator block
It somehow turns parameters, like:
Acceleration ...into Velocity and Velocity ...into Position
10
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
the Integrator block
It somehow turns parameters, like:
Acceleration ...into Velocity and Velocity ...into Position
Note:
11
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
the Integrator block
It somehow turns parameters, like:
Acceleration ...into Velocity and Velocity ...into Position
Note:
Acceleration is the rate-of-change of Velocity
12
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
the Integrator block
It somehow turns parameters, like:
Acceleration ...into Velocity and Velocity ...into Position
Note:
Acceleration is the rate-of-change of Velocity
Also note:
13
An Interpretation of How Simulation Software might Work
Well,
I think it boils down to...
the Integrator block
It somehow turns parameters, like:
Acceleration ...into Velocity and Velocity ...into Position
Note:
Acceleration is the rate-of-change of Velocity
Also note: Velocity is the rate-of-change of Position
14
An Interpretation of How Simulation Software might Work
Let’s take a closer look...
15
An Interpretation of How Simulation Software might Work
16
An Interpretation of How Simulation Software might Work
I wondered if its glyphs
offered any clues?
17
An Interpretation of How Simulation Software might Work
18
An Interpretation of How Simulation Software might Work
This one just means
that it’s part of
LabVIEW’s
Control Design &
Simulation Library
19
An Interpretation of How Simulation Software might Work
20
An Interpretation of How Simulation Software might Work
‘Coined’ by
Pierre-Simon Laplace
It represents a number
that's based on
frequency, instead of
time.
21
An Interpretation of How Simulation Software might Work
‘Coined’ by
Pierre-Simon Laplace
It represents a number
that's based on
frequency, instead of
time.
22
An Interpretation of How Simulation Software might Work
‘Coined’ by
Pierre-Simon Laplace
It represents a number
that's based on
frequency, instead of
time.
When an equation is converted
from being based on time to
frequency, then
Integration
becomes Division by ‘s’.
23
An Interpretation of How Simulation Software might Work
‘Coined’ by
Pierre-Simon Laplace
It represents a number
that's based on
frequency, instead of
time.
When an equation is converted
from being based on time to
frequency, then
Integration
becomes Division by ‘s’.
24
An Interpretation of How Simulation Software might Work
‘Coined’ by
Pierre-Simon Laplace
It represents a number
that's based on
frequency, instead of
time.
When an equation is converted
from being based on time to
frequency, then
Integration
becomes Division by ‘s’.
So, in a ‘twisted’
sort of way,
1/s means Integrate
25
I wondered...
26
I wondered...
is this how the
Integrator block works?
27
I wondered...
is this how the
Integrator block works?
...does it do the
time-to-frequency
conversion thing?
28
Nope!
29
Oh well.
30
I then wondered...
31
I then wondered...
...what does it want?
32
An Interpretation of How Simulation Software might Work
What does it want?
33
An Interpretation of How Simulation Software might Work
Well, it wants to know
two things...
34
An Interpretation of How Simulation Software might Work
Well, it wants to know
two things...
35
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
36
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
37
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
38
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
39
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
40
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
41
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
What the...? Why is it asking me
for the output? Isn’t that what
it’s suppose to figure-out?
42
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
What the...? Why is it asking me
for the output? Isn’t that what
it’s suppose to figure-out?
43
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
What the...? Why is it asking me
for the output? Isn’t that what
it’s suppose to figure-out?
Here’s the catch... It can only
figure-out the output of the next
time-step with the input from the
given one (e.g. initial time-step).
44
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
What the...? Why is it asking me
for the output? Isn’t that what
it’s suppose to figure-out?
Here’s the catch... It can only
compute the output of the next
time-step, not the present one
(e.g. initial time-step).
45
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
What the...? Why is it asking me
for the output? Isn’t that what
it’s suppose to figure-out?
Here’s the catch... It can only
compute the output of the next
time-step, not the present one
(e.g. initial time-step).
46
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
What the...? Why is it asking me
for the output? Isn’t that what
it’s suppose to figure-out?
Here’s the catch... It can only
compute the output of the next
time-step, not the present one
(e.g. initial time-step).
47
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
48
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
49
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
Well... Not like what is taught in a calculus class.
50
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
Well... Not like what is taught in a calculus class.
51
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
Well... Not like what is taught in a calculus class.
The methods taught there, are only able to solve
52
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
Well... Not like what is taught in a calculus class.
