ME 481/581 Class Information

Department of Mechanical Engineering

1. Syllabus, schedule, and other miscellaneous documents.

A syllabus for the course is available as a PDF file. It's not very detailed, but perhaps worthwhile to have...much more detailed is the schedule (Rev. C) for the Spring 2008 semester... just modified to reflect the Final (state-space) Project validation on Wednesday, May 7 (instead of Friday, May 9).

Complex numbers. Some folks are uneasy with imaginary and complex numbers. I wrote this little essay to perhaps help out.

Aliasing demo. On February 22 (Friday) we're meeting at MTTC to view a demo of the effects of aliasing (and the notch filter). Here's a discussion of what you will see. Please look this over before the demo. UPDATE 2/22/08 1503 MST: When does aliasing occur? This is now answered in Section 1.4...

MTTC Map. Here's a map of where the MTTC building is located. This is where the demos and project validations will be held (I think). We will meet in the lobby.

Z-Transform Table. I promised a better Z-transform table... here are page 1 and page 2 of a better Z-transform table. I hope the formatting and resolution are good enough.

MATLAB Tutorial. There are a couple options:

Here is a MATLAB Tutorial prepared by the UNM Math Department (PDF file). It is quite general, and doesn't contain anything about controls.
You can also go to the Mathworks' MATLAB Tutorial...click on the "View Tutorial" below the MATLAB Tutorial heading. You have to register for the online tutorial, and it takes some time, but it is MUCH more comprehensive. Recommended.

2. Homework "hints, etc.."

Here are PDF files containing hopefully helpful hints, answers, plus various handouts for the homework assignments.

Chapter 2 Hints
Chapter 2 MATLAB example (some MATLAB commands...similar to HW Problem 4)
Chapter 3 Hints
Chapter 3 Frequency Response Example (shows some useful MATLAB functions)
DC Gain of Transfer Functions with an Integration (you recall my ill-fated example on the board Wednesday 2/6)
Chapter 4 Hints NOTE: There has been a small update to the discussion of the "train.m" function for Problem 1.
Here is the sinc.m function you should use for Problem 4. The standard MATLAB "sinc" function has a factor of PI which we do not want. Copy and paste this into the MATLAB editor and save it as "sinc.m" in your working directory.
Chapter 8 Hints
quantize.m, a MATLAB function I wrote that performs N-bit quantization of a variable over a given range of magnitude. It's actually very simple. You might find it interesting to quantize the output for one of the ID runs in your HW and see what difference it makes.
Chapter 8 ID Example (I got a little carried away here---I enjoy doing this stuff-- this MATLAB example might help with the Chapter 8 HW)
Chapter 5 HW I Hints
Z-Plane Root Locus Example similar to the "pure inertia" system I will do in class on Friday and Monday. It might be helpful to download this and print it out before class on Friday 3/7.
Chapter 5 HW II Hints. Sorry it took so long. This assignment is optional (extra credit).
Chapter 6 Hints, late as usual... (Note that Problem 2 is not required).
Chapter 7 HW I Hints
Chapter 7 HW II Hints Note that I have added portions to both homework problems. Also, this is the hopefully FINAL revision as of 12:04 p.m. 4/25/08.

3. Homework Solutions.

Here are PDF files containing the entire homework solution, plus a few other things.

Chapter 2 solution
Chapter 3 solution Sorry it's a little late...
Chapter 4 solution
Chapter 8 solution.
idlsq.m, the MATLAB function that I wrote to do least-squares identification. If you use it, please verify that it simply constructs and evaluates equations (8.9--8.13).
Chapter 5 HW I solution with hopefully the errors corrected. Problem 2 is quite similar to the TF project.
Chapter 5 HW II Solution. Not a very complete solution, but perhaps better than nothing.
Chapter 6 solution; you will use this system in Problem 2 of the Chapter 7 HW I assignment when you design a state-feedback discrete-time controller.
Chapter 7 HW 1 solution
Chapter 7 HW 2 solution I also included the analysis on finding the controller and plant transfer function and doing a root locus; this was not required in the assignment.

4. Grading your Homework.

Here is a document describing submission and grading of your homework for the Spring 2008 semester. Please read this carefully and follow the guidelines.

5. Exam Solution.

Here is a PDF file of the exam solution.

6. Semester Project, Part I (Midterm Project)

This is the transform-based portion of the semester project.

The transform-based project assignment is now available. I will hopefully have the input/output data for system ID purposes by Friday evening.
Here is the data.mat MATLAB MAT-file containing the ID data. This should be "right-clicked" (or CTRL-click on a Mac) and "Download link as ..." That should get you a binary MAT-file. Let me know if you have problems. All the data is in this single MAT-file.
Here is A MOVIE showing the ID runs on the single-link rotary positioning system. In the movie, there are:
- Binary random: 501 samples (0..500) at 25 Hz (20 sec total)
- Gaussian random: 501 samples (0..500) at 25 Hz (20 sec total)
- Step response: 16 samples (0..15) at 25 Hz (0.6 sec total)
This should give you an idea of how the data was collected.
Here is a PDF file describing the transform-based controller submission process (Revised April 3, 2008 1151 MDT).
Here are the gpslead.m, gpsPD.m, and gpsPID.m, and gpsPIDlead.m M-files. Be sure to change my "GPS" initials to your own and to change the "XX.XX" coefficients to your own values. Please email these to me as attachments.
Here is a PDF file describing the experimental plot assignment that is due Monday, April 14.
If your simulations differed from the experimental runs, you may wish to compare your simulations to mine (by doing this I reveal the plant model that I used). You will probably have to "right-click" these:
- tf_lead.mdl, the lead compensator
- tf_PD.mdl, the PD controller
- tf_PID.mdl, the PID controller
- tf_PIDlead.mdl, the PIDlead controller

7. Semester Project, Part II (Final Project)

This is the state-space portion of the semester project.

The state-space project assignment is now available. You will be designing both a SISO and MIMO controller for the rotary positioning system. The plant will be the same, so if you were satisfied with your G(z) plant model from before, you don't need to change it.
Here is a design example of a state-space controller for the voltage-controlled DC motor and load of the Chapter 6 and 7 HW. It's similar to the project, and may be helpful. However, it's not the same as the project...
Here are the xyzsiso.m, and xyzmimo.m M-files for submitting your results. I have indicated the correct dimensions for each term as comments. Be sure to change the "xyz" initials to your own and to change the coefficients to your own values. Please email these to me as attachments by 5:00 p.m. on Tuesday, May 6.
Finally, here is the photograph of the RMS errors from the state-space project validations in the MTTC lab. Sorry that these are a few days late, but if you still have time you can comment on any discrepancies in your project reports.
Oops, one more things! I said I'd put my Simulink models online; well here is the SISO model and here is the MIMO model. It turns out I forgot to change the plant to the G(z) that I had used in the TF models, so I did that. My simulated RMS errors increased slightly, and agreed even more closely to the experimental errors.