MTRE 4000
Advanced Controls
Spring 2015
Dr. Chan Ham
Class Schedule:
• Jan. 6th: Class overview
• Jan. 8th: Quiz#1, reviewing of control & math background
• Jan. 13th: Sign up for class, agreement with class (name,
email address, and signature) & 1st Lecture (Ch. 13)
1. Attendance check by 10:00AM
2. Lecture notes will be posted: spsu.pbworks.com
Required technical background: Quiz#1
Closed-book & closed-note. No calculator
•
Matrix: inverse & determinant
•
Laplace Transform (LT): including partial fraction
expansion & inverse LT
•
Modeling of system dynamics (Transfer Function):
mechanical & electrical
•
Mason’s rule: find a Transfer Function for a system
given by a block diagram
Class Jan. 6th
• Introduction to class: syllabus, major policies, and
grading scheme
• Class overview: subjects
• Review of EE 4201 & Mathematical Backgrounds (Quiz)
– Mason’s rule
– Laplace Transform: including partial fraction
expansion & inverse LT  z-transform
– Modeling of system dynamics: mechanical & electrical
– Matrix: inverse & determinant
Intro. to Class
• Office Hours: Q322, [email protected]
– M 8:30 AM – 11:00 AM & Wed 2:00PM – 4:30PM
– By appointment (email preferred)
• Class Website: http://spsu.pbworks.com/
– Announcements, solutions, etc
• Policy: Attendance, HW, Test, & Others
– Read class syllabus
– No laptop or electronic devices during the class
– Make sure everybody's fairness!
Tests: 60%, Open-book for Test 1~3
Will be announced at least one week in advance. The tentative
coverage is:
1. Test 1: Digital Control Systems
2. Test 2: State-space Variable Modeling (SVM) & Analysis
3. Test 3: Control Design (SVM) & Modern Control Theories (15%)
4. Final Exam: Comprehensive, closed book & notes
• 20 % each except Test 3 (count only the best 3 out of 4)
• With “Best 3 out of 4” arrangement you may elect either to
drop or not take (regardless of your reason) any one of the four
scheduled tests  No make-up
• If missed two tests with the written excuse from the instructor
 Final may be 40% (35% if one of missed exams is TEST 3)
Homework and Quiz: 25%
HW: assigned regularly, mostly once a 1~2 weeks
1. Grade only one problem randomly chosen  Quiz if HW
isn’t collected (solutions will be posted in advance)
2. One problem/page
3. Grading:
– 10 points: correct answer & work all problems
– 7~9 points: showed all necessary works regardless of
the correctness of the final answer
– 7 points: Late, but with all necessary works (within a
week)
– 4 points: on time, but same as the solution
– Any violation: 1~2 penalty points/violation
Homework and Quiz: 25%
• HW is due at the beginning of the class (tardy -3 points
after 10:00 AM).
• Students are encouraged to work together  Just
don’t copy each other or from solution manual
• HW: is based on the 5th ed. (solved the 6th ed.
Problems?  - 2 penalty points) & will be posted.
Project: 20%
1. Both individual & term projects
• Individual: Matlab/Simulink Simulations
• Team, term project: 1~3 students
2. Topics (team project)
1) Design of a control system for a dynamic system:
• Analysis, modeling, and design of a control system
• Simulation using Matlab / Simulink
2) Survey and investigation of a state-of-art control or
mechatronics system  Preparing Sr. Design Project
3. Introduction to the Project – on 1/22
4. Project Schedule (TBA)
– Proposal & Approval  Mid Report  Final Report & PPT
Slides (Presentation by invitation)
Attendance
• Attendance: mandatory
1. May be checked by HW submission & return: in case
did not do HW, still submit a paper with your name
2. Also randomly checked
3. May be used as a bonus
4. Late attendance is counted as a half absences  - 2
penalty points/absence from the final class credit
after 1.5 absences (e.g. two absences cause -4 while
no penalty is given for 1.5 absences)
Introduction to Class
1. Major Topics
– Mechatronics: Systems & Control
– Basic theories and technical inspirations!
– Control system applications
2. Direction, coverage, and policy
– Interested in control or not? For a good control or
intellectual foundation
– Essential for an interdisciplinary work and
collaboration
– For learning or just credits  should be fair!
Design of a Control System
Class is based on linear systems exactly modeled
Mathematical Backgrounds – Operational Calculus
Matrix: State-space Variable Method
Z-Transform: Digital control system analysis & design
Major Class Subjects:
Modeling & Control of dynamic systems
1. Digital control: Ch. 13
2. State-space Variable Method (SVM): Ch. 2 ~ 7
3. Advanced control theories/techniques: Ch. 12
1. Digital control
– Discrete-time systems / z-transforms for analysis and
design of digital control systems
2. State-space Variable Method (SVM)
• An alternative method for System modeling using time-domain
methods:
nth order system (nth order DE)  n # of 1st order DE 
One 1st order DE
• Utilizing a (non-unique) set of variables
– x1(t), x2(t), …, xn(t)
– function of time
– describe the future response if initial condition is known
• In matrix form
• Readily to computer solution & analysis

x (t )  u( t )


x(t ) 
2
d x
dt
2
 u( t )
3. Advanced Control Theories/Techniques
•
•
Advanced controls
– Fundamentals of modern control systems controllability, observability, Ackerman’s formula,
and pole placement
– Control algorithms: optimal control
Systems & applications (Project)
– Application of various control systems
– Robotics, Maglev, Satellite – attitude control & orbit
changing
– Computer (Matlab/Simulink) simulations
Covered in this class: Linear Systems
1. Principle of Superposition
f ( x1 )  f ( x 2 )  f ( x1  x 2 ) ex.
f ( x)  3 x,
f ( x)  x
2. Homogeneity
If output is y for input x  y = βx for input βx where β:const.
3. Linearization: Taylor series expansion
– For small range around operating point
– Laplace Transform: only for linear system
– Example: pendulum oscillator
But, SVM can also be applied to nonlinear systems!
(spring board to advanced controls!)
2
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Class overview - spsu