Introduction to Control Systems

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Introduction to Control Systems
G(s)
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Course Objectives

• To provide a general understanding of the
  characteristics of dynamic systems and feedback
  control.
• To teach classical methods for analysing control
  system accuracy, stability and dynamic
  performance.
• To teach classical control system design methods.

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Course Contents

• Introduction to control systems
• Modelling of the physical systems
• Time domain analysis, Laplace transforms,
  Transfer functions, System Responses
• Closed loop control systems
• Classical design in the s-domain
• Classical design in the frequency domain
• Digital control systems
• Nonlineer control systems, on/off control
• Design examples

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Course Book

• Advanced Control Engineering
• Roland S. Burns
• Butterworth-Heineman
• Paperback, 464 pages, publication date
  OCT-2001ISBN-13 978-0-7506-5100-4ISBN-10
  0-7506-5100-8

http//www.elsevier.com/wps/find/bookdescription.c
ws_home/677158/descriptiondescription
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Introduction to Control Systems
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Control System Concepts

• A system is a collection of components which are
  co-ordinated together to perform a function.
• Systems interact with their environment across a
  separating boundary.
• The interaction is defined in terms of variables.
• system inputs
• system outputs
• environmental disturbances

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Systems
Disturbance Inputs
System Outputs
System
Engineering systems Biological systems Information
systems
Environment
Control Inputs
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System Variables

• The systems boundary depends upon the defined
  objective function of the system.
• The systems function is expressed in terms of
  measured output variables.
• The systems operation is manipulated through the
  control input variables.
• The systems operation is also affected in an
  uncontrolled manner through the disturbance input
  variables.

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Car and Driver Example

• Objective function to control the direction and
  speed of the car.
• Outputs actual direction and speed of the car
• Control inputs road markings and speed signs
• Disturbances road surface and grade, wind,
  obstacles.
• Possible subsystems the car alone, power
  steering system, braking system, . . .

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Antenna Positioning Control System

• Original system the antenna withelectric motor
  drive systems.
• Control objective to point theantenna in a
  desired reference direction.
• Control inputs drive motor voltages.
• Outputs the elevation and azimuth of the
  antenna.
• Disturbances wind, rain, snow.

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Antenna Control SystemFunctional Block Diagram
Wind force
Antenna System
Angular position
volts
torque
volts
power
Ref. input
_
Antenna
Motor
Power amp
Diff. amp
Error
volts
Angle sensor
Feedback Path
Physical Variables
Information Variables
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Control System Components

• System or process (to be controlled)
• Actuators (converts the control signal to a power
  signal)
• Sensors (provides measurement of the system
  output)
• Reference input (represents the desired output)
• Error detection (forms the control error)
• Controller (operates on the control error to form
  the control signal, sometimes called
  compensators)

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Feedback System Characteristics

• Consider the following speed control system

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Open Loop System Characteristics

• The accuracy of the open loop system depends upon
  the calibration of the gains and prior knowledge
  of the disturbance (choose the control u to give
  the desired wo ).
• Problems
• nonlinear or time varying gains
• unknown and varying disturbances

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Closed Loop Characteristics

• Now consider the case with feedback

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Closed Loop Characteristics

• If Ka is very large such that,
• then,
• Ks is the sensor gain in units of volts per
  rad/s.
• The input/output relationship is not very
  sensitive to disturbances or changes in the
  system gains

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Closed Loop Characteristics System Error

• The control error is
• Again, if the loop gain, Ka Km Kl Ks is large,
  then the error is small.

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Note Gain Definitions

• forward gain Ka Km Kl
• feedback gain Ks
• loop gain Ka Km Kl Ks
• closed loop gain forward gain
• 1 loop gain

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System Dynamics

• Consider a sudden change in the speed reference,
  ?r .
• The output speed, ?o will not respond
  instantaneously due to the inertial
  characteristics of the motor and load, i.e. their
  dynamic characteristics.
• The motor and load need to be represented by
  dynamic equations rather than simple gains.
• The output response will generally lag the input
  and may be oscillatory.

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System Dynamics Step Responses
Ka 20
Ka 2
?o
?r
?o
?r
Tm
Tm
Assume Ks 1.0
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Control System Design Objectives

• Primary Objectives
• 1. Dynamic stability
• 2. Accuracy
• 3. Speed of response
• Addition Considerations
• 4. Robustness (insensitivity to parameter
  variation)
• 5. Cost of control
• 6. System reliability

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Control System Design Steps

• Define the control system objectives.
• Identify the system boundaries.
• define the input, output and disturbance
  variables
• Determine a mathematical model for the components
  and subsystems.
• Combine the subsystems to form a model for the
  whole system.

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Control System Design Steps

• Apply analysis and design techniques to determine
  the control system structure and parameter values
  of the control components, to meet the design
  objectives.
• Test the control design on a computer simulation
  of the system.
• Implement and test the design on the actual
  process or plant.

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Control System Design Steps
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Examples of Control SystemsRoom Temperature
Control System

• Proportional mode Better accuracy, complex
• On/Off control mode Thermostatic control,
  simple, low accuracy

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Examples of Control SystemsAircraft Elevator
Control System

• Hydraulic servomechanisms have a good
  power/weight ratio, and are ideal for
  applications that require large forces to be
  produced by small and light devices.

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Examples of Control SystemsComputer Numerically
Controlled (CNC) Machine

• The purpose of this latter device, which produces
  an analog signal proportional to velocity, is to
  form an inner, or minor control loop in order to
  dampen, or stabilize the response of the system.

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Examples of Control SystemsShip Autopilot
Control System

• Actual heading is measured by a gyro-compass (or
  magnetic compass), compared with desired value.
  Error are send to autopilot (Course-keeping
  system)
• Actual rudder angle is sensed, and autopilot
  controls the ship course by steering-gear.