Control
Systems Design Project – ECE147C
& Advanced Mechanical Engineering Laboratory – ME 106A
Spring 2007
Tu Th 2:00-3:15pm, Building 387,
Room 103
Course summary
The objective of this course
is to provide students with the necessary knowledge to design, implement, and
document a control engineering project.
The course has three components: lectures, prepared laboratories (in the form of a project that is the same for all students), and a design project (specific to each group of students).
The lectures and laboratories cover a range of special topics related to the practical implementation of control systems that are not covered in introductory control courses but that are likely to arise in the professional career of controls engineers. These include:
1. Model identification and parameter estimation (least-square identification of a auto-regressive model; nonparametric identification in the time domain; and nonparametric identification in the frequency domain)
2. Robust Control (Nyquist-plots, small-gain, and passivity)
3. Optimal control (LQR/LQG for state-space systems and time-optimal controller for the positioning of a mass using force actuation)
4. Nonlinear control (Lyapunov’s stability method; feedback linearization controller for a fully actuated 2nd order mechanical system; backstepping for triangular nonlinear systems)
The course is heavily project-oriented and the students will be required to design, implement, document, and present a significant control systems project, which requires them to address the issues covered in the lectures.
Prerequisites: ECE147A or ME155A or ME173 or equivalent. Open to all engineering majors.
Instructors
Bassam Bamieh (bamieh at engineering.ucsb.edu), phone (805) 893-4490, office Engineering II
João P. Hespanha (hespanha at ece.ucsb.edu), phone: (805) 893-7042, office: Frank Hall, 5157.
Teaching assistant
Max Subbotin (maxim_sub at yahoo.com)
Ryan Mohr (mohrrm at engr.ucsb.edu)
Office hours: Tue Wed 9-9:50am, held at
the controls educational lab: Engr. I, 3120A
Textbook
The course will be based on a collection of modules and papers provided by the instructors.
Assessment format
- 1-2 homework
assignments (individual, needed
for the laboratory) – 5 %
- Laboratories
(group mid-term report) – 40%;
- Final Project
(includes a group end-of-term report
and a group in-class
presentation) – 55%
5 units (ECE147C)
- 5-6 homework
assignments (individual) – 25 %
- Laboratories
(group mid-term report) – 35%;
- Final Project
(includes a group end-of-term
report and a group in-class
presentation) – 40%
Projects
The second half of the laboratory time is devoted to the final project.
Possible projects include
- Identification
and control of the seesaw system [in hardware]
- Identification
and control of an inverted pendulum [in hardware]
- Identification
and control of a flexible beam [in simulation]
- Identification
and control of an F-16 [in simulation, model available, e.g., here]
- other … [in
hardware or simulation]
The final project must make extensive use of two out of the four topics taught in the lectures, which are Model Identification, Robust Control,
LQG/LQR, Nonlinear Control.
See due dates below…
Course's Web Page
The syllabus, homework, laboratories handouts, and all other information relevant to the course will be continuously posted at the course's web page. The URL is
http://www.ece.ucsb.edu/~hespanha/ece147c/
Detailed Syllabus
The following is a tentative schedule for the course. As revisions are needed, they will be posted on the course's web page. Recommended readings for the topics covered on each class will be posted in the 3rd column.
|
Class |
Lecture content |
References |
Laboratory |
|
#1 Apr 3 |
Course overview Computer-controlled systems (review) |
Laboratory session enrollment No laboratory class |
|
|
#2 Apr 5 |
Part I—Model identification and
parameter estimation ·
Parametric
identification ·
Least-squares
fitting |
(initially posted
on |
|
|
#3 Apr 10 |
·
ARX
model ·
ARX
model identification |
|
Introduction to laboratory |
|
#4 Apr 12 |
·
Partial
identification (known parameters) ·
Choice
of inputs, model order and sampling frequency
|
|
|
|
#5 Apr 17 |
Nonparametric identification |
Parametric identification of the
two-cart system |
|
|
#6 Apr 19 |
Nonparametric identification (cont.) |
|
|
|
#7 Apr 24 |
Rijke Tube experiment |
|
Parametric identification of the
two-cart system (cont.) |
|
#8 Apr 26 |
Rijke Tube experiment (cont.) |
|
|
|
# 9 May 1 |
Part II—Loop shaping control design |
Review notes on loop-shaping (see also last chapter of Robust
control notes) |
Nonparametric identification of the
Rijke tube |
|
#10 May 3 |
|
|
|
|
#11 May 8 |
Part III—Robust Control ·
Frequency
domain uncertainty ·
Nyquist
criteria |
MATLAB script used to generate the plots in the notes Simulink file for Noisy identification Exercise 2 |
Nonparametric identification of the
Rijke tube (cont.) |
|
# 12 May 10 |
·
Small-gain ·
Loop-shaping
control design |
|
|
|
#13 May 15 |
Part IV—Optimal control: LQR/LQG ·
LQR
problem ·
Solution
to the LQR problem ·
Stability
and robustness |
MATLAB script used to generate the plots in the notes |
Final project |
|
#14 May 17 |
·
Loop-shaping
using LQR ·
Output
feedback ·
LQG
state-estimation |
|
|
|
#15 May 22 |
·
LQG/LQR
output-feedback ·
Separation
principle |
|
Final project (cont.) |
|
#16 May 24 |
·
Loop-gain
recovery ·
Set-point
control |
|
|
|
#17 May 29 |
Part V—Control of Nonlinear systems ·
Feedback
linearization ·
Lyapunov
stability |
|
Final project (cont.) |
|
#18 May 31 |
·
Lyapunov
stability theorem ·
LaSalle’s
invariance principle |
|
|
|
#19 Jun 6 |
·
Liénard equation ·
Lyapunov-based
control design |
|
Project
presentations The
project presentations will take place in the laboratory, June 6 and 7, from
3:30 to 5:30pm. A
computer projector will be available. |
|
#20 Jun 8 |
TBA |
|
Laboratory
There will be weekly laboratory sessions to complement the material covered in the lectures. A portion of the laboratory should be prepared before the lab session.
