Feedback Control Systems

(KON 313E)
Week 1

Prof.Dr. Volkan Sezer

Control and Automation Engineering Department

 Course Plan
Weeks Topics
1 Introduction to feedback control Systems (Control system examples, modeling, open loop control closed loop control..)
2 Transfer function, block diagrams, modelling electrical and mechanical systems in the frequency domain
3 Modelling electromechanical systems in the frequency domain, linearization
4 Modelling dynamic systems in time domain, linearization
5 Time domain analysis of control systems: 1st and 2nd order dynamic models
6 Time domain analysis of control systems: high order and complex dynamic models, steady state responses

7 Root-locus techniques and properties

8 Root-locus based controller design
9 Frequency domain analysis of control systems: Bode plots
10 Frequency domain analysis of control systems: Nyquist diagrams and stability
11 Frequency domain analysis of control systems: Relative Stability of control systems

12 Frequency domain analysis of control systems: Relationships with the time domain

13 Analysis and design of state space control systems

14 Introduction to design of digital control systems
 Textbook

 Control
Systems
Engineering,
N. Nise, John
Wiley & Sons
 Other References

1. Feedback Control of Dynamic Systems, Global Edition, G.

Franklin, J. D. Powell and A. Emami-Naeini, Pearson, 2020

2. Automatic Control Systems, B. J. Kuo, Wiley & Sons, 2003

3. Otomatik Kontrol Sistemleri, B. J. Kuo, A. Bir (translator/

çeviren), Literatür Yayınları, 2005

4. Feedback Control Systems, C.J. Phillips and R.D. Harbor,

Prentice-Hall, 2011.
 Evaluation

 1% Pretest (Week 3) 14 October

 24% Midterm1 (Week 7) 11 November
 25% Midterm2 (Week 12) 23 December
 10% Homeworks (%5 each, 2 homeworks, Matlab
based)
 40% Final (10% Posttest 30%Classical Part)
 VF Border

 Requirement for entering the final exam:

⚫ Average of midterms must be equal or

greater than 15
⚫ (Midterm1+ Midterm2)/2 >= 15
 Exam Dates

 11 November 2023 (Week 7) Midterm1

 23 December 2023 (Week 12) Midterm2

Ninova system will be used to share the necessary files.

Teaching Assistant: Ertuğrul Keçeci kececie@itu.edu.tr

Smart and Autonomous System
Laboratory (SASlab, 8105)
What is Control – What is
Control System?
 What is Control – What is
Control System?

The work to change the behavior of a system as desired, is called control.

Systems whose behavior is controlled are control systems.

In general, systems that contain strategies to achieve goals are called

control systems.
 History

Input Valve

Float

Output

Ctesibius’ Flow Rate Regulator , (B.C. Third Century) Watt’s Steam Engine, 1820
 Basic Elements of Control System

1) Purpose of control (input, reference)

2) Control system components (controller, system,
sensor..)
3) Result or output

Reference Control Output

System
 Control System
Control systems generally consist of two parts:
1) Controlled system: The system whose outputs are to be
controlled.
2) Controller: A collection of elements that produce the
control signals required for the controlled system to
produce outputs for a given purpose (It usually appears as
an electronic circuit or a software).
Reference u Controlled Output
Controller y
r system
Control Signal
 What is System? What is Signal?
System: A system is any process that produces an output
signal in response to an input signal.
Signal: Any measurable quantity that enables system
elements and systems to interact with each other.

Input Output
System
Example: Electrical System

 System: An electric
circuit
 Possible signals:
⚫ Voltage,
⚫ Current
Example: Mechanical System

 System: Car
 Possible signals:
⚫ Car position
⚫ Steering Wheel
position
⚫ Throttle, brake, gear
position
⚫ Car speed
⚫ Wheel slip
⚫ ..
Example: Social System

 System: Society
 Possible signals:
⚫ Population growth
⚫ Happiness status
⚫ Education status
Example: Economic System

 System: Economy of
a specific country
 Possible signals:
⚫ Inflation
⚫ Economic growth
⚫ Tax ratios
⚫ ..
 Common Point!

The common point of all these systems is that

the mathematical expressions of their
behavior are similar to each other.
 Solution Approach

Mathematical
model of the
system
Physical Conceptual
system Side
Mathematical
Solution
 Control Techniques

The control methods that can be used to control a system

can be divided into two main groups:

1. Open loop control

2. Closed loop control
 Open Loop Control

Systems whose block diagram is given as follows are called open

loop control systems.

