NMJ32703
Control System
Introduction to Control System
What is control system?
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 An interconnection of components that provide a
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
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desired system response
Used whenever some quantity (e.g., temperature,
altitude, speed, concentration) must be made to
behave in some desirable way over time
Often exploits feedback to help regulate the system
response
Compare actual behavior with desired behavior
Take corrective action based on the difference
Human control
System control
GPS Control
Force Control
Vision Control
Sound Control
24 cm
Primary Source
(Loudspeaker)
Sensor Microphone
Secondary source
(Actuator)
Primary path
36 cm
Error path
12 cm
Error Microphone
Block Diagram for Active Noise Cancellation
BEFORE ANC
AFTER ANC
Satellite Control
Satellite Control
Why do we need control systems?
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 Convenient (room temperature control, laundry
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machine)
Dangerous (hot/cold places, bomb removal)
Impossible for human (nanometer scale precision
positioning, work inside small space that human
cannot enter)
Exist in nature (human body temperature control)
Lower cost, higher efficiency
Simplified description of a control system
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Control System History
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Table 1.1 (continued)
Selected Historical Developments of Control Systems
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Classification of Control System
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Control systems are often classified as
 Open-loop control system
 Closed-loop control system (also called as Feedback
or Automatic Control System)
Open-Loop Control System
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 Commanded by the input
 Utilize a controller or control actuator to obtain the
desired response
 A system without feedback
Example: Open-Loop Speed Control
of Rotating Disk
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Example : Toaster
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 A toaster toasts bread by setting
timer
Setting of timer
Toasted bread
Toaster
 Objective: make bread golden
browned and crisp.
 A toaster does not measure the
color of bread during toasting
process
 A toaster would be more
expensive with sensors to
measure the color and actuators
to adjust the time based on the
measured color.
Example : Washing machine
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 A washing machine washes
clothes by setting a program
 A washing machine does not
measure how clean the
clothes become
 Control without measuring
devices (sensors) are called
open-loop control
Program setting
Washed clothes
Machine
Closed-Loop Control System
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 Commanded by the error via feedback
 Utilizes feedback to compare the actual output
to the desired output response
 Take corrective action based on the difference
 Improved performance and stability
Desired o/p
response
Controller
Measurement
Process
Output
Example : Rotating Disk
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Open-Loop vs. Closed-Loop
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 An open-loop control system utilizes an actuating device to
control the process directly without using feedback.
Desired Output
Response
Actuating
Device
Process
Output
 A closed-loop feedback control system uses a measurement of the
output and feedback of the output signal to compare it with the
desired output or reference.
Desired
Output
Response
Comparison
Controller
Measurement
Process
Output
Open Loop Systems Pros and Cons
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• Simple construction and
ease of maintenance.
• Less expensive than a
corresponding closed-loop
system.
• There is no stability
problem.
• Convenient when output
is hard to measure or
measuring the output
precisely is economically
not feasible.
Advantages of
Open Loop
• Disturbances and changes
in calibration cause errors,
and the output may be
different from what is
desired.
• To maintain the required
quality in the output,
recalibration is necessary
from time to time.
• They are less accurate.
• If external disturbances
are present, output differs
significantly from the
desired value.
Disadvantages
of Open Loop
Closed Loop Systems Pros and Cons
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• They are more accurate.
• The effect of external
disturbance signals can be
made very small.
• The
variations
in
parameters of the system
do not affect the output of
the system i.e. the output
may be made less sensitive
to variation is parameters.
Hence
forward
path
components can be of less
precision. This reduces the
cost of the system.
Advantages of
Closed Loop
• They are more complex
and expensive
• They require higher
forward path gains.
• The systems are prone to
instability. Oscillations in
the output many occur.
• Cost of maintenance is
high.
