Instructor: Prof. Dan Cobb
Office: 3621 Engineering Hall
Email: cobb@engr.wisc.edu
Office Hours: 3:45 TR
Text: Fundamentals of Linear State Space Systems, John S.
Bay, McGraw-Hill, 1999.
Lecture: 2:30-3:45 TR, 2534 EH
Homework: 1 assignment every 2 weeks
Grading: Exam #1 - 30%, Exam #2 - 30%, Final Exam - 40%
Prerequisites: ECE 330 and (Math 320 or Math 340 or concurrent
registration).
You do not need any previous background in control theory (such as ECE
332). ECE 334 is an entry-level course in the Automatic Control course sequence. (See ECE Undergraduate
Program in Automatic Control.) You will, however, need a solid background
in linear algebra and matrix theory. Coming into the course, you will be expected
to know what a matrix is, how to add and multiply matrices, and how to find
determinants and inverses. Other topics in linear algebra will be reviewed, but
it will help if you already know about eigenvalues, eigenvectors, and linear
independence.
Goals: The course will give you a basic understanding of the state-space
methodology for linear system analysis. The second half of the semester will
emphasize automatic control techniques for closed-loop stabilization and
eigenvalue placement. In contrast to the frequency-domain concepts of ECE 332,
the material in ECE 334 focuses on differential equations and linear algebra.
The course culminates in the development of the "separation
principle" and its implications to feedback control.
|
Week |
Beginning |
Pages |
Topics |
|
1 |
Jan 19 |
3-22 |
state equations, integrator diagrams |
|
2 |
Jan 26 |
515-522 |
vectors, matrices |
|
3 |
Feb 2 |
148-153, 211-215 |
eigenvalues, matrix exponential |
|
4 |
Feb 9 |
229-232 |
solution of state equations |
|
5 |
Feb 16 |
108-114, 155-158 |
similarity transformation, eigenvectors, diagonalization |
|
6 |
Feb 23 |
245-248, 326-330 |
modal expansion, companion form |
|
7 |
Mar 2 |
94-100 |
subspaces, asymptotic stability |
|
8 |
Mar 9 |
232-245, 292-299 |
stable subspace, phase plane diagrams, BIBO stability |
|
9 |
Mar 23 |
311-321 |
controllability |
|
10 |
Mar 30 |
334-339 |
controllability decomposition, stabilizability |
|
11 |
Apr 6 |
311-321 |
observability, detectability, duality |
|
12 |
Apr 13 |
class notes |
Kalman decomposition |
|
13 |
Apr 20 |
405-412 |
state feedback, eigenvalue placement, stabilization |
|
14 |
Apr 27 |
430-433 |
observers, output feedback |
|
15 |
May 4 |
433-438 |
separation principle, minimal conditions for stabilization |