INC 341 Feedback Control Systems

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INC 341 Feedback Control Systems

• ?????????????
• ??.??. ???? ????????????
• ??. ??????? ????????????

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??????????????????????
Office ?????????????? INC CB40603 (CB4 ????
6) Tel x-9094, x-9101 E-mail
poj.tan_at_kmutt.ac.th benjamas.pan_at_kmutt.ac.th Of
fice hours ??? e-mail ????????????????? ????????
? lecture ?.?. ?????? lecture ???????????????????
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Course Webpage
http//www.inc.eng.kmutt.ac.th/inc341/
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??????????????

• 3 ????????
• Lecture 3 ?????????????????
• ????? ???????????? 3 ?????????????????
• Prerequisites
• INC212 Signals and Systems
• (????.?.?????????????????????????????
• time-domain ??? frequency-domain)

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?????????????????????
??????????????? Midterm exam 40 Final
exam 40 Assignments 20
???? ?????????????? distribution curve
????????????????????????????????
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Textbooks

• "Control Systems Engineering", Norman Nise, 4th
  Edition, John-Wiley Sons, Inc., ISBN
  0-471-445770 , 2003.

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Textbooks

• ???????????
• Control Systems Engineering, Norman S. Nise, John
  Wiley Son
• ????????????
• Control Systems Principles and Design, M. Gopal,
  McGrawHill
• Modern Control Engineering, Katsuhiko Ogata,
  Prentice Hall
• Feedback Control Systems, Charles L. Phillips
  and Royce D. Harbor,
• Prentice Hall

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Topics
Week 1 Introduction to Feedback Control
System Week 2 Differential equation to transfer
function Week 3 Differential equation to
transfer function (cont.) Week 4 Differential
equation to state space model Week 5 First-order
Second-order systems Week 6 Stability Week
7 Steady-State Errors Midterm Exam Week 8 Root
locus 1 Week 9 Root locus 2 Week 10 Lead-lag
compensation 1 Week 11 Lead-lag compensation
2 Week 12 Intro to Freq Response Week 13 Freq
Response (Nyquists Criterion) Week 14 Freq
Response (Bode plot) Final Exam
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Global View
Obtaining Math Models week 1-3 Transfer
function State Equation Characteristic of
Systems week 4-7 Basic Properties Stability Ste
ady state error Analysis Methods Root
locus week 8-11 Frequency Response week 11-14
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e-learning Materials
Full archives of lecture VDO are available. One
DVD disc will be given to the representative of
class.
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Important !
Watch VDO before coming to class !!!!
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????? ?
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What is a control system?

• Subsystems and processes (plants) assembles for
  the purpose of controlling the outputs of the
  process.
• Example AC, elevator, antenna system, remote
  controlled robot
• Why do we need to study???
• Example student performance (inputstudy time,
  output grade)

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Overall picture of the class?
??????????????????????????
???????????????????????????????? input
????? ???????????????????? input ???????????
output ?????????????
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Block diagram
???????????????????????? block diagram
Output y
Input, u
'System' or 'Plant'
??????????????????????? input/output ?????????????
???? input ???????????????? output ??????????
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Block Diagram
Transfer function ??? ????????????????????? ???
output ??? input ??? ??????????? frequency domain
Input
Output
System H(s)
X(s)
Y(s)
Transfer function
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How to get a block diagram?
Physic Theorem
Electric Circuits
Mechanics

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Examples
Output, ???????
Input, ???
Elevator
F
x
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?????????? system ????? control
Newtons Second Law
Force Mass x Acceleration
Input ???
Output ???????
Question how is acceleration related to distance?
Now, we know how much force to put in to get a
desired distance
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Control Systemscan be viewed as

• Open-loop Systems
• Closed-loop Systems

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Open-loop system

• Disturbance can easily be found in most systems
• Need a controller to adjust input to plant
• Called it as open-loop system

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Open-loop system (cont.)

