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.
Addition of Pole kConsider the system with G(s)H(s) = s (s 2)This is thecorrespondingroot locus
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.
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.
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.
Effect of Addition of ZeroThe general effect ofaddition of zeroes is atendency to pull the rootlocus to the left of s-planand hence improvesstability.
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.
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.
SummaryThe 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.