Ziegler–Nichols method
The Ziegler–Nichols tuning method is a heuristic method of tuning a PID controller.
It was developed by John G. Ziegler and Nathaniel B. Nichols. It is performed by
setting the I (integral) and D (derivative) gains to zero. The "P" (proportional) gain,
Kp is then increased (from zero) until it reaches the ultimate gain Ku , at which the
output of the control loop oscillates with a constant amplitude. Ku and the oscillation
period Tu are used to set the P, I, and D gains depending on the type of controller used:
- Z–N tuning creates a "quarter wave decay". This is an acceptable result for some
purposes, but not optimal for all applications.
"The Ziegler-Nichols tuning rule is meant to give PID loops best disturbance rejection
- Z–N yields an aggressive gain and overshoot – some applications wish to instead
minimize or eliminate overshoot, and for these Z–N is inappropriate.
Example :-Tuning a PI controller with the Ziegler-Nichols’
closed loop method
I have tried the Ziegler-Nichols’ closed loop method on a level control
system for a wood-chip tank with feed screw and conveyor belt which runs
with constant speed, see Figure 3. The purpose of the control system is
to keep the chip level of the tank equal to the actual, measured level.
The level control system works as follows: The controller tries to keep the
measured level equal to the level setpoint by adjusting the rotational speed
of the feed screw as a function of the control error (which is the diļ¬erence
between the level setpoint and the measured level).
Figure 4 shows the signals after a step in the setpoint from 9 m to 9.5 m
with a ultimate gain of Kpu = 3.0. The ultimate period is approximately
Pu = 1100 s. From Table 1 we get the following PI parameters:
Kp = 0.45 * 3.0 = 1.35 (5)
Ti =1100 s/1.2 = 917 s (6)
Td = 0 s (7)
Figure 5 shows signals of the control system with the above PID parameter
values. The control system has satisfactory stability. The amplitude ratio
in the damped oscillations is less than 1/4, that is, which means that the
stability is a little better than prescribed by Ziegler and Nichols’.
