# ECE 486 Control Systems Lab (Fall 2017)

 Day 1 Day 2 Day 3 Day 4 Short labs, weekly Day 5 Day 6 Day 8 Long labs, biweekly Day 7 Day 9 Day 10 Day 11 Final project, weekly

## Week 2 – Final Project: Reaction Wheel Pendulum

Day 91 of ECE 486 Lab, Week 2 of Final Project.

### What Chapters Should We Complete during Second Week?

First off, for those who have not yet demoed the frictionless motor at the end of Chapter 2, they are encouraged to show the demo at the beginning of this lab.

#### Chapter 3

In this chapter, we want to undergo system identification so that we can get numerical information about parameters of equations of system dynamics (Eqn. 18 in the manual).

We are going to calculate

• $J \hspace{.7em}$ - based on its definition as in Eqn. 3 in Chapter 1.
• $m \hspace{.55em}$ - the mass sum of both rotor and pendulum arm (motor included) as in Eqn. 4 in Chapter 1.
• $l \hspace{1.15em}$ - based on its definition as in Eqn. 5 in Chapter 1.
• $\omega_{\rm np}$ - based on its definition as in 1-b in Chapter 1.

We will measure

• $\omega_{\rm np\ meas}^\prime$.

If $\omega_{\rm np\ meas}^\prime$ is close to the calculated $\omega_{\rm np}^\prime$ then you can ignore Eqn. 17 and use this measured $\omega_{\rm np}$ in your script for a = wnp^2.

Finally, use the script from course website to calculate $b_p$ and $b_r$.

#### Chapter 4 (First Half)

A useful fact to consider is the linearization of sine function around $\pi$.

$\sin(\delta \theta_p + \pi) \approx - \delta \theta_p.$

Why we want to consider $\pi$ position? How is it related to the state vector $x = (\delta \theta_p, \dot{\theta}_p, \delta \theta_r, \dot{\theta}_r)^T$?

### A Few Suggestions

• A recap of suggested schedule of Final Project,

 Week 1 (Oct 30) Complete Chapter 1 - 2 Week 2 (Nov 30) Complete Chapter 3 - 4 (first half) Week 3 (Dec 7) Complete Chapter 4 (second half) - 5 Week 4 (Dec 14) Complete Chapter 6 - 7 or catch-up
• Important: A TA is not supposed to give “hand-holding” guidance during the period of students’ Final Project. There is no constraint on how fast or how much work each group needs to complete each week. Students can go as fast as they wish. But it is always strongly recommended that students document their work each week and write up pieces of Final Project Report on the go. Start typesetting Final Project Report one day before it is due is the very first thing each group should avoid.
• There is no official template for the report so students are free to design their own. However all questions in the guidelines should be responded to with clear answers; these are the minimum requirements of the report.
• Since we are going to use Simulink™ Windows Target®, it is not a good idea to run your files from a network path. For example, you may need to create a folder named after your NetID in local C:\ drive and save your Matlab WinTarget files there. Move the folder to your thumb drive once you are finished.

Always keep C:\ drive clean and organized.

• To protect the RWP module, make sure power cords and data cable are firmly plugged in before turning on the power strip.
• As for exporting data, a scope block is recommended. To save data, click the gear icon (options) then go to Logging tab and name your data variable. Use Save format Array.
• Each time you are done with the RWP, you are supposed to restore the RWP back to the cabinet; you can work on the final project any time you want but you are not supposed to take it outside the lab.
• Always clean up before exiting. Specifically,
• Clean up bench table, restore pot, motor lock etc, reinstall screws;
• Sort out wires color by color, type by type and put them back to racks;
• Turn off oscilloscope, meters etc;
• Restore chairs.

## Follow-up

Note: Please take warnings in today’s mass email seriously.

I hope you are progressing towards the last chapter of the Final Project. Here are some comments on the remaining two labs.

• I have to clarify one thing: it is not the case that there is always a demo at the end of a chapter. The official three are:
• Frictionless motor (or reasonably good friction compensation block) at the end of Chapter 2.
• A working state feedback controller that can stabilize pendulum arm around unstable equilibrium position $\theta_p = \pi$ at the end of Chapter 4.
• A working state feedback controller based on estimated state vector by a working observer at the end of Chapter 5.
• Next meeting (Thu, Dec 7) is for Final Project Week 3, the remaining half of Chapter 4, and Chapter 5. So you need to finish Chapters 3 and 4 by the first hour of next lab and save yourself some time to finish all Chapters 1–7 by the end of our last lab (Thu, Dec 14, it is Reading Day but I will run our lab).
• I need to remind you of the due date of Final Project Report: it is Mon, Dec 18. (drop-off in lab) All demos should be finalized by the Friday before, i.e., Dec 15. That’s almost 20 days ahead but again you are encouraged to work on it early, e.g., you can write something up to the point where you have already showed me the demo. Please don’t wait and wait, then rush into it at last moment.

### Due Date

Demos should be finalized by 5pm on Dec 15 and Final Project Report is due 5pm on Dec 18. Final Project Report must be typeset.

### Questions

You are always very welcome to stop by office hours on Mondays. Emailing questions is another way. You can always include [ECE486]blah in the title of your question emails.

Spot any typos? Email me at once. You will earn up to +5 points for each typo/technical error reported.

## Footnotes:

1
There are only three lab sessions left including this one.

Last updated: 2017-11-30 Thu 21:23