PID Control System Design and Automatic Tuning using MATLAB/Simulink. Liuping Wang

      thus, we can determine the time constant using 63.2% of the rising time in the step response. This estimation of time constant gives a different value from the case when using the maximum slope approach. For the majority of the applications, this will result in a smaller time constant , and from the empirical tuning rules stated in the later part of the section, a smaller proportional gain will follow. One can evaluate this approach as an exercise using Problem 1.2.

Essentially, the step response test gives the parameters in the first order plus delay description of the process as in (1.44).

There is a second set of Ziegler–Nichols tuning rules that is based on the plant step response test data. This is also called the Ziegler–Nichols tuning rules using reaction curve. With these parameters, Ziegler–Nichols tuning rules using a reaction curve are given in Table 1.2. By the nature of this testing procedure (open-loop testing), the tuning rules should apply to stable systems.

Table 1.2 Ziegler-Nichols tuning rules with a reaction curve.

P
PI
PID

Table 1.3 Cohen–Coon tuning rules with a reaction curve.

P
PI
PID

There is another set of tuning rules that are derived based on the reaction curve, termed Cohen and Coon tuning rules. Table 1.3 gives the PID controller parameters calculated from Cohen and Coon tuning rules.

      For the estimation of time delay , , and when using MATLAB, it is a fairly straight forward procedure to draw the lines and pinpoint the data points. The MATLAB command for finding the point on a graph is called ginput. For example, by typing

      [a,b]=ginput(1)

      a cross hair will appear on the MATLAB figure and a double click on the point of interest will yield the exact values we need. This graphic procedure will be demonstrated in the example section (see Section 1.5).

      1.3.3 Food for Thought