Lecture 1 - Rowan University

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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