Explain-ziegler-nichols tuning method

Question

Problem:PID Controller : Ziegler-Nichols Tuning Method

Consider the following system shown in Fig.2 in which a PID controller is used to control the system.

Fig.2

The PID controller has the transfer function

G_c(s)= K_p  (1+1/T_is+T_ds)

Design a PID controller for this system using Ziegler-Nichols tuning method for determination of K_p, T_i and T_d. Then obtain a unit-step response curve and check to see if the designed system exhibits approximately 25% maximum overshoot. If the maximum overshoot is excessive(40% or more), make a fine tuning (most suitable tuning) and reduce the amount of the maximum overshoot to approximately 25% or less.