black box vs equation-based modeling in simulink€¦ · running an optimization 2 - 1 black box vs...
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![Page 1: Black box vs equation-based modeling in Simulink€¦ · Running an Optimization 2 - 1 Black box vs equation-based modeling in Simulink Paolo Panarese Training Engineer - MathWorks](https://reader034.vdocuments.net/reader034/viewer/2022042314/5f02661b7e708231d4041546/html5/thumbnails/1.jpg)
Running an Optimization 2 - 1©
20
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Black box vs equation-based
modeling in Simulink
Paolo Panarese
Training Engineer - MathWorks
Milano, Sala Gonzaga (30 posti)13:40 – 14:10
Mini-Training Lecture
![Page 2: Black box vs equation-based modeling in Simulink€¦ · Running an Optimization 2 - 1 Black box vs equation-based modeling in Simulink Paolo Panarese Training Engineer - MathWorks](https://reader034.vdocuments.net/reader034/viewer/2022042314/5f02661b7e708231d4041546/html5/thumbnails/2.jpg)
Running an Optimization 2 - 2
Agenda and Learning Outcomes
Black box modeling of experimental data
Equation-based modelling starting from physical laws
Physical Network Modeling
![Page 3: Black box vs equation-based modeling in Simulink€¦ · Running an Optimization 2 - 1 Black box vs equation-based modeling in Simulink Paolo Panarese Training Engineer - MathWorks](https://reader034.vdocuments.net/reader034/viewer/2022042314/5f02661b7e708231d4041546/html5/thumbnails/3.jpg)
Running an Optimization 2 - 3
Example: DC Motor
Input
signal
Output
signal
SISO system:
Input = voltage
Output = angle or an angular speed
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Running an Optimization 2 - 4
Example: DC Motor
Measured
Input signal
How can we
determine the
input-output
relationship?
Measured
output signal
![Page 5: Black box vs equation-based modeling in Simulink€¦ · Running an Optimization 2 - 1 Black box vs equation-based modeling in Simulink Paolo Panarese Training Engineer - MathWorks](https://reader034.vdocuments.net/reader034/viewer/2022042314/5f02661b7e708231d4041546/html5/thumbnails/5.jpg)
Running an Optimization 2 - 5
Lookup Table vs Dynamic System
Case 1: output signal depends on input only.
Then a LUT is a good way to interpolate measured data.
Same input (2 Volt)
with different
output (angles)
at different times
Case 2: output does NOT depend on input only.
Then data are hiding some «memory state » that can be
represented as a dynamic system
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Running an Optimization 2 - 6
System Identification
System identification techniques are useful to estimate
and validate the «best» dynamic system to represent
data, i.e. ARX, Transfer Function, Space State, etc
>> systemIdentification
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Running an Optimization 2 - 7
Black box modeling of experimental data
Equation-based modelling starting from physical laws
Physical Network Modeling
Agenda and Learning Outcomes
![Page 8: Black box vs equation-based modeling in Simulink€¦ · Running an Optimization 2 - 1 Black box vs equation-based modeling in Simulink Paolo Panarese Training Engineer - MathWorks](https://reader034.vdocuments.net/reader034/viewer/2022042314/5f02661b7e708231d4041546/html5/thumbnails/8.jpg)
Running an Optimization 2 - 8
DC Motor’s Equations
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Running an Optimization 2 - 9
DC Motor (equation based model)
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Running an Optimization 2 - 10
DC Motor’s Space State
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Running an Optimization 2 - 11
DC Motor (Space State)
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Running an Optimization 2 - 12
Black box modeling of experimental data
Equation-based modelling starting from physical laws
Physical Network Modeling
Agenda and Learning Outcomes
![Page 13: Black box vs equation-based modeling in Simulink€¦ · Running an Optimization 2 - 1 Black box vs equation-based modeling in Simulink Paolo Panarese Training Engineer - MathWorks](https://reader034.vdocuments.net/reader034/viewer/2022042314/5f02661b7e708231d4041546/html5/thumbnails/13.jpg)
Running an Optimization 2 - 13
Physical Network Modeling
Each system is represented by functional components that
interact with each other by exchanging energy through
nondirectional ports.
Electrical
Energy Conserving
ports
Rotational Mechanical
Energy Conserving
ports
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Running an Optimization 2 - 14
Physical Network Modeling
𝝎
𝑻𝒊
𝑽
𝑽,𝝎: ACROSS variables
𝒊, 𝑻: THROUGH variables
Every energy flow is associated with 2 dual variables:
Across and Through (whose product is energy).
![Page 15: Black box vs equation-based modeling in Simulink€¦ · Running an Optimization 2 - 1 Black box vs equation-based modeling in Simulink Paolo Panarese Training Engineer - MathWorks](https://reader034.vdocuments.net/reader034/viewer/2022042314/5f02661b7e708231d4041546/html5/thumbnails/15.jpg)
Running an Optimization 2 - 15
Across vs Through variables
𝑽,𝝎: ACROSS variables (𝑽 source and 𝝎 sensor in parallel)
𝒊, 𝑻: THROUGH variables (𝑻 source and 𝒊 sensor in series)
![Page 16: Black box vs equation-based modeling in Simulink€¦ · Running an Optimization 2 - 1 Black box vs equation-based modeling in Simulink Paolo Panarese Training Engineer - MathWorks](https://reader034.vdocuments.net/reader034/viewer/2022042314/5f02661b7e708231d4041546/html5/thumbnails/16.jpg)
Running an Optimization 2 - 16
Physical Signals (with Unit)vs Simulink signals (unitless)
Physical Signal
Input port
(from Simulink)
Physical Signal
Output ports
(to Simulink)
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Running an Optimization 2 - 17
SimElectronics vs Simscape language
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Running an Optimization 2 - 18
Black box modeling
Equation-based modelling
Physical Network Modeling
Conclusions
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Running an Optimization 2 - 19
Thank you