Discrete-time linear systems: solution of difference equations, analysis using z-transforms,
state models and their analysis, state space realization of transfer functions.
Sampled-data systems: sample and hold operations, continuous-time state equations
and their discretizations; transform analysis and discretization of continuous-time
transfer functions; effects of sampling on frequency response, aliasing.
Control design by discretization of continuous-time controllers: the bilinear
transformation and its properties, discretization errors, pole-zero matching.
The following table shows the lecture topics. The events column shows
suggested reading and homework for each week, as well as deliverable dates.
This schedule may be updated as the semester progresses,
so it's a good idea to check this webpage periodically.
| Week |
Date |
Lecture |
Topics |
Weekly Events |
| 1 |
Jan 10 |
1 |
Introduction |
Chapter 0, 2 |
| |
|
2 |
Difference equations (DE's) |
|
| |
|
3 |
The z-transform |
|
| 2 |
Jan 17 |
4 |
Inverse z-transform |
Chapter 2, Homework 1 |
| |
|
5 |
Properties of z-transforms |
|
| |
|
6 |
Solving DE's using z-transforms |
|
| 3 |
Jan 24 |
7 |
State space models |
Quiz 1 , Chapter 2, Homework 2 |
| |
|
8 |
SS --> TF conversion, controllable canonical form |
|
| |
|
9 |
Solution of SS models, computing A^k |
|
| 4 |
Jan 31 |
10 |
Computing A^k |
|
| |
|
11 |
Transient response and pole locations |
|
| |
|
12 |
Sampled data systems, sample and hold |
|
| 5 |
Feb 7 |
13 |
Discretization, computation of e^At |
Chapter 3, Homework 3 |
| |
|
14 |
Computation of G(z) from G(s) |
|
| |
|
15 |
Spectral mapping theorem |
Lab 1 |
| 6 |
Feb 14 |
16 |
Discrete time Fourier transform |
Chapter 4 |
| |
|
17 |
Frequency response and sampling theorem |
|
| |
|
18 |
Stability of discrete-time systems |
Quiz 2 |
| |
Feb 22 |
|
Reading Week
| |
| 7 |
Feb 28 |
19 |
Stability of discrete-time systems |
Chapter 4, Homework 4 |
| |
|
20 |
Controllability |
|
| |
|
21 |
Pole placement |
|
| 8 |
Mar 7 |
22 |
Deadbeat control, intersample ripple |
Chapter 4 |
| |
|
23 |
PBH test and stabilizability |
|
| |
|
24 |
Observability, PBH test and detectability |
Quiz 3 |
| 9 |
Mar 14 |
25 |
Observer design |
Chapter 4, Homework 5 |
| |
|
26 |
Separation principle, pathological sampling |
Midterm |
| |
|
27 |
Minimal order observer |
|
| 10 |
Mar 21 |
28 |
Regulator problem |
Chapter 4 |
| |
|
29 |
Regulator problem |
|
| |
|
30 |
Regulator problem |
|
| 11 |
Mar 28 |
31 |
Regulator problem design example |
Chapter 5 |
| |
|
32 |
Real-time scheduling |
|
| |
|
33 |
Rate-monotonic and EDF scheduling |
|
| 12 |
Apr 4 |
34 |
RM schedulability theorem |
Chapter 6, Homework 6 |
| |
|
35 |
Discretization of controllers |
|
| |
|
36 |
Discretization of controllers |
Quiz 4 |
| 13 |
Apr 11 |
37 |
Discretization of controllers |
|
| |
|
38 |
Review |
|
| |
|
39 |
Review |
|
Homework problems are posted on Quercus for your practice and are also a source
of problems for the quizzes and exams.
The official lab schedule is: PRA01 on F9-12, and PRA03 on M12-15, alternating weeks.
Labs are Matlab-based and performed in groups of one or two. You may select your own
lab partner, or your assigned practical TA can help you form a group.
For Lab 1 we have two help sessions on Tuesday, 5-6pm in the two weeks preceding
the due date of the lab. You can attend either help session or both.
Each group submits a preparation and a lab report or Matlab code (depending on the lab
instructions) on Quercus by 5pm on the due date. Note that
currently we are skipping Lab 4.