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Running an Optimization 2 - 1©
20
12
Ma
thW
ork
s, In
c.
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
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
Running an Optimization 2 - 3
Example: DC Motor
Input
signal
Output
signal
SISO system:
Input = voltage
Output = angle or an angular speed
Running an Optimization 2 - 4
Example: DC Motor
Measured
Input signal
How can we
determine the
input-output
relationship?
Measured
output signal
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
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
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
Running an Optimization 2 - 8
DC Motor’s Equations
Running an Optimization 2 - 9
DC Motor (equation based model)
Running an Optimization 2 - 10
DC Motor’s Space State
Running an Optimization 2 - 11
DC Motor (Space State)
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
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
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).
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)
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)
Running an Optimization 2 - 17
SimElectronics vs Simscape language
Running an Optimization 2 - 18
Black box modeling
Equation-based modelling
Physical Network Modeling
Conclusions
Running an Optimization 2 - 19
Thank you