The following document provides a general description of what the students are expected to do before and during the lab and it also serves as a template for the final lab report that will be turn in the middle of the quarter. The final project report (due at the end of the quarter) should also follow this basic template:
laboratory project
(posted on April 12, 2007), addendum for the Rijke
Tube experiment
The first laboratory class will be on 4/12/2006. The TA will
use this class to introduce students to the equipment. Please print and read
the following handout before the class (you can ignore the pre-lab exercises):
Deadlines & additional information
|
Description |
Due date |
|
Final project topic 1-2
paragraph description of your project. Please make sure that you include the
following information: 1) Which
system do you plan to control? 2) What
variables to you plan to control, which variables can you measure? 3) What
type of closed-loop specifications make sense for that problem? 4) Do you
plan to use simulation or experiments? In case you plan to use simulations,
where will you get the model from? [We may be able to give you a hand here] 5) Which two out of the four topics taught in the lectures (Model
Identification, Robust Control, LQG/LQR, Nonlinear Control) will the project
make extensive use? |
May 3 |
|
Mid-term project report The report,
must follow the template in the handout that you were previously given (http://www.ece.ucsb.edu/~hespanha/ece147c/web/project1.pdf) There is a
strict limit on the page length: at most 10 pages, 10pt. This must include
all figures, plots, abstract, introduction, discussion of results,
conclusions, etc. To fit
everything in 10 pages, you must be very selective in which figures to
include. You will also need to overlay several plots. E.g., you may show the
identified process bode plots for several different inputs all in the same
figure (remember to label everything so that it is clear which line
corresponds to what!). Your report
must also include text (and equations) to explain the process model, to
justify the choices that you made, and to discuss the results that you
obtained. The main objective of the report is to support the claim that the
model that you identified is accurate and that the controller that you designed
is good. You should think of the report as a conference paper and not as a
homework assignment. A significant portion of the grade
will be based on the quality of the report (length, completeness, how well it
reads, etc.) |
May 22 |
|
Final project presentation The
presentations of the final project will take place in the laboratory and take
30 minutes. For group
projects all students should participate in the presentation. The
presentation should use a computer projector. The
presentation should include: ·
presentation
outline ·
description
of the system to be controlled, sensors, and actuators (use pictures!) ·
description
of the control objectives ·
identification
method and summary of the identification results (if the project involves
identification) ·
control
design method and summary of the closed-loop performance achieved ·
simulation
results ·
hardware
results (if the project involves hardware) ·
hardware
demo (if the project involves hardware) ·
conclusions
and discussion of future work |
June 6 and 7, from 3:30 to
5:30pm |
|
Final project report This report
should follow the same guidelines as the mid-term project report. Please read
all comments that you will receive regarding the mid-term project report and
make sure that you follow any advice given when you prepare the final project
report. A significant portion of the grade
will be based on the quality of the report (length, completeness, how well it
reads, etc.) |
June 11 |
Homework assignments
The following exercises should be solved to prepare for the laboratory sessions and to complement the lectures
Please respect the deadlines for the homework assignments. The TA may accept late assignments for a couple of days after the deadline, but these will only get 50% of the full grade. Moreover, once solutions are posted you will get no credit for the assignment.
|
Number |
Posted on |
Due date |
Exercises |
|
#1 |
April 1 |
April 16 |
Exercises 5,
6, 7, 8 of the identification module. Data for Exercise 5 (selected parameters) Simulink file and m-script for Exercise 6 (input magnitude) Data for Model-order Exercise 7 (model order) For the lab
work, you will need to adapt exercise 4 to take into account that the system has
an integrator (instead of a zero at a known location). The MATLAB
scripts for exercises 6, 7, 8 will be useful to perform parametric
identification with the data collected in the lab |
|
#2 |
April 24 |
May 1 |
Download
the exercise from here. |