# ELEC 4123 Electrical Design Proficiency : Identify Mathematical Model

System Identification
In this task, you are required to understand the dynamic behaviour of the DC MG system and identify mathematical model for it through analysing the actual recoded data and the equivalent Simulink model of the
device as shown in Figure 1. These data are recorded via an Oscilloscope (short-period state-state response
at a high resolution) and an Arduino (long-period dynamic and state-state response).

Four different sets of measured data are available for you to analyse the actual behaviour of the system. The
DC MG was hooked up to a motor driver (TB67H420FTG H-Bridge). Oscilloscope data were recorded for a
period of 50ms at a high resolution during steady-state response (50,000 samples) for duty cycles of 20% to
80%. This provides a detailed behaviour of the system including high frequency noise, low frequency vibration,
input current ripple, and issues with Arduino PWM generator. In reality, we would use a microcontroller to
implement a control system for real time control, so the measurements have to be recorded and processed
by, for example, an Arduino. Therefore, I have recorded the output voltage across a 10Ω high-power load
resistor (which you can use to estimate the output current) as well as reading the PWM signal back into
Arduino (which is useless due to a massive aliasing).
All the tests were carried out with 4 different PWM frequencies, 490Hz, 976.5Hz, 1.96kHz and 7.81kHz (some
other frequencies are also available, but I did not use them like 3.92kHz, 31.37kHz and 62.5kHz). The Arduino
real time operation was compiled in Simulink with a baud rate of 57600. As a result of many overhead codes
used by Simulink, a low-resolution sampling frequency of 100Hz had to be chosen to have a consistent
sampling rate in the recorded data via Arduino. This gives you a practical insight into the impact of heavy
aliasing in the measurements and the impact of quantization and down-sampling noise introduced into the
data, which you need to consider when using these data for dynamic modelling.
Another practical aspect of this task is to investigate how the PWM control affects the operation of the DC
motor. It is known that a DC motor can be more efficiently controlled through changing the duty cycle of the
PWM (compared to using a linear voltage regulator) because the DC motor responds to the average value of
the PWM signal (think why that is the case!). However, this introduces new issues for the motor such creating
input current ripple and triggering some nonlinearity (think about what the impacts of the large current ripple
are or what happens to the H-Bridge switching MOSFETs if the frequency of PWM is too high). There is a
technique called motor current smoothing where a motor choke is added in series with the positive terminal
of the motor to reduce the ripples. But you have to consider a trade-off between the size of the current
smoothing inductance and the PWM frequency. You need to think about and make a choice on their values
for this task (there are other techniques like LC filtering which you might want to look into as well).
The Simulink model of the system is shown in Figure 2. You will be provided with nominal estimated
parameters of an actual DC MG to derive two transfer functions, one with the load resistance voltage (