Disadvantages
of Closed
Loop
Elements of a control system
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Desired o/p
response
Error
Controller
Plant
Output
Sensor
 Normally depicted in a block diagram
 Plant provides the system output
 Controller takes the control input and provides a control
output
 Sensor takes the output and feeds it to the subtractor (or
comparator) that compares the demand with the output
of the sensor to produce an error
 All connected by arrows, which represent signals
Elements of a control system
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disturbance
input
+
output
plant
controller
disturbance
input
+
error
+
controller
+
plant
Disturbance is
unwanted signal that
may sway the output
Error is a signal made
up of the difference of
input and output
-
Input
System
Feedback Loop
Output
Feedback is a process where
some proportion of the output
signal of a system is passed
(fed back) to the input. This is
often used to control the
dynamic behaviour of the
system.
Control System Design
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 Understand the general schemes that can be used to
control a system.
 Understand the system you’re trying to control. You need
to predict how a system behaves – mathematical
techniques that involve differential equation
solution
 Common goals:
- Stability
- Performance
▪
▪
Transient response (short-term characteristics)
Steady-state response (long-term characteristics)
- Robustness and sensitivity to disturbances, modeling
errors, noise, etc.
Control System Design Steps
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1. System analysis – establish requirements (talk to
users)
2. Formal specification of required system
performance
3. System modelling – system must be accurately
modelled before controller design can begin. Usually
using a differential equation (some quantity that
changes w.r.t. time)
4. Control algorithm development – the controller is
developed using the model and standard control
theory to meet the specifications.
Types of Control System
 Linear System
 Non linear system
 Time variant system
 Time invariant system
 Linear time variant system
 Linear time invariant system
Types of Feedback
 Positive Feedback
Negative Feedback
Transfer Function System
 Transfer function of control system is the ratio of
Laplace transform of output to Laplace transform of
input
 Transfer function =
𝐿𝑎𝑝𝑙𝑐𝑒 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚 𝑂𝑢𝑡𝑝𝑢𝑡
|𝑧𝑒𝑟𝑜 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛
𝐿𝑎𝑝𝑙𝑐𝑒 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚 𝐼𝑛𝑡𝑝𝑢𝑡
The control system design process
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The design of a control system follows these steps;
Step 1: Transform Requirement into a Physical System.
Step 2: Draw the Functional Block Diagram.
Step 3: Create the Schematic.
Step 4: Develop the Mathematical Model or Block Diagram.
Step 5: Reduce the Block Diagram.
Step 6: Analyze and Design.
Analysis
o Transient state
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a state whereby the system response after a perturbation
before the response approach to a steady state
o Steady state
a state whereby the system response becomes steady after a
transient state
o Stability
The condition of the steady state. If the response converges to
a finite value, it is said to be in a stable condition. If the
response diverges, it is known to be unstable.
Effects of Feedback
 Gain
 Sensitivity
 Stability
𝐺
𝐺=
1 + 𝐺𝐻
Con’t - Sensitivity
 S=
% 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑇
% 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐺
𝑦 = 𝑈𝑉
𝑑𝑦
𝑑𝑈
𝑑𝑉
=𝑉
+𝑈
𝑑𝑥
𝑑𝑥
𝑑𝑥
𝑈
𝑉
𝑑𝑈
𝑑𝑉
𝑉
−
𝑈
𝑑𝑦
= 𝑑𝑥 2 𝑑𝑥
𝑑𝑥
𝑉
𝑦=
Response Characteristics
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 Transient response:
 Gradual change of output from initial to the desired condition
 Steady-state response:
 Approximation to the desired response
 For example, consider an elevator rising from ground to the
4th floor.
Analysis and Design Objectives
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Transient Response
• In the case of elevator, slow transient response makes
passengers impatient.
• Excessive response makes passenger uncomfortable and
could also cause permanent physical/ structural damage.
Steady-State Response
• This response resembles the input and is usually refers to the
response remains after transients have decayed to zero.
• This response refers to the accuracy
• E.g. the elevator stop near the fourth floor, head of disk stop
at the correct track
• Steady-state error is analyzed for corrective action
Mathematical Model of Control System
 Differential Equation Model
 Transfer function Model
 State Space Model
So what did you learn today?