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

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 . . . .