control//feedback control//PID controller//PID tuning//Ziegler-Nichols method

The Ziegler-Nichols method is a PID tuning procedure, published by John Ziegler and Nathaniel Nichols in 1942, that measures the plant through the closed loop itself by driving it to the edge of instability and then reads the three gains from a table. It needs no model and no software, which is why it spread through process plants for decades, and it still appears in every textbook and in many controllers as the starting point engineers soften by hand.

The Ziegler-Nichols method is a PID tuning procedure, published by John Ziegler and Nathaniel Nichols in 1942, that measures the plant through the closed loop itself by driving it to the edge of instability and then reads the three gains from a table. It needs no model and no software, which is why it spread through process plants for decades, and it still appears in every textbook and in many controllers as the starting point engineers soften by hand.

The test is done with integral and derivative action off. Raise the proportional gain until the loop oscillates steadily, neither growing nor dying: that gain is the ultimate gain KuK_uKu​, and the period of the oscillation is the ultimate period PuP_uPu​ (also written TuT_uTu​). The table then gives, for a PID,

Kp=0.6 Ku,Ti=Pu/2,Td=Pu/8,K_p=0.6\,K_u,\qquad T_i=P_u/2,\qquad T_d=P_u/8,Kp​=0.6Ku​,Ti​=Pu​/2,Td​=Pu​/8,

and for a PI Kp=0.45 KuK_p=0.45,K_uKp​=0.45Ku​ with Ti=Pu/1.2T_i=P_u/1.2Ti​=Pu​/1.2, for P alone Kp=0.5 KuK_p=0.5,K_uKp​=0.5Ku​. What the test really measures is one point of the plant's frequency response, the most important one: at PuP_uPu​ the loop has exactly 180 degrees of lag, and KuK_uKu​ is the inverse of the plant's gain there, which is the gain margin of a unit controller (stability margins).

The settings are aggressive by design. They aim at a quarter-amplitude decay, each overshoot a quarter of the one before, which suits load rejection in process plants and gives a large overshoot on setpoint steps and small margins. Engineers usually start from them and soften the gains.

The test itself is the bigger problem. Driving a production plant into sustained oscillation, with an amplitude nobody controls, is often unacceptable, and on a slow plant it takes a long time. Relay autotuning measures the same two numbers with a small oscillation of chosen amplitude, and is what modern controllers run instead.

Ziegler and Nichols also proposed a second rule from the open-loop step response (the process reaction curve), the ancestor of model-based rules such as the SIMC rules, which trade speed for robustness through one parameter and need no oscillation at all.

The rest of the toolbox, trial tuning in a fixed order and the checklist before touching any gain, is in PID tuning.