The Ziegler–Nichols Method..

PID controllers are probably the most used controller structures in industry. They do, however, present some challenges to control and instrumentation engineers in the aspect of tuning of the gains required for stability and good transient performance. 

A popular method for tuning P, PI, and PID controllers is the Ziegler–Nichols method. This method starts by zeroing the integral and differential gains and then raising the proportional gain until the system is unstable.

What is the Ziegler-Nichols Rule?

In 1942 Ziegler and Nichols, both employees of Taylor Instruments, described simple mathematical procedures, the first and second methods respectively, for tuning PID controllers. These procedures are now accepted as standard in control systems practice. Both techniques make a priori assumptions on the system model, but do not require that these models be specifically known. Ziegler-Nichol’s formulae for specifying the controllers are based on plant step response.

Ziegler and Nichols conducted numerous experiments and proposed rules for determining values of Kp, Ki, and Kd based on the transient step response of a plant.

There are two methods which are described as follows: -

The First Method: -

The first method is applied to plants with step responses of the form displayed in Figure 4. 

This type of response is typical of a first order system with transportation delay, such as that induced by fluid flow from a tank along a pipeline.  It is also typical of a plant made up of a series of first order systems. The response is characterised by two parameters, L the delay time and T the time constant. These are found by drawing a tangent to the step response at its point of inflection and noting its intersections with the time axis and the steady state value. The plant model is therefore as follows: -

 The Second Method: -

The second method targets plants that can be rendered unstable under proportional control. The technique is designed to result in a closed loop system with 25% overshoot. This is rarely achieved as Ziegler and Nichols determined the adjustments based on a specific plant model. 

The steps for tuning a PID controller via the 2nd method is as follows

Using only proportional feedback control: -

·      Reduce the integrator and derivative gains to 0.

·      Increase Kp from 0 to some critical value Kp=Kcr at which sustained oscillations occur. If it does not occur, then another method must be applied.

·     Note the value Kcr and the corresponding period of sustained oscillation, Pcr The controller gains are now specified as follows:

The controller gains are now specified as follows:

Tuning rules such as the Z-N rule and its variants are embedded into well established, very convenient generalized controller products.