This document discusses poles and zeros and their effect on system stability. It states that poles are the roots of the denominator of a transfer function, while zeros are the roots of the numerator. The addition of poles generally shifts the root locus to the right, lowering stability by delaying response and making the system more oscillatory. The addition of zeros shifts the root locus left, improving stability by speeding up response time. In conclusion, poles and zeros determine the stability and behavior of a system.

2. TABLE OF CONTENT
• INTRODUCTION
• POLES
• ZEROS
• ADDITION OF POLES
• ADDITION OF ZEROS
• CONCLUSION

3. INTRODUCTION
POLES ARE THE ROOTS OF THE DENOMINATOR OF A TRANSFER
FUNCTION. GENERALLY, THE NUMBER OF POLES IS EQUAL OR GREATER
THAN ZEROS.
SIMILAR TO POLES, ZEROS ARE THE ROOTS OF NOMINATOR OF A
TRANSFER FUNCTION. ZEROS MEAN THAT THE OUTPUT AT THOSE
FREQUENCIES IS ZERO.

4. ADDITION OF POLES
•THE GENERAL EFFECT OF ADDITION OF A POLE IS A TENDENCY TO
SHIFT THE LOCUS TOWARDS RIGHT SIDE OF S-PLANE AND THIS
LOWERS THE STABILITY.

5. CONSIDER THE SYSTEM WITH G(S)H(S) =
The corresponding root locus

6. NOW, LET US ADD A POLE S= -4.
G(S)H(S) =
IT IS SEEN THAT THE ROOT LOCUS HAS SHIFTED TO ITS RIGHT. STABILITY OF
THE SYSTEM GETS RESTRICTED.

7. NOW, IF ONE MORE POLE IS ADDED AT S= -6
G(S)H(S) =
BREAKAWAY POINT IN SECTION S=0 AND S= -2 GETS SHIFTED
TOWARDS RIGHT AS COMPARED TO PREVIOUS CASE. SO SYSTEM
STABILITY FURTHER GETS RESTRICTED.

8. EFFECT OF ADDITIONAL POLES
ADDITIONAL POLES DELAY THE RESPONSE OF A SYSTEM.
THE ROOT LOCUS CHANGES ITS NATURE, SHIFTS TOWARDS
IMAGINARY AXIS.
LOWERS THE STABILITY.
SYSTEM BECOMES OSCILLATORY.
INCREASES SETTLING TIME.
RANGE OF K REDUCES.

9. ADDITION OF ZEROS
•THE GENERAL EFFECT OF ADDITION OF ZEROES IS A TENDENCY TO
PULL THE ROOT LOCUS TO THE LEFT OF S-PLAN AND HENCE
IMPROVES STABILITY.

10. CONSIDER THE SYSTEM WITH
G(S)H(S) =
ADD A ZERO S= -4. NOW,
G(S)H(S) BECOMES
The corresponding root locus The corresponding root locus

11. ADDING ONE MORE ZERO AT S= -6. G(S)H(S)=
WE CAN SEE, THE ROOT LOCUS HAS SHIFTED TOWARDS ITS LEFT. AND, THE
BREAKAWAY POINTS SHIFTS TOWARDS LEFT OF THE S PLANE. SO
RELATIVELY STABILITY OF SYSTEM INCREASES.

12. EFFECT OF ADDITIONAL ZEROS
 THE ROOT LOCUS CHANGES ITS SHAPE AND SHIFTS TO THE HALF OF
S-PLANE.
 LEFT HALF-PLANE ZEROS SPEED UP THE RESPONSE OF A SYSTEM AND
THE RIGHT HALF-PLANE CAUSE THE RESPONSE TO GO IN THE
OPPOSITE DIRECTION.
 SYSTEM BECOMES STABLE.
 GAIN MARGIN INCREASES.
 SPEEDS UP SETTLING TIME.
 RANGE OF K INCREASES.

13. CONCLUSION
THE FREQUENCIES THAT TURN NOMINATOR OR DENOMINATOR ZERO
ARE CALLED ZERO AND POLES OF A TRANSFER FUNCTION RESPECTIVELY.
THEY DETERMINE THE STABILITY AND WORKING OF A SYSTEM.

14. THANK YOU . . . .