Question $39$

The figure below shows the closed loop response of a system when subjected to a step input. A

proportional controller is used and the gain is set to a critical value of $2\mathrm{.}94.$

The proportional controller is to be replaced with a PID controller. The values of time at points A and

B are $190ms$ and $398ms$ respectively. Given that you are to use time units of $ms$ for all calculation

and for this Ziegler$-$Nichols tuning method:

$K_p=0\mathrm{.}60K_c$

$T_i=\frac{T_c}{2\mathrm{.}0}$

$T_d=\frac{T_c}{8\mathrm{.}0}$

a$)$

What value would the Ziegler$-$Nichols method imply for the proportional gain term of the controller

Give your answer to $3$ decimal places.

Round your answer to $3$ decimal places. b$)$ what value would the ziegler$-$ nichols method imply for the integral gain term of the contollert c$)$ what value would the ziegler$-$ nichols method imply for the derivative gain term of the controller