Ziegler–Nichols method

                    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 difference

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’.