Homework 6, due April 11, 2014

[goodwine]

You must complete two parts of the pendulum project: 1) system identification and 2) theoretical (paper) design for the control system in the frequency domain.

It is not necessary that you type this as a report.

1) For the system identification part, you must at least validate your model for a few different inputs that weren't the data used for the identification, i.e., use some data to find the damping ratio, natural frequency and scale factor. Plot the step response in both positive and negative directions for different magnitude inputs and compare each of them (on the same plot) with the actual system response. So, what to hand in would be something like "4 step responses are illustrated in the next four plots. I used the first one to determine zeta, omega_n and k to be xxxxxxxx. Using these parameters the next four plots illustrate this model response with the actual response. The differences can be attributed to ...."

Then, you need to figure out, based on simple mechanics, how the system you determined relates to the *inverted* pendulum. You should show your work for this, and submit your inverted pendulum transfer function.

2) I didn't assign specific performance specifications, so you may choose your own. Design a compensator (lead/lag would be best) to achieve reasonable transient and steady state response. Plot what the designed step response should look like using either step() or simulink as a theoretical design verification.

Next week you will implement your controller and then verify it is doing what you intend by making a change in your design and then verifying that the theoretical predictions in how the response changes actually occurs in the real system.