• Advantage
• Cheap and easy to design
• Disadvantages
• Sensitivity to disturbances
• Inability to correct disturbances
• Example toasters

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Closed-loop system

• ?????? output, ???????????????????????????
  feedback path, ??????????????????????? ??? input

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Closed-loop system (cont.)

• Advantages
• Less sensitive to noise, disturbances, changes in
  environment
• More flexibility to control system
• Disadvantage
• More expensive!!!
• Example air condition (AC)

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Open-loop vs Close-loop
Open-loop ??????? input/output block diagram
?????????? output ??????????????? Close-loop
???????/??????? output ?????????????????? ????????
??????????????????????????????
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3 terms needed to know

• Transient response ?????????????????????????????
• Steady state response ???????????????????????????
  ?????????????? (??????? transient response has
  decayed to zero) ???output ????????????????
• Stability most important thing in analysis and
  design objectives

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Transient and steady state response
?????????????
?????????????????????????????
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??????????? Design ???? control system
?? specification ???????
??????????????????? Block Diagram
?????????????????? Schematics
?? transfer function ???????? block
????? Block Diagram
????????????? ?????
Diagram ??????????????? Norman S. Nise
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Analysis and design of FCS
Analysis and design
Modern Control ??????????????? Time domain (Ch. 3)
Classical Control ??????????????? Frequency
domain (Ch. 2)
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Analysis and design of FCS
Analysis and design
Modern Control ??????????????? Time domain (Ch. 3)
Classical Control ??????????????? Frequency
domain (Ch. 2)
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Chapter 2
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Block diagram to differential equation

• ???????????????????????? input ??? output
  ????????????????????? differential equation, i.e.
  
• ?????????????????????????????????????????
  ?????????????????????
• ????????????????????????? ?????????????????
  output ??????????????? input

Input ???
Output ???????
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Solution to differential equation

• Easy way Matlab
• Labored way solve by hand
• In frequency domain Laplace (Ch 2)
• In time domain
• state space representation (Ch 3)
• homogenous and non-homogenous solution
  (????????????? class ???)

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Frequency Domain
Convolution
Time domain solution
Linear differential equation
Time Domain
Laplace Transform
Inverse Laplace Transform
Freq Domain
Laplace Solution
Laplace transformed Equation
Algebraic manipulation
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Metaphor of Laplace Transform
(1,1,1)
(2,-3,0)
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Laplace Transform

• Use formula
• table

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Laplace transform properties
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example

• ??? Laplace transform ?????????????????
• (assume zero initial condition)
• Solution

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Inverse Laplace

• Formula
• ????????????????????????? ??????????????????????
  Polynomial

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example

• ???????? Laplace transform ?? differential
  equation ??? transfer function
• (assume zero initial condition)
• solution

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??????????? Design ???? Control system
?? specification ???????
??????????????????? Block Diagram
?????????????????? Schematics
?? transfer function ???????? block
????? Block Diagram
????????????? ?????
Diagram ??????????????? Norman S. Nise
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Transfer Function of Subsystems

• Electrical Systems
• Mechanical Systems
• Translational
• Rotational
• Electromechanical Systems

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??????? !! Transfer function ??????????????????
input, output ?? frequency domain
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Procedure

• ???????? input ??? output ???????
• ????????????????????????????????????????????
  input ??? output
• Ohms law VIR
• Kirchoffs law
• Newtons laws of motion fma, etc.
• Hookes law of stiffness fkx
• Damper characteristics fcv

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Electrical System Components
Impedance Admittance
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Example
?????? input ??? v(t) output ?????????????????
vc(t)
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??? impedance ??????????????? (????????????????
frequency domain)
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Kirchoffs Voltage Law
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Another Example
Find
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Operational Amplifier (OP-AMP)
Ideal amplifier has A infinity. In practice A
is large (105 to 107)
Implications
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Inverting Amp
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Example
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Non-inverting Amp