Definition:
Systems whose control signal is not affected by the output signal are
called open loop control systems.

Examples: Classical versions of; washing machines, toasters, traffic

lights..
 Open Loop Control
An open loop control system cannot correct changes in
the system output due to changes in system parameters or
disturbances acting on the system!

Example: Temperature control in a room.

Disturbance
Desired Room
Temperature u temperature
r Controller Heater Room y

C Desired temperature The moment the

disturbance hits the
system.
t
 Closed Loop Control
Definition:
Control systems in which the control signal affecting the
system is produced by taking into account the system output
is called closed loop (feedback) control systems.
reference error u Controlled output
r + Controller
System y
-

Measuring
Device
Definition: The process of reflecting the output to the system
input in this way is called feedback.
 Closed Loop Control
A closed loop control system can correct changes in the
system output due to changes in system parameters or
disturbances acting on the system!
Example: Temperature control in a room.
Disturbance
Desired
Room
Temperature error u temperature
r
+ Controller Heater Room y
-
Measurement
Device
C Desired temperature
The moment the disturbance
hits the system.
 Closed Loop Control
Room temperature with on/off control:

Desired Room
Temperature e u temperature
r =T + error Heater Room y
-

y
Unit feedback
T+

T- 
T0

t
 Sytem Modeling

The methods used to find the mathematical model of a given

system can be divided into two categories:

1. Analytical Methods
2. System Identification Methods
 Analytical Methods
Here, the elements that make up the system, how these
elements are related to each other and the equations related
to each element are known.

Using the known laws of physics, chemistry, etc., the

relationship between the signals in the system is expressed
mathematically.
 Analytical Methods

The relation between the input signal and the output signal
of the system has a special meaning for us. (Transfer
function)

input output
System

Systems that appear to be completely different from

each other can have similar mathematical expressions!
Vehicle Acceleration Model
Vehicle Acceleration Model
Vehicle Acceleration Model
RC Circuit Model
RC Circuit Model
 System Identification

In some cases, the elements that make up

the system may not be completely clear,
or it may be very difficult to find the
model of the system based on the
equations related to them.

Such systems are often treated as a black box

representing a system in which it is not known exactly
what is inside.

input output
System
 System Identification

In this case, various test signals are

applied to the system input and the system
output is observed. The model of the
system can be estimated by looking at the
output signals.

input output
System

This type of work is called system identification.

 System Types
Dynamic System: Systems whose behavior at any
moment depends on the input applied to the system at that
moment and some of the inputs applied to the system
before that moment.
 They are systems with memory.
 They are expressed by differential equations.

Static System: Its behavior at any given moment

depends only on the input applied to the system at
that moment.
• They have no memory.
• They are expressed by algebraic equations.
 System Types
Example
(integrating system)
Linear System: Let y be the response of
1

a system to input x and y be the

1 2

response to input x . The system is linear

2

if the following 2 properties are satisfied.

 The response to input x +x is y + y
1 2 1 2

 The response to input ax is a y . 1 1

Whether it provides the above 2

features at the same time can be tested
by looking at the following property:
a1x1 + a2x2 → a1y1 + a2y2
This means the system is linear.
 System Types
Example
Is this system with input x and
output y linear?
Linear System: Let y be the response of
1

a system to input x and y be the

1 2

response to input x . The system is linear

2

if the following 2 properties are satisfied.

 The response to input x +x is y + y
1 2 1 2

 The response to input ax is a y . 1 1

Whether it provides the above 2

features at the same time can be tested
by looking at the following property:
a1x1 + a2x2 → a1y1 + a2y2
So the system is not linear.
 System Types
 Time Invariant System, TI: If the output of a Example
system depends only on the input, regardless of
time, this system is time invariant.
Time Variant

Example At t=1 if the input is sin(t), output is y(t)=sin(t)

At t=5 if the input is sin(t), output is y(t)=5sin(t)

Time Invariant

t=1 For a sin(t) input, the output

t=5 for both is 10sin(t).
System Types

 Causal System : If the output of a system at any time depends only

on the inputs at that time and at past times and does not depend on
the future value of the input, it is called a causal system.

Example
Casual

Casual

Not casual (physically unrealizable)