Mathematical Models
SYSTEMS AND CONTROL I
ECE 09.321
09/04/07
–
Lecture 1
ROWAN UNIVERSITY
College of Engineering
Prof. John Colton
DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING
Fall 2007

Semester One
2
Welcome to Systems and Control I
Course Learning Objectives
●
Develop mathematical tools for analysis and design of modern
feedback control systems
●
Apply these tools to many types of closed loop feedback control
systems, evaluating the beneficial effects that feedback provides
for steady
–
state and transient performance of these systems
●
Evaluate the beneficial implications of feedback on system
performance, including sensitivity to parameter variation,
tracking, and disturbance rejection
●
Develop the design criteria and tools for optimizing closed loop
system performance and ensuring system stability
●
Develop tools for frequency response analysis and design of
feedback control systems.
●
Use MATLAB for assignments and lab projects to supplement
direct calculations
3
Systems and Control I Topics
●
Historical Perspective
●
Mathematical models and tools: differential equations of
physical systems, Laplace transforms, convolution integral
and impulse response, transfer functions, block diagram
manipulation, and signal flow graphs
●
Closed loop system performance: sensitivity reduction,
disturbance rejection, transient performance and steady

state error, use of s

plane for analysis and design, cost of
feedback, design criteria and tools, frequency response
methods
●
Stability of feedback control systems: stability concepts,
Routh

Hurwitz Stability Criterion, root locus design methods,
Bode diagrams, phase and gain margin, Nyquist stability
criterion
●
Design of feedback control systems
4
●
Lectures M/W 9:50 AM

10:40 AM Rowan 102
●
Laboratories T 3:15 PM

6:00 PM Rowan 239
●
Course Website:
users.rowan.edu/~colton/fall07/systems/index.html
●
Required Text:
Modern Control Systems
, Dorf and Bishop,
11
th
Edition 2007, ISBN: 0132270285
●
Syllabus: see website (read ahead in text
–
Chapters 1/2)
●
Problem Sets: see website (issued each Wednesday, due 9:50 AM
the next Monday
–
show all work for any credit,
no
credit for
late problem sets)
●
Labs: see website (labs conducted Tuesday, reports due 12:15 PM
the next Tuesday
–
lab report format,
no
credit for late lab reports
●
Course announcements: made regularly in class
●
Email: check regularly (daily)
Course Potpourri
5
Learning Evaluation
Grading Policy
●
6 Quizzes 30%
●
Final Exam 40%
●
Assignments and labs 30%
─
Problem Sets and Class participation (15%)
─
Lab Reports, participation, homework (15%)
6
Introduction to Control Systems
●
Historical perspective
●
Introduction to Feedback Control Systems
●
Closed loop system examples
7
Historical Perspective
●
13.7B BC
Big Bang
●
13.4B
Stars and galaxies form
●
5B
Birth of our sun
●
3.8B
Early life begins
●
700M
First animals
●
200M
Mammals evolve
●
65M
Dinosaurs extinct
●
600K
Homo sapiens evolve
8
Feedback Control Systems emerge rather recently
●
1600
Drebbel Temperature regulator
●
1781
Pressure regulator for steam boilers
●
1765
Polzunov water level float regulator
9
Closed loop example: Polzunov’s Water
level float regulator
10
Feedback Control Systems emerge rather recently
●
1600
Drebbel Temperature regulator
●
1681
Pressure regulator for steam boilers
●
1765
Polzunov water level float regulator
●
1769 James Watt’s Steam Engine and Governor
11
Closed loop example: James Watt’s flyball
governor
12
Feedback Control Systems emerge rather recently
●
1600
Drebbel Temperature regulator
●
1681
Pressure regulator for steam boilers
●
1765
Polzunov water level float regulator
●
1769 James Watt’s Steam Engine and Governor
●
1868 James Clerk Maxwell formulates a mathematical model for
governor control of a steam engine
●
1927
Harold Black discovers and patents the feedback amplifier
●
1927 Hendrik Bode analyzes feedback amplifiers
●
1932
Nyquist develops methods for analyzing feedback amplifier
stability
13
Open loop and closed loop control systems
Open Loop System
14
Open loop and closed loop control
system models
Open Loop System
Closed Loop System
15
Example: Feedback Control Amplifiers
16
Feedback Control Systems emerge rather recently
●
1600
Drebbel Temperature regulator
●
1681
Pressure regulator for steam boilers
●
1765
Polzunov water level float regulator
●
1769 James Watt’s Steam Engine and Governor
●
1868 James Clerk Maxwell formulates a mathematical model for
governor control of a steam engine
●
1927
Harold Black discovers and patents the feedback amplifier
●
1927 Hendrik Bode analyzes feedback amplifiers
●
1932
Nyquist develops methods for analyzing feedback amplifier
stability
●
1940s Norbert Wiener leads gun positioning effort; feedback control
engineering becomes an engineering discipline
●
1950s Increased use of Laplace transform, s

plane, root locus
●
1960s Sputnik, highly accurate control systems for space vehicles,
●
robotics, and missiles
●
1980s Routine use of digital computers as control elements
●
1990s Feedback control in automobiles, automation, planetary
exploration
17
Example: Feedback in everyday life
18
Quotable Quotes
●
“Take warning! Alternating currents are
dangerous! They are fit only for powering the
electric chair. The only similarity between an AC
and a DC lighting system is that they both start
from the same coal pile.”
Thomas Edison
–
Pamphlet of 1887
●
“Heavier than air flying machines are impossible”
Lord Kelvin
–
Royal Society 1895
●
“There is no likelihood man can ever tap the
power of the atom”
Robert Milliken Nobel Laureate Physics 1923
19
Multivariable Control System Model
20
Multivariable Control System
21
Robotics
A robot is a programmable computer integrated with a machine
22
Example: Disk Drive
23
Example: Automatic Parking Control
24
Feedback Control: Benefits and cost
Benefits:
Cost:
25
Feedback Control: Benefits and cost
Benefits:
Cost:
•
Reduction of sensitivity to process parameters
•
Disturbance rejection
•
More precise control of process at lower cost
•
Performance and robustness not otherwise achievable
26
Feedback Control: Benefits and cost
Benefits:
Cost:
•
More mathematical sophistication
•
Large loop gain to provide substantial closed loop gain
•
Stabilizing closed loop system
•
Achieving proper transient and steady

state response
•
Reduction of sensitivity to process parameters
•
Disturbance rejection
•
More precise control of process at lower cost
•
Performance and robustness not otherwise achievable
27
Homework for next week
●
See website for Problem Set 1
–
Due Monday 09/10
8 AM
–
Show
all work
for any credit
●
See website for Lab Assignment 1
─
Mostly reading tutorials
─
Report due Monday 09/10
12:15 PM
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