The methods taught there, are only able to solve
some of the equations that: consist of 1 or more
53
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
Well... Not like what is taught in a calculus class.
The methods taught there, are only able to solve
some of the equations that: consist of 1 or more
‘rate-of-change derivations’ of a variable... and can
also simulate a real-world situation. However, if we
can live with estimates, in-place of exact solutions,
54
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
Well... Not like what is taught in a calculus class.
The methods taught there, are only able to solve
some of the equations that: consist of 1 or more
‘rate-of-change derivations’ of a variable... and can
also simulate a real-world situation. However, if we
can live with estimates, in-place of exact solutions,
55
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
Well... Not like what is taught in a calculus class.
The methods taught there, are only able to solve
some of the equations that: consist of 1 or more
‘rate-of-change derivations’ of a variable... and can
also simulate a real-world situation. However, if we
can live with estimates, in-place of exact solutions,
56
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
Well... Not like what is taught in a calculus class.
The methods taught there, are only able to solve
some of the equations that: consist of 1 or more
‘rate-of-change derivations’ of a variable... and can
also simulate a real-world situation. However, if we
can live with estimates, in-place of exact solutions,
57
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
Well... Not like what is taught in a calculus class.
The methods taught there, are only able to solve
some of the equations that: consist of 1 or more
‘rate-of-change derivations’ of a variable... and can
also simulate a real-world situation. However, if we
can live with estimates, in-place of exact solutions,
then the Integrator block can
help us solve any equation that
consists of 1 or more
‘rate-of-change derivations’ of a variable.
58
An Interpretation of How Simulation Software might Work
The Integrator block
wants to know...
What its output will be
(in DBL format), before it does
its ‘Integration thing’.
And what value to integrate.
(Also in DBL format)
Value...? Isn’t it
suppose to integrate
an equation?
Well... Not like what is taught in a calculus class.
The methods taught there, are only able to solve
some of the equations that: consist of 1 or more
‘rate-of-change derivations’ of a variable... and can
also simulate a real-world situation. However, if we
can live with estimates, in-place of exact solutions,
then the Integrator block can
help us solve any equation that
consists of 1 or more
‘rate-of-change derivations’ of a variable,
a.k.a. Ordinary Differential Equations (ODE)
59
Let’s
look
inside...
60
An Interpretation of How Simulation Software might Work
61
An Interpretation of How Simulation Software might Work
Reset
Button
Solver
62
An Interpretation of How Simulation Software might Work
Reset
Button
Solver
63
An Interpretation of How Simulation Software might Work
Reset
What’s in the
Solver?
Button
Solver
64
Solver
Button
Reset
An Interpretation of How Simulation Software might Work
65
Solver
Button
Reset
An Interpretation of How Simulation Software might Work
66
Solver
Button
Reset
An Interpretation of How Simulation Software might Work
67
An Interpretation of How Simulation Software might Work
Solver
Button
Reset
An Integrator’s Solver has
several solving-formulas at
its disposal.
For most Simulations, no two
Solver-Formulas yield the same
result.
68
An Interpretation of How Simulation Software might Work
Solver
Button
Reset
An Integrator’s Solver has
several solving-formulas at
its disposal.
For a given Simulation, each
Solver-Formula may produce a
different result.
69
An Interpretation of How Simulation Software might Work
Solver
Button
Reset
Note:
A Solver-Formula is
selected, prior to running a
given Simulation.
70
An Interpretation of How Simulation Software might Work
Solver
Button
Reset
Note:
A Solver-Formula is
selected, prior to running a
given Simulation.
71
An Interpretation of How Simulation Software might Work
Solver
Button
Reset
Also note:
The Solver-Formula choice
is made in the Simulation’s
global settings.
So whichever one is chosen, all
of the Solvers in all of the
Integrator blocks in the given
Simulation, use the same one.
72
An Interpretation of How Simulation Software might Work
Solver
Button
Reset
Also note:
The Solver-Formula choice
is made in the Simulation’s
global settings.
So whichever one is chosen, all
of the Solvers in all of the
Integrator blocks in the given
Simulation, use the same one.
73
An Interpretation of How Simulation Software might Work
Solver
Button
Reset
Also note:
The Solver-Formula choice
is made in the Simulation’s
global settings.
So whichever one is chosen, all
of the Solvers in all of the
Integrator blocks in the given
Simulation, use the same one.
74
An Interpretation of How Simulation Software might Work
To be continued...
75