EE 231 Laboratory Exercise 01

System Modeling

As discussed from the lectures, one way of coming up with a
mathematical model of a system is to look at the physics of the process 
and write down differential equations that govern the process.  
We saw this in modeling electrical, mechanical, electromechanical 
and thermal systems.  However, this procedure may not apply in some cases.
One such scenario is where you do not have physical access to the
internal components of the system and thus are not able to determine
what components are in the system much less know how they are interconnected.

Another way to model your system is by looking at the actual step response
of the physical system.  From the actual step response, 
you first try to identify a general system transfer function that
will have a theoretical step response similar to the actual step response.
Then, you find the system parameters of the general system transfer function
such that the theoretical step response from your identified transfer function
closely matches the actual step response.

For this exercise, 
you are given the data points of the actual step response of an unknown system.
The system started from zero initial conditions when the response was gathered. 
The data points were sampled at 100 ms intervals.
You are required to determine the transfer function of the unknown system.

For your lab report, you need to 

1. Determine the general form of the transfer function.
Plot the actual step of the unknown system and
determine a general form of a system (transfer function)
that has response similar to the actual response.
Discuss why you arrived at that general form.
Use a transfer function with the lowest possible order
that will capture the behavior of the unknown system.

2. Completely identify your system. 
Determine the system parameters of your identified transfer function, and
discuss thoroughly how you were able to get the parameters.

3. Compare the step responses. 
Plot the actual step response of the unkwown system and 
the theoretical step response of your completely identified system
in one graph.  Plot the modeling error, i.e., the difference
of the actual and theoretical step responses.
Discuss your results.