School of Electrical and Computer Engineering
Purdue University
465 Northwestern Avenue
West Lafayette, IN 47907-2035
Ph: (765) 494-6443
e-mail: zak@purdue.edu
T,Th: 9:00--10:15am in EE 226
M,W,F: 12:30--1:30pm
Elements of linear algebra, ordinary differential
equations, calculus of several variables. In particular: matrix manipulation,
linear spaces, quadratic forms, differentiation of real-valued functions of n
variables, gradients, the chain rule. Working knowledge of linear dynamic
systems.
S. H. Żak, Systems
and Control,
MATLAB (a math-tools program)
“Real world” control problems
are non-linear. Design techniques based on the linear system theory have
difficulties with accommodating non-linear effects and modeling uncertainties.
In this course, we study different approaches to the analysis and design of
non-linear and uncertain, dynamical control systems. We then apply these
methods to modeling and analysis of biological systems, specifically two
endocrine systems are analyzed in order to demonstrate the power of non-linear
methods.
Upon completion of the course, the student should
understand common non-linear phenomena. The student will become familiar with
concepts and tools that are useful in the analysis of non-linear systems and in
the design of controllers and observers for such systems. The emphasis will be
on design to show how nonlinear system theory fits into practical applications.
An introduction to modeling of dynamical control systems.
State-plane and numerical methods for solving modeling equations. Linearization
techniques. Stability. Controller and observer design for non-linear systems.
Variable structure sliding-mode control. Vector field techniques. Introduction
to chaos.
·
LaSalle’s invariance principle
o
Video
o
Two
interesting examples illustrating LaSalle’s invariance principle
o
A
generalization of the LaSalle’s principle and its application to the
information systems
·
Observer
design for systems with unknown inputs
·
Potential extra topic
INSTRUCTIONS:
·
The
assignments must be typed. Recommended package for typing math is LaTeX. A
friendly introduction to LaTeX is the book by Jane Hahn, LaTEX for Everyone.
·
Clearly
identify the steps you have taken to solve each problem.
·
Your
grade depends on the completeness and clarity of your work as well as the
resulting answer.
·
Make
sure to cite completely all sources used.
FunWork
#1 ---Submit only
html or pdf file of your MATLAB m-file prepared using the cell mode. Use the
publish button in the toolbar to obtain an html file, or go to the workspace
and type
publish('your
m-file name without extension','pdf')
to obtain a pdf file. Submit
either html or pdf file.
·
Here
is a YouTube
video about hypothyroidism related to the modeling of this assignment.
·
American
Thyroid Association (ATA) Hypothyroidism Booklet
·
Three
fun to read papers on modeling endocrine systems:
·
L. Danziger and G. L. Elmergreen
1954 paper
·
L. Danziger and G. L. Elmergreen
1956 paper
·
L. Danziger and G. L. Elmergreen
1957 paper
·
HPA-HPT axes interconnections
·
Some
papers on modeling hypothalamus-pituitary-adrenal/thyroid axes:
·
Thyroid-pituitary axis model with
delays
·
Modeling the
hypothalamus-pituitary-adrenal axis: A review and extension
·
Dynamics of a simplified HPT model with delays
·
Patient specific modeling of the HPA axis related
to clinical diagnosis
·
Effects of the HPA axis dysregulation
·
Modeling the hypothalamus-pituitary-thyroid (HPT)
axis
·
Implications of HPA and HPT axes
interactions
·
HPA model based human stress estimation
·
Manual for solving delay differential equations with
MATLAB’s dde23
·
A model of
intelligent controller for hypothyroidism treatment
·
FunWork #2
·
FunWork #3
·
FunWork #4
·
FunWork #5
There will be two midterm exams from the material
covered in class. Each midterm will be worth 100 points. The final exam will be
worth 200 points. FunWork assignments will be averaged
out to be worth 200 points. The course grade will be based on 600 points.
|
Cutoffs |
|
|
A, A+ |
540--600 |
|
A- |
500--539 |
|
B+ |
470--499 |
|
B |
440--469 |
|
B- |
410--439 |
|
C+ |
380--409 |
|
C |
350--379 |
|
C- |
320--349 |
|
D+ |
290--319 |
|
D |
270--289 |
|
D- |
250--269 |
|
F |
<250 |
In order to receive consideration, all requests for
re-grades, regardless of type, will have to be submitted within one week of the
return of the exam or homework in question.
|
Exam Schedule |
|
|
Midterm Exam #1 |
Thursday, February 22 in EE 226; 09:00--10:15am |
|
Midterm Exam #2 |
Thursday, April 21 in EE 226; 09:00--10:15am |
|
Final Exam |
TBA |
|
FunWork Schedule |
|
|
FunWork #1 |
Thursday, February 03 |
|
FunWork #2 |
Thursday, March 03 |
|
FunWork #3 |
Thursday, March 10 |
|
FunWork #4 |
Thursday, March 24 |
|
|
Thursday, April 28 |
This page last updated on February 23, 2022