Question

Assertion (A): The closed-loop pole-zero dipole introduced by the PI controller does not contribute significantly to the transient response of the closed-loop system.

Reason (R): The PI controller adds a pole at s = 0 and a zero at s = −z to the closed-loop transfer function.
1. Both (A) and (R) are true and (R) is the correct explanation of (A)
2. Both (A) and (R) are true, but (R) is not the correct explanation of (A)
3. (A) is true, but (R) is false
4. (A) is false, but (R) is true

Answer 1

Correct Answer - Option 3 : (A) is true, but (R) is false

• Increasing the type number of the system drastically improves its steady-state response.
• If an integral controller is added to a closed-loop system, the type number increases, but its transient response deteriorates or the system becomes unstable.
• If a proportional control term is added to an integral term, the controller has a pole and a zero.
• The transfer function of the PI controller is. 

          \(C\left( S \right) = {K_p} + \frac{{{K_I}}}{S}\)

          \(\Rightarrow {K_P}\frac{{s + a}}{s}\)

          \(a = \frac{{{K_I}}}{{{K_p}}}\)

By placing the controller zero close to the pole at the origin, the controllers pole-zero almost cancels, having a negligible effect on transient response. Hence Assertion (A) is true.

⇒ The PI controller adds poles and zero’s, near the origin. So the Reason (R) is false.

∴ (A) is true, but (R) is false.