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.