CONTROL

1. CAREER POINT UNIVE
MAJOR ASSIGNMENT
Design and analysis of effect of adding poles and
zeros to the open loop transfer function

2. Introduction
 In modern era , control system play a vital role
in human life. A control system is an
interconnection of component forming a
system configuration in which any quantity of
interest or altered in accordance with a desired
manner. The basic control system are :
 Input
 Control system
 output

3. Open loop control system
Definition
 Without feedback or non feed back control
system is known as open loop control system.
 The element of an open loop control system
can usually be divided into two parts:
The actuating device
The controlled process

4. Example of open loop control system
.Bread Toaster
Input : raw bread
Output :bread toasted
Control action: heating the bread
Heating bread
Raw bread Toasted bread
Block diagram of bread toasted

5. 2. Automatic washing machine
Input : dirty cloths
Output : clean cloths
Control action: washes the cloths for set
Washes the cloths
Dirty cloths
Clean cloths
Block diagram of washing machine

6. Advantages of open loop control
system
• Open loop control systems are simple in
construction.
• Open loop control system in cheap.
• Generally the open loop systems are stable.
• The maintenance required for open loop
system is less.
• Calibration of open loop control system is
easily.

7. Disadvantages
• Open loop system are inaccurate. The
accuracy is depend up on the calibration of
input.
• The open loop systems are not reliable, the
operation of these is affected due to the
presence of non linearties in its element.
• Optimization of open loop system is not
possible.

8. Transfer Function
• “The transfer function is define as the ratio of
the Laplace transform of the output quantity
to the Laplace transform of the input quantity,
with all initial condition assumed to the zero.”
Then the transfer function is
Transfer function=output/input
G(s)=Y(s)/R(s)

9. Block diagram of open loop transfer
function
R(S) G(s) Y(s)
G(S)=Y(S)/R(S)

10. Advantages of transfer function
• Its provide the gain of the system.
• Integral and differential equation are
converted to algebraic equation.
• The transfer function is dependent on the
parameters of the system and independent of
the system.
• If transfer function G(s) is known than any
output for any given input , can be known.

11. Disadvantages
• Transfer function can be calculated only for
linear and time invariant system.
• Consider only when initial condition are zero.
• Its does not give any information about
physical structure of the system.

12. Poles and Zeros
• Zeros are defined as the root of the
polynomial of the numerator of the transfer
function.
• Poles are the defined as the root of the
polynomial of the denominator of the transfer
function.

13. Generalized transfer function
• G(s)=(S-Z1)(S-Z2)----------(S-Zn)
(S-P1).(S-P2)---------(S-Pn)
Zeros are Z1,Z2,---------Zn and the pole are
P1,P2,------Pn.

14. Poles of the transfer function
• The value of s which are substitued in the
denominator of the transfer function after
substituting the value of y the transfer
function becomes “infinite “, these values are
called poles of the transfer function.
Like P1,P2,------Pn are those value which makes
the transfer function infinite when substitute
in previous equation.

15. Zeros of the transfer function
• The value of s which are substituted in the
numerator of the transfer function, after
substituting the value, the transfer function
becomes “Zeros” these values are the called
zeros of the transfer function.
Like Z1,Z2,--------Zn are those value which
makes the transfer function zero.

16. Important Point
• When the value of poles and zeros are not
repeated , such poles and zeros are called
simple poles and zeros . If repeated such poles
and zeros are called multiple poles and zeros .
• The order of repeated pole and zeros is equal
to the number of times they are repeated.

17. Poles-Zero Plot
• If we locate all poles and zeros of the transfer
function in the s plane (or complex plane )
that diagram is called as the poles-zero plot.
s=σ+jω
where
σ= real part and locate on X axis or real axis.
jω= imaginary part and locate on Y axis or
imaginary axis.

18. Poles and Zeros plots
Zeros: roots of N(s)
Poles: roots of D(s)
Poles must be in the left half plane for the
system to be stable.
As the poles goes to the closer to the
boundary ,the system is the stable.

19. Stability of Control Systems
• If all the poles of the system lie in left half
plane the system is said to be Stable.
• If any of the poles lie in right half plane the
system is said to be unstable.
• If pole(s) lie on imaginary axis the system is
said to be marginally stable.

20. • All the poles
s-plane
LHP RHP

j

21. Examples
103,1if,)( 

 CandBA
BAs
C
sG
Then the only pole of the system lie at
Poles =-3
s-plane
LHP RHP

j
X
-3

22. Coding
• P1=[8 56 96];
• Q1=[1 4 9 10];
• Sys=tf(P1,Q1)
• Roots(P1);
• Roots(Q1);
• pzMAP(sys);

23. Figure

24. Coding.2
• Num=[49];
• Den=[ 1 4 9 ];
• Sys=tf(num,den);
• load ltiexamples
• ltiview

25. Graph

26. Coding
• Num=[49 89 96];
• Den=[1 4 9];
• Sys=tf[Num,Den];
• Load ltiexamples
• ltiview

27. Graph