Basic Concepts

download Basic Concepts

of 23

  • date post

    31-Dec-2015
  • Category

    Documents

  • view

    23
  • download

    0

Embed Size (px)

description

Basic Concepts. Block diagram representation of control systems Transfer functions Analysis of block diagrams P, PI and PID controllers ( Continuous and discrete forms) Stability of feedback control systems. Basic Block Diagram. PID:Process Instrumentation Diagram. - PowerPoint PPT Presentation

Transcript of Basic Concepts

  • Basic Concepts

    Block diagram representation of control systemsTransfer functionsAnalysis of block diagramsP, PI and PID controllers ( Continuous and discrete forms)Stability of feedback control systems

  • Basic Block Diagram

    SYSTEM

    OUTPUT VARIABLE

    INPUT VARIABLE

  • PID:Process Instrumentation Diagram

    TT

    101

    temperature

    transmitter

    Thermocouple

    TC

    101

    temperature

    controller

    cooling water

    inlet

    cooling water

    out

    Feed

    electronic

    transmission line

    Product

    Manual

    Valve

    sensor

    pneumatic line

    Automatic Control Valve

  • Block Diagram of Feedback Control System

    CONTROLLER

    CONTROL VALVE

    TANK

    TRANSMITTER

    WATER FLOW

    VALVE

    Tset

    ERROR

    SETPOINT

    ACTUATOR

    PROCESS

    TEMPERATURE

    Tm (MEASURED VARIABLE)

    SIGNAL TO

    CONTROLLER

    OUTPUT

    MANIPULATED

    VARIABLE

    CONTROLLER

    VARIABLE

    _1026103252.doc

    TRANSMITTER

    CONTROL VALVE

    TANK

    CONTROLLER

    WATER FLOW

    VALVE

    Tset

    SETPOINT

    ERROR

    ACTUATOR

    PROCESS

    TEMPERATURE

    Tm (MEASURED VARIABLE)

    SIGNAL TO

    _1026104132.doc

    TRANSMITTER

    CONTROL VALVE

    TANK

    CONTROLLER

    WATER FLOW

    VALVE

    Tset

    SETPOINT

    ERROR

    ACTUATOR

    PROCESS

    TEMPERATURE

    Tm (MEASURED VARIABLE)

    SIGNAL TO

    CONTROLLER

    OUTPUT

    MANIPULATED

    VARIABLE

    CONTROLLER

    VARIABLE

    _1026103000.doc

    CONTROL VALVE

    TRANSMITTER

    CONTROL VALVE

    TANK

    CONTROLLER

  • Laplace Transform

    embed Equation.2

    _1026104598.unknown

    _1026104631.unknown

  • Common Signals

    Name

    Function, f(t)

    Laplace transform, F(s)

    Unit step function

    embed Equation.2

    Unit impulse function(Dirac delta function)

    embed Equation.2

    1

    Ramp function

    embed Equation.2

    Sine function

    _1026104689.unknown

    _1026104693.unknown

    _1026104695.unknown

    _1026104696.unknown

    _1026104697.unknown

    _1026104694.unknown

    _1026104690.unknown

    _1026104687.unknown

    _1026104688.unknown

    _1026104661.unknown

  • Properties of Laplace Transform

    Property

    Description

    Linearity Property

    Time Delay

    Differentiation

    Integration

    Final Value Theorem

    provided the limit on the left hand side exists.

    _1026104807.unknown

    _1026104814.unknown

    _1026104817.unknown

    _1026104776.unknown

  • Transfer functions

    (BC.3)

    (BC.4)

    (BC.5)

    _1039628288.unknown

    _1039784332.unknown

    _1039628145.unknown

  • Proportional Control

  • Proportional Integral Control

  • Proportional Integral Derivative (PID) Control

  • Common Transfer Functions

    Second-Order Transfer Functions

  • First-Order Plus Dead-Time (FOPDT)

  • Stability of Systems

    (BC.19)

    (BC.20)

    (BC.22)

    _1039629117.unknown

    _1039787936.unknown

    _1040454555.unknown

    _1039787878.unknown

    _1039628913.unknown

  • Location of pole

  • Generalization

  • Stability and Pole Location

    Sustained Oscillations

    Sustained Oscillations

    Oscillatory Decay

    Oscillatory Decay

    Expnential Decay

    Oscillatory growth

    Exponential growth

    Oscillatory growth

    Real Axis

    Imaginary Axis

    (

    (

    (

    (

    (

    (

    (

    (

    "For a transfer function to be stable, all its poles must lie to the left of the imaginary axis in the complex plane, i.e. in the left half plane (LHP)".

  • Stability of Closed Loop Systems

    CONTROLLER ACTUATOR

    PROCESS OUTPUT

    TRANSMITTER

    MEASURED VARIABLE

    y

    set

    +

    e(s)

    m(s)

    q(s)

    y(s)

    EMBED Equation.3 G (s)

    EMBED Equation.3

    EMBED Equation.3

    EMBED Equation.3

    EMBED Equation.3

    -

    _1039670029.unknown

    _1039670828.unknown

    _1039670841.unknown

    _1039670851.unknown

    _1039670840.unknown

    _1039670782.unknown

    _1039669922.unknown

  • Example: Third order process

  • Root Locus

    Table BC.4 Table of roots of the characters equation for various valves of

    Kc

    root1

    root2

    root3

    0.1

    0.2

    0.39

    0.6

    1.0

    10.0

    20.0

    30.0

    60.0

    100.0

    -3.0467

    -3.0880

    -3.1564

    -3.2212

    -3.3247

    -4.3089

    -4.8371

    -5.2145

    -6.0000

    -6.7134

    -1.8990

    -1.7909

    -1.4218 - 0.0542i

    -1.3894 - 0.3442i

    -1.3376 - 0.5623i

    -0.8455 - 1.7316i

    -0.5814 - 2.2443i

    -0.3928 - 2.5980i

    0 - 3.3166i

    0.3567 - 3.9575i

    -1.0544

    -1.1211

    -1.4218 + 0.0542i

    -1.3894 + 0.3442i

    -1.3376 + 0.5623i

    -0.8455 + 1.7316i

    -0.5814 + 2.2443i

    -0.3928 + 2.5980i

    0 + 3.3166i

    0.3567 + 3.9575I

    _1039672039.unknown

  • Root Locus Graph

    Imag Axis

    Real Axis

    6

    4

    2

    0

    -2

    -4

    -6

    6

    4

    2

    0

    -2

    -4

    -6

    B. Joseph 12/30/00 ~WRO1619

  • CONTROLLER TUNING

    EMBED Equation.2

    e(t), Error in control

    B

    Rise time, Tr

    Overshoot, A

    New set point

    0

    1

    2

    3

    4

    5

    6

    0

    0.2

    0.4

    0.6

    0.8

    1

    1.2

    1.4

  • Ziegler Nichols Tuning

    Table BC.5 Ziegler-Nichols tuning correlation

    _1039673091.unknown