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# Effects of poles and zeroes

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### Effects of poles and zeroes

1. 1. Effect of addition of polesThe general effect ofaddition of a pole is atendency to shift the locustowards right side of s-planeand this lowers the stability.
2. 2. Addition of Pole kConsider the system with G(s)H(s) = s (s 2)This is thecorrespondingroot locus
3. 3. Addition of PoleNow, let us add a pole s= -4. k G ( s) H ( s) s ( s 2)( s 4)Root locusbecomes:It is seen that the root locus hasshifted to its right. Stability ofthe system gets restricted.
4. 4. Addition of PoleNow, if one more pole is added at s= -6 k G ( s) H ( s) s ( s 2)( s 4)( s 6)Breakaway point in section s=0 and s= -2gets shifted towards right as compared toprevious case. So system stability further getsrestricted.
5. 5. SummaryEffect of addition of open loop poles can besummarised as follows:The root locus changes its nature and shifts towards imaginary axis.The system becomes oscillatory.Gain Margin enhances relatively, thus stability decreases.Range of k reduces.Settling time increases.
6. 6. Effect of Addition of ZeroThe general effect ofaddition of zeroes is atendency to pull the rootlocus to the left of s-planand hence improvesstability.
7. 7. Addition of Zeroes kConsider the system with G(s)H(s)= s (s 2) It is the corresponding Root loci.Add a zero s= -4.Now, G(s)H(s) becomes k ( s 4) s( s 2)The root locus here, is shiftedto its left.
8. 8. Addition of ZeroesAdding one more zero at s= -6. G(s)H(s)= k ( s 4)( s 6) s ( s 2)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.
9. 9. SummaryThe root locus changes its nature and shifts to left away from imaginary axis.Relative stability of system increases.System becomes less oscillatory.Gain margin increases and so does the range of K.Settling time decreases.