1. FEEDBACK CONTROL SYSTEMS
Dr. Basil Hamed

2. Key Words:
Feedback Systems
Automatic Control
Estimation & Identification
Mathematical Modeling
Process Optimization
Decision Making

3. Systems and Control
A System is a device or process that takes a given input and produces some output:
A DC motor takes as input a voltage and produces as output rotary motion
A chemical plant takes in raw chemicals and produces a required chemical product
System
Input
Output

4. Closed Loop Control Open-loop control is ‘blind’ to actual output
Closed-loop control takes account of actual output and compares this to desired output
Measurement
Desired
Output + -
Process
Dynamics
Controller/
Amplifier
Output
Input

5. An Open-Loop Control System
The controlled ‘output’ is the resulting toast
System does not reject changes in component characteristics

6. What is a Control System ?
A process to be controlled
A measurement of process output
A comparison between desired and actual output
A controller that generates inputs from comparison
Measurement + -
Process
Controller
Output
Desired
Comparison

7. Control Many control systems can be characterised by these components
Disturbance
Plant
Control
Signal
u(t)
Reference
r(t)
Error
e(t)
Output
y(t)
Control
Actuator
Process + -
Feedback
Sensor
Sensor Noise

8. Actuation
A device for acting on the environment

9. Sensing
A device for measuring some aspect of the environment

10. Computing A combination of electronics and software Fill Stop Wash
Empty
Wash
Fill
Done
Ready
Spin
Rinse
Stop
Fail
Timeout
Overflow
Yes
Check Level
Fill Achieved?
Start
Fail
Stop
Open Valve No
Close Valve

11. Examples of Control Applications
Biological Systems:
Central Nervous System is the controller for the body
Robotics:
Robots perform automated tasks in assembly lines, where precision is important and dangerous tasks physically impossible for humans

12. Examples of Control Applications
Aerospace Applications:
Aircraft or missile guidance and control
Space vehicles and structures

13. Examples : Washing Machine
System Requirements
Understanding of load sizes
Receptacle to hold clothes
‘Plumbing’
Agitation of drum
Ease of use, Reliability
Low Cost
Actuators
AC or DC Motors
Water inlet/drain
Sensors
Water level
Load speed/balance
Control
Choice depends on design

14. Examples : The CD Player
A CD player is an example of control system
Requires
Accurate positioning of the laser read head
Precise control of media speed
Conversion of digital data to analogue signal

15. Examples : Hard Drive
A computer disk drive is another example of a rotary control system
Requires
Accurate positioning of the magnetic read head
Precise control of media speed
Extraction of digital data from magnetic media

16. Examples : Modern Automobiles
Modern Automobiles are controlled by a number of computer components
Requires
Control of automobile sub systems
Brakes and acceleration
Cruise control
ABS
Climate control
GPS
Reliability
Low cost
Ease of use

17. Example: DC Motor Speed Control
Desired speed wd
Actual speed w
Tachometer measurements plus noise
Control signal is a voltage
Variations in Load Torque wd +
Tacho
Power
Amplifier
Controller
Motor
Load Torque - w
Actual Speed Measurement

18. Example: Batch Reactor Temperature Control
Goal: Keep Temperature at desired value Td
If T is too large, exothermic reaction may cause explosion
If T is too low, poor productivity may result
Feedback is essential because process dynamics are not well known
Controller
Steam
Water
Measured Temperature
Coolant
Reactants
Desired
Temperature

19. Example: Aircraft Autopilot
Standard components in modern aircraft
Goal: Keep aircraft on desired path
Disturbances due to wind gust, air density, etc.
Feedback used to reject disturbances
Disturbances
Sensors
Actuators
GPS/Inertial
Path controller
Rudder
Elevons
Measured path
Route

20. Mathematical Modelling
To understand system performance, a mathematical model of the plant is required
This will eventually allow us to design control systems to achieve a particular specification

21. Block Diagrams Formalise control systems as ‘pictures’
Components can be combined to produce an overall mathematical description of systems
Interaction between elements is well defined

22. Block Diagrams: Summation
Ideal, no delay or dynamics
Two inputs:
Three or more:

23. Laplace Example I
Physical model

24. For Example I
Block Diagram model
Physical model

25. For Example I
Transfer Function
Physical model

26. For Example II

27. For Example II
Laplace Transform

28. For Example II
Physical Model
Block Diagram model

29. Block Diagrams: Transfer Functions
Transfer Function G(s) describes system component
An operator that transfers input to output
Described as a Laplace transform because

30. Single-Loop Feedback System
Error Signal
The goal of the Controller C(s) is:
To produce a control signal u(t)
Which drives the ‘error’ e(t) to zero
Desired
Value
Output
Transducer + -
Feedback
Signal
error
Controller
Plant
Control

31. Controller Objectives
Controller cannot drive error to zero instantaneously as the plant G(s) has dynamics
Clearly a ‘large’ control signal will move the plant more quickly
The gain of the controller should be large so that even small values of e(t) will produce large values of u(t)
However, large values of gain will cause instability

32. Control Criteria Speed of Response
Robustness to unknown plant and load
Stability

33. Response of a First-Order System
General Solution:

34. Step Response

35. Speed of Response
Equations:

36. System Descriptions

37. Speed of Response
Increasing K increases Speed of Response

38. Speed of Response to Step
Increasing K increases Speed of Response

39. Tracking Error
Input
Output
Steady-State Error
Initial Response

40. signal cond. & amplification
computer hardware
control software
A/D
signal cond. & amplification
D/A
sensors
actuators
DYNAMIC SYSTEM

41. Integrated Product Design
PHYSICAL SYSTEM
DYNAMIC MODEL
COMPUTER
MODEL
PROTOTYPE
TEST & MEASUREMENT
SIMULATION - +
DESIRED PERFORMANCE
ANALYSIS - +

42. A Word About Stability BANG !
Start here
180o phase
inversion
Bigger here
Another phase inversion
BANG !
If G is such that input is phase reversed
(180o out of phase) for any frequency,
then input will be back in phase
If loop gain >1 then
system will be unstable
If System is unstable for one input,
it will be unstable for all inputs

43. Thank you and good luck in your Final Exams