INTRODUCTION TO CONTROL SYSTEM

1. Unit 1.
Introduction to Control System

2. Today we are going to learn and understand about
 System
 Control system
 Difference between system and control system
 Classifications of control system

3.  System is a combination or an arrangement of different
physical components which act together as a entire unit
to achieve certain objectives
INPUT
SYSTEM
PROPER
OUTPUT
May or may not
be desired

4. INPUT OUTPUT
 Input is something
entered into a machine or
other system in order to
produce the output.
• The actual response
obtained from a system is
called output.

5.  system is a combination or an arrangement of different
physical components which act together as a entire unit
to achieve certain objectives.

6. System + Control = Control System
CONTROL SYSTEM
DESIRED
OUTPUT
INPUT

7.  This process of regulating the inputs or directing the
system so that the desired objective is attained is called
control

8.  It is defined as an arrangement of different physical
elements connected in such a manner so as to regulate,
direct or command itself to achieve a certain objective.

10. ➢ A Fan without regulator can be a “SYSTEM” Because it
can provide a proper output (airflow).
➢ But it cannot be a “Control System” Because it
cannot provide desired output

12. ➢ A Fan with regulator can be a “CONTROL SYSTEM”
Because it can provide a Desired output (Controlled
airflow).

14.  Asystem in which the control action is totally
independent of the output of the system is called as open
loop system.
Controller
Process
Reference
input
Controlled
output
r(t) u(t) c(t)
Fig.1 Block Diagram of Open loop Control System

15.  Electric hand drier
 Hot air (output) comes out
as long as you keep your
hand under the machine,
irrespective of how much
your hand is dried.
Fig.2

16.  Automatic washing
machine
 This machine runs
according to the pre-set
time irrespective of
washing is completed or
not.
Fig.3

17. Bread toaster
 This machine as per
adjusted time
irrespective of toasting
is completed or not.
Fig.4

18.  Automatic tea/coffee
Vending Machine –
These machines also
function for pre
adjusted time only.
Fig.5

19. Fig.5

20. Fig.6

21.  Asystem in which the control action is totally
independent of the output of the system is called as
open loop system

22.  Simple in construction and design.
 Economical.
 Easy to maintain.
 Generally stable.

23.  They are inaccurate
 They are unreliable
 Any change in output cannot be corrected
automatically.

24.  Control system which uses feedback signals to both
control and adjust itself is called a Closed-loop System.
 The quantity of the output being measured is called
the feedback signal.

25. Fig.7

26.  Automatic Electric Iron-
Heating elementsare
controlled by output
temperature of the iron.
Fig.8

27. Fig.9

28.  Closed loop control systems are more accurate even in
the presence of non-linearity.
 Highly accurate as any error arising is corrected due to
presence of feedback signal.
 Facilitates automation.
 This system is less affected by noise.
 Decision Making & Initiative Action is very fast

29.  They are costlier.
 They are complicated to design.
 Required more maintenance.
 Feedback leads to oscillatory response.
 Overall gain is reduced due to presence of feedback.
 Stability is the major problem and more care is
needed to design a stable closed loop system

30. Fig.10

31. Any closed loop system will have the following five
elements
 Comparison element
 Control element
 Correction element
 Process element
 Measurement element

32. Consider a room heater used to maintain 24
centigrade temperature during a cold night.
Fig.11

33.  Controlled Variable – The room temperature.
 Reference Value – The required room temperature.
We want to maintain 24 degree temperature in a
room.
 Comparison Element- The person in the room
comparing the measured value with required
temperature.
 Error Signal- Difference between measured and
required temperature. It may be positive or
negative.

34.  Control Unit – The person in the room.
 Correction Unit- The on-off switch present on the on the
heating equipment.
 Process – The heating of the air by the heating
equipment.
 Measuring Device – A thermometer.

36. Fig.11

37.  The relationship between input & output of a system is given
by the transfer function.

38.  Transfer Function is defined as the ratio of Laplace
transform of the output to the Laplace transform of
the input under the assumption of zero initial conditions.
Laplace transform of the output
Laplace transform of the input

39.  T
o evaluate the performance of an automatic control
system commonly used mathematical tool is Laplace
Transform
 The Laplace transform of a function, f(t), is defined as
 F(s) -is the symbol for the Laplace transform,
 L is the Laplace transform operator
 f(t) is some function of time, t.
L f (t) = F(s)

40. SYSTEM
G(t)
r(t) c(t)
INPUT OUTTPU
T SYSTEM
G(s)
r(s) c(s)
INPUT OUTTPU
T

41. 𝑮(𝒔)=𝑪(𝒔)/𝑹(𝑺) 𝒂𝒍𝒍 𝒕𝒉𝒆 𝒊𝒏𝒊𝒕𝒊𝒂𝒍
𝒄𝒐𝒏𝒅𝒊𝒕𝒊𝒐𝒏𝒔=𝟎

42. Amit Nevase
6/30/2016
System
g(t)
r(t) c(t)
LT
System
G(s)
R(s) C(s)
For the system shown,
c(t)= output
r(t)= input
g(t)= System function
L{c(t)}= C(s)
L{r(t)}= R(s)
L{g(t)}= G(s)
Therefore transfer function G(s) for above system is given by,
G(s)=
Laplace of output
=
C ( s )
R ( s )
Laplace of input
42

43. R-Input
G-Open loop gain
H-Feedback path gain
C-Output
r(s) G(s)
H(s)
C(s)

44.  If the output or some part of the output is returned to
the input side and utilized as part of the system input,
then it is known as feedback.
 Feedback plays an important role in order to improve
the performance of the control systems.

