SKEDSOFT

Ziegler-Nichols second method for tuning PID controllers

In the second method, we first set T_i = ∞ and T_d = 0. Using the proportional control action only (see Figure 1), increase K_p from 0 to a critical value K_cr where the output first exhibits sustained oscillations. (If the output does not exhibit sustained oscillations for whatever value K_p may take, then this method does not apply.) Thus, the critical gain K_cr and the corresponding period P_cr are experimentally determined (see Figure 2). Ziegler and Nichols suggested that we set the values of the parameters K_p , T_i, and T_d according to the formula shown in Table 1.

Fig: 1 Closed-loop system with a proportional controller                                          Fig: 2 Sustained oscillation with period P_er

Table 1: Ziegler-Nichols Tuning Rule Based on Critical Gain K_cr and Critical Period P_cr (Second Method)

Notice that the PID controller tuned by the second method of Ziegler-Nichols rules gives

Thus, the PID controller has a pole at the origin and double zeros at S = -4/P_cr.