Consider the following statements: 1. Adding a zero to the G(s)H(s) tends to push root locus to the left. 2. Adding a pole to the G(s)H(s) tends to push root locus to the right. 3. Complementary root locus (CRL) refers to root loci with positive K. 4. Adding a zero to the forward path transfer function reduces the maximum overshoot of the system. Which of the above statements are correct?

Option 3 : 1, 2 and 4 only

Effect of addition of zero to the system:

• The angle of asymptotes increases and this root locus shift towards left side of s-plane slightly more
• Breakaway point shifts towards the left in s plane
• The system becomes more stable i.e. less oscillatory
• The range of ‘K’ value of stability increases
• The relative stability increases

Effect of addition of pole to the system:

• The angle of asymptotes decreases and this root locus shift towards right side of s-plane slightly more
• Breakaway point shifts towards the right in s plane
• The system becomes less stable i.e. more oscillatory
• The range of ‘K’ value of stability decreases
• The relative stability decreases

Complementary root locus:

Complementary root locus (CRL) refers to the root loci of the closed-loop poles in the function of a negative open-loop gain K.

Effect on peak overshoot:

• Addition of pole to forward path transfer function – increases
• Addition of pole to the closed-loop transfer function – decreases
• Addition of zero to forward path transfer function – decreases
• Addition of zero to the closed-loop transfer function – increases