45.  To counteract disturbance signals affecting the
output.

46.  To improve system
performance in the
presence of model
uncertainty

47. There are two types of feedback systems
 Positive feedback
 Negative feedback

48.  The set point and output values are added together
by the controller as the feedback is “in-phase” with
the input.
 The effect of positive (or regenerative) feedback is
to “increase” the systems gain

49.  cattle running in a village.
It will lead to panic. Panic
will cause more number
of cattle to run.
 The output is contributing
to the input in such a way
that output further
increases.

51. R(s)
G(s) C(s)
Output
H(s)
+-
Error Signal
E(s)
Feedback
Signal
Input
Error signal is given by;
E(s) = R(s) + B(s) − − − − − (1)
 R(s) = E(s)− B(s)
Gain of feedback network is given by;
H(s) =
B(s)
C(s)
B= H(s).C(s)−−−−−−(2)
Gain for system
G(s) =
C(s)
E(s)
C(s) = G(s).E(s) − − − − − −(3)
Substitute value of E(s) from eq. 1 to 3
C(s)=G(s).(R(s) +B(s))
C(s) =G(s).R(s) +G(s).B(s) −−−−−−(4)
Substitute value of B(s) from eq. 2 to 4
C(s) = G(s) R(s) +G(s).H(s).C(s)
G(s).R(s) = C(s) − G(s).H(s).C(s)
G(s).R(s) = C(s)(1 − G(s).H(s))
Transfer function is given by;
C(s) G(s)
=
R(s) 1 − G(s).H(s)
T
.F
.=
B(s)

52.  In a negative feedback control system, the set point and
output values are subtracted from each other as the
feedback is “out-of-phase” with the original input.
 The effect of negative (or degenerative) feedback is to
reduce the gain.

54.  When we feel cold we shiver. Shivering increases
body temperature. If body temperature increases
then we sweat and decrease the body temperature.
 The positive and negative changes are reduced by
adding or subtracting the feedback.
 Negative feedback reduces the error between the
reference input, R(s) and system output.

55. E(S)
C(S)*
H

56. R(s)
G(s) C(s)
Output
H(s)
B(s)
+-
Error Signal
E(s)
Feedback
Signal
Input
Error signal is given by;
E(s) = R(s) − B(s) − − − − − (1)
 R(s) = E(s)+ B(s)
Gain of feedback network is given by;
H(s) =
B(s)
C(s)
B= H(s).C(s)−−−−−−(2)
Gain for system
G(s) =
C(s)
E(s)
C(s) = G(s).E(s) − − − − − −(3)
Substitute value of E(s) from eq. 1 to 3
C(s)=G(s).(R(s) −B(s))
C(s) =G(s).R(s) −G(s).B(s) −−−−−−(4)
Substitute value of B(s) from eq. 2 to 4
C(s) = G(s) R(s) − G(s).H(s).C(s)
G(s).R(s) = C(s) + G(s).H(s).C(s)
G(s).R(s) = C(s)(1 + G(s).H(s))
Transfer function is given by;
C(s) G(s)
=
R(s) 1 + G(s).H(s)
T
.F
.=

57. Basic Elements of Electrical based system are
 Resistor
 Inductor
 Capacitor

58.  Consider an electrical
circuit having the
resistance R and the
voltage applied across
this circuit is V and the
current flowing through
resistor is i.
V=IR
I=V/R

59.  Capacitors are
device that can
store an electrical
charge when it
connected to a
voltage source.
 𝑖 = 𝑑𝑞/𝑑𝑡
 𝑞 = ∫ 𝑖*dt
 V = 1/C ∫ I𝑑𝑡

60.  Inductors resist or
oppose changes of
current
 V= 𝐿 𝑑𝑖/𝑑𝑡
 𝑖 = 1 /𝐿 ∫ V. 𝑑t

61.  Inductance is the property of the coil due to which it
resists any variation in the current passing through it.
 The current passing through the coil generates the field
about it, the magnitude of the field depends on the
strength of the current.

