Control Number: CE 291F, ME236, EE291. This class
is cross listed between EECS, ME and CE so that students can fit it in their respective
curricula. Announcements:
- 04/26/09. Final project assignment is posted. Scheulde of presentation is set. Final reports are due on the last day of finals.
- 04/26/09. All chapters are posted
- 04/26/09. All lecture notes are posted
- 03/11/09. All notes until differential flatness are posted
- 03/09/09. Project assignment 2 posted, it is due on March 16.
- 02/09/09. Lecture notes for chapter 4 are posted, homework 1 is posted, it is due on Feb. 23 in class.
- 01/28/09. Review session will be on wed. 28 (today), Davis Hall 615
- 01/28/09. 100 words description of project is due on wed. February 4, in class
- 01/28/09. Slides for lecture 2, are posted.
- 01/26/09. Time and location of the class will not be changed.
- 01/26/09. Slides for lecture 1, are posted.
- 01/21/09. Slides for lecture 0, homework 0, chapter 1 to 4 are posted.
- 01/21/09. Preliminary description of projects is posted
- 01/13/09: Updated expanded course description is
available here.
Course
description Course
Description
This
is an introductory course to control and optimization of systems driven by partial
differential equations (PDEs). The first part of the class will focus on fundamental
techniques to solve these equations both analytically (when possible), and numerically.
This part of the course will be accessible to students with exposure to control
and no (or very little) exposure to partial differential equations. The techniques
presented in class will include separation of variables, spectral decomposition,
self-similar solutions, characteristics, complex embedding. The second part of
the class will address stability, control and optimization of these PDEs. It will
be accessible to students without background in control. Stability will be investigated
using spectral analysis. Adjoint-based optimization, Hamilton-Jacobi and differential
flatness techniques will be applied for open loop trajectory design. Lyapunov
techniques will be devised for stabilization and control. The
class will put emphasis on networks. Applications (in particular course projects)
will include networks of one dimensional systems: water distribution channels,
electromagnetic waves in transmission cables, towed cable systems for marine oil
exploration, highway systems, oil drilling, mine ventilation networks, blood circulation
in vessels. Examples in higher dimensions will include 2D or 3D fluid mechanics,
in particular propagation of contaminants in water. Here
is a list of partial differential equations and corresponding applications that
will be covered in class: -
The wave equation
- The
Euler-Bernoulli beam equation (materials)
- The
heat equation (thermosciences)
- The
LWR equation for highway traffic (transportation)
- The
Saint-Venant equations, shallow water equations, Hayami'e equation (hydraulics)
- The
membrane equation (mechanical engineering, MEMS)
- The
Telegraph equation (communication)
- Maxwell’s
equations (electromagnetism)
- Vibrating
string (acoustics)
- Vorticity
equation (aerodynamics)
- Euler’s
equations (fluid mechanics)
An
expanded description of the class is
available here. General
information - There will be 4 homeworks.
- There will be a midterm, open-book, and open notes.
- There
will be one class project. Students are encouraged to bring their own research-related
projects. Projects will be suggested to students (list below), if they need. Students
are allowed to team up for projects, if the scope of the project is large.
