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Running an Optimization 2 - 1©

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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

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