linear control system introduction &ch#1

2. Introduction
System – An interconnection of elements and devices for a desired purpose.
Control System – An interconnection of components forming a system
configuration that will provide a desired response.
Plant/Process – The device, plant, or
system under control. The input and
output relationship represents the
cause-and-effect relationship of the
process.
Linear Control System
Linear system- is a mathematical model of a system based on the use of
a linear operator. Linear systems typically exhibit features and properties
that are much simpler than the nonlinear case and obey Superposition and
Homogeneity principal.

3. A linear system is any system that obeys the superposition principle means if it
satisfies the additively and homogeneity property which is further described below.
A nonlinear system is any system that does not have at least one of these
properties.
Now if x(t) = H[f(t)] is the response of the system to an input f(t), 'A' is a constant
To show that a system 'H' obeys the scaling or homogeneity property is to show that

5. Introduction
Open-Loop Control Systems
utilize a controller or control
actuator to obtain the desired
response.
Closed-Loop Control
Systems utilizes feedback to
compare the actual output to
the desired output response.

6. Multivariable Control System

8. Control System Classification
Open-Loop Control System
Missile Launcher System

9. Control System Classification
Closed-Loop Feedback Control System
Missile Launcher System

10. What is Feedback?
1. The controlled variable is measured.
2. It is then compared to a desired value, or set point.
3. The difference between set point and measurement is
called the error.
4. The controller calculates a control output depending
on the error.
5. The control output is sent to some physical equipment,
a valve or similar, to affect the process. This physical
equipment is called the Final Control Element.
6. The process responds to the change made by the final
control element.
7. or 1. The process response is measured

11. What is Feedback?
1. The controlled variable is measured.
2. It is then compared to a desired value, or set point.
3. The difference between set point and measurement is called the error.
4. The controller calculates a control output depending on the error.
5. The control output is sent to some physical equipment, a valve or similar, to affect
the process. This physical equipment is called the Final Control Element.
6. The process responds to the change made by the final control element.
7. or 1. The process response is measured
Speed
Speed
Sensor
Speed in km/h
Speed
Error in
km/h
Desired
speed in
km/h
-
+
Cruise
Control
Desired
Throttle
Position Throttle
Actuator
Actual
Throttle
Position Engine,
Transmission,
Wheels
Disturbances -
wind, slope, bad
fuel

12. What are those block diagrams?
• Block diagrams are a visual representation of the actual
dynamic system and its governing equations.
• Each line is a signal - something that varies over time, and can
be measured or calculated.
• Each block is a “functional element” - something that does
something, and is governed by differential, integral or
algebraic equations, and describable as a transfer function.

13. Block Diagram
Cruise
Control
Engine,
Transmission,
Wheels
Throttle
Actuator
Speed
Sensor
Speed
Speed in km/h
Desired
speed in
km/h
Speed
Error in
km/h
-
+
Desired
Throttle
Position
Actual
Throttle
Position
Disturbances - wind,
slope, bad fuel

14. History
Water-level float regulator

15. History

16. (a) Automobile steering
control system.
(b) The driver uses the
difference between the
actual and the desired
direction of travel
to generate a controlled
adjustment of the
steering wheel.
(c) Typical direction-
of-travel response.
Examples of Modern Control Systems

17. Examples of Modern Control Systems

18. History

19. Examples of Modern Control Systems

20. Examples of Modern Control Systems

21. Examples of Modern Control Systems

22. Six Step Approach to Dynamic System Problems
• Define the system and its components
• Formulate the mathematical model and list the
necessary assumptions
• Write the differential equations describing the model
• Solve the equations for the desired output variables
• Examine the solutions and the assumptions
• If necessary, reanalyze or redesign the system