Sample
projects
Here
are a few sample projects final presentations (Spring 2007)
- Safe aerial refueling using Hamilton-Jacobi techniques (Jerry Ding,
EECS)
- Control of epileptic seizures in the human cortex (Beth Lopour, ME)
- Using the viability algorithm to develop a value function for an air traffic control problem (Andrew Tinka, CEE)
- Moskowitz surface and fundamental diagram generation (Eric Lew and Shuo Yang, ME)
- Parameter identification for soil dynamic systems (Min Chen, CEE)
- Active water absorber (Matthiew Carney, ME)
- Modeling of single flagellum bacterial motion (Justin Hsia, EECS)
- Modeling river dynamics on the Niger river (Emily Kumpel, CEE)
- Frequency model in open channel with lateral flow (Qingfang Wu, CEE)
Here
are a few sample projects final presentations (Spring 2006)
- Modeling
and Optimization Analysis of Single Flagellum Bacterial Motion (Edgar Lobaton,
EECS)
- Liquid
Phase Boundary Control for Fabrication of Features in Thermoplastic, Micro-Hair
Arrays (Jessica Pannequin, Brian Schubert, EECS)
- The
Generalization and Application of Particular Solutions to Lamb’s Problem
(Greg McLaskey, CEE)
- Active
Control of Suspension Bridges (Patricia Decker, CEE)
- Study
on Level Set Approach to Image Segmentation (Xu Guan, CEE)
- PDE
methods for image processing (Andrew Aquila, EECS)
- Reachability
Analysis for a Lower Extremity Exoskeleton (Kurt Amundson, ME)
- Computing
the reachability of the LWR Equation (Ram Rajagopal, EECS)
- Planar
Cell Polarity in Drosophila melanogaster (Anil Aswani, EECS)
Grading
Your final grade will be determined based on
your performance on homework assignments, the midterm, laboratory results and
final report. Homeworks will include the possibility to extend the results derived
in class to gain additional credit. Homework, midterm and lab will be weighted
as follows: Homework
40% (4 @ 10%)
Midterm
20%
Lab
40%
Projects For
the project, you will be expected to conduct significant work on one of the following
topics, or a topic of your choice related to the material covered in class:
- Modeling
systems with PDEs for control purposes
- Algorithm
design for control and/or optimization of PDE driven systems
- Simulation
tools for control of PDE driven systems
- Hardware
implementation of control and/or optimization algorithms on a PDE driven system
You
will first review the literature on the subject you have chosen.
If you choose your own research topic, you will be responsible for finding the
proper set of articles relevant for your problem. If you choose one suggested
project, some references will be provided to you as a basis for further reading.
Depending on your topic, you will balance your time between algorithm design,
simulation, and/or hardware implementation. In the first weeks of the project,
you will be expected to set up clear goals with the instructor, and a plan to
achieve these goals. You will meet with the instructor several time to assess
the progress made on the project. You will give a short presentation of your project
to the class at the end of the semester. Reporting You
will be expected to write a report, to summarize your work. We suggest that you
use these LaTeX files to write up your report, but you are free to use any editing
software you like. Remember that your report should be written in a way which
is understandable for someone who does not have exposure to the field. Number tables and figures sequentially and refer to them in the
text of the results section. Be sure to label all plot axes and tables and show units
of measure. For calculated quantities, report the
appropriate number of significant figures. Here is a rough outline of what
a good technical report would look like: - Introduction: objectives of your project, background and motivation.
- Literature
review: describe the state of the art in the field; include
all proper references, explain where your project fits.
- Problem
investigated. Describe the physical system you are modeling, eventually describe
the derivation of the model. Pose the problem of controlling the system.
- Control.
If you are deriving your own control or optimization algorithm, include all derivations.
If the derivations are too long, put them in the appendix, in order to have a
clear flow in this section. Summarize your theoretical contributions.
- Simulation.
If you are designing a simulation tool for control or optimization purposes, describe
which algorithms you have used, and how they address your problem. Describe the
software implementation, and the validation of the software (for example on model
problems).
- Hardware
implementation. If you are implementing control algorithms on an experimental
testbed, describe which algorithms you have used, and how they address your problem.
Describe the hardware implementation.
- Results: present the results of your
experiments in tabular and/or graphical form, but include text that organizes
and describes the results to guide the reader through them.
- Discussion:
discuss the results, compare with theory, comment on the significance of
the results, discuss reasons for disagreement, and suggest how the measurements
and the experiment could be improved.
- Summarize the main results and findings of the experiment.
Nothing new here; just provide a brief restatement and summary of what
is already presented in previous sections.
- Bibliography:
list all references used in the text.
- Appendix:
include derivations,
raw data, calculations, and spreadsheets if appropriate.
Course
material
All
course material used for the class can be downloaded from
the following URL.
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