62. Consider the electrical
 Resistor having the
resistance R
 Inductor having the
inductance as L
 Capacitor having the
capacitance as C.
v

63. Apply KVL, so we will get the sum of the voltage in this
loop is equal to zero
V-VR-VL-VC =0
V=VR+VL+VC
v =𝑅𝑖 + 𝐿 𝑑𝑖 /𝑑𝑡 + 1 /𝑐 ∫ 𝑖𝑑𝑡
V = 𝑅𝑖 + 𝐿 𝑑𝑖/𝑑𝑡 + 1/ 𝑐 ∫ 𝑖𝑑t ---------------2
Where 𝑖 = 𝑑𝑞/dt
v = 𝑅 𝑑𝑞/𝑑𝑡 + 𝐿 𝑑²𝑞/𝑑𝑡² + 𝑞/𝑐---------3

64. v

65.  Consider the
electrical circuit
having the parallel
combination of the
three elements
resistor, inductor
and capacitor

66.  Apply KCL the circuit
 𝑖(𝑡) = 𝑖𝑅 + 𝑖𝐿 + iC
Where 𝑖𝑅 = V/R
𝑖𝐿 = 1/𝐿 ∫ V𝑑𝑡
𝑖𝐶 = 𝑐 .𝑑V/𝑑𝑡
𝑖(𝑡) = V/𝑅 + 1/𝐿 ∫ V𝑑𝑡 + 𝑐 𝑑V/𝑑t

67.  Basic Elements of Electrical based system

69.  To understand the behavior of systems,
mathematical models are used.
 These mathematical models are equations
which describe the relationship between the
input and output of a system.

70.  The mass of a body though distributed, we
can assume that the entire mass is
concentrated at one point called the CG of
the body.

71.  The elastic deformation of a body is
represented by the ideal element known as
spring.
 It stores energy during the variation of its
shape due to elastic deformation resulting
from the application of the force.

73.  Dampers are used to minimize the vibrations
to improve the dynamics of the system.
Damper/Dash-pot is represented by,

76. Mechanical systems can be divided into two basic
systems based on type of motion .
(a) Translational systems.
(b) Rotational systems

77. Translational motion is taking place along a straight line is
known as Translational motion.
• These systems are characterized by
Displacement
Linear velocity
Linear acceleration

78. When a force ‘F’ is applied to a mechanical body of
mass M displacement takes place then it is opposed
by an opposing force 𝒇𝒎 due to mass. This
opposing force is proportional to the acceleration of
the body

80.  If a force (f) is applied on spring K, then it is
opposed by an opposing force due to elasticity
of spring 𝒇𝒌. This opposing force is
proportional to the displacement of the spring
(x)

84.  In physics, restraining of vibratory
motion, such as mechanical oscillations,
noise, and alternating electric currents,
by dissipation of energy is known as
damping force. Unless a child keeps
pumping a swing, its motion dies down
because of damping. A system may be so
damped that it cannot vibrate.

85. A dashpot is a mechanical device, a damper
which resists motion via viscous friction. The
resulting force is proportional to the velocity,
but acts in the opposite direction, slowing the
motion and absorbing energy. It is commonly
used in conjunction with a spring (which acts to
resist displacement).

86. Damper /Dashpot
Damper absorbs the velocity of a body. If a force
(f) is applied on dashpot B, then it is opposed by
an opposing force due to friction of the dashpot
𝒇𝒃. This opposing force is proportional to the
velocity of the body

89. Rotational Mechanical System involves rotational
motion (motion of an object about its own axis)
Rotational motion in
mechanical System

90. Mechanical System and
basic Elements
In the analysis of rotational mechanical system,
three essential basic elements are
•Moment of inertia (J) of mass
•Stiffness constant (k) of the spring
Rotational friction coefficient (B) of dash-pot

91. Mass (Rotation)
in rotational mechanical system, moment of
inertia stores kinetic energy.
A torque is a force applied to a point on an
object about the axis of rotation.
The angular displacement Ɵ is equivalence of
displacenet. The moment of inertia is
represented by (J), angular displacement (Ɵ)
and torque T.

93. Spring
In rotational mechanical system, torsional spring
stores potential energy.
If a torque is applied on torsional spring K
This opposing torque is proportional to the
angular displacement of the torsional spring.
Assume that the moment of inertia and friction
are negligible

94.  Spring represented in rotational motion, Comparing
with F = Fk = K x in linear motion,
For rotational motion we get
T=Tk =kθ

96. Damper/Dash-pot
Damping occurs whenever a body moves
through a fluid.
Dampers are used to minimize the vibrations to
improve the dynamics of the system.
These are different rotary dampers can be found in
rotational motion of mechanical system

97. Damper/Dash-pot
If a torque is applied on dashpot B, then it is
opposed by an opposing torque due to the
rotational friction of the dashpot.
This opposing torque is proportional to the
angular velocity of the body.
Assume the moment of inertia and elasticity are
negligible

102. We can represent mechanical systems in terms
of equivalent electrical systems
 Force voltage analogy
 Force current analogy
 Torque voltage analogy
 Torque current analogy

103.  The mathematical equations of translational
mechanical system are compared with
equations of the electrical system.

109.  In force current analogy, the mathematical
equations of the translational mechanical
system are compared with the nodal
equations of the electrical system.

110. All these electrical elements are
connected in parallel.

112. In this analogy, the mathematical equations of the rotational
mechanical system are compared with the nodal mesh equations of
the electrical system