to control the control system shown in the following figure in which a PID controller is used system. The PID controller has the transfer function $G(s) = K_p(1 + \frac{1}{T_is} + T_ds)$ apply a Ziegler-Nichols tuning rule for the determination of the values of parameters $K_p$, $T_i$ and $T_d$ Use the following tables, where the first row of PID is for the first method and the second row is for the second method. Type of Controller $K_p$ $T_i$ $T_d$ PID $\frac{1.2T}{L}$ $2L$ $0.5L$ PID $0.6K_c$ $0.5P_c$ $0.125P_c$
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