First, note whether the required proportional control gain is positive
or negative. To do so, step the input u up (increased) a little, under
manual control, to see if the resulting steady state value of the process
output has also moved up (increased). If so, then the steady-state process
gain is positive and the required Proportional control gain, Kc,
has to be positive as well.
Turn the controller to P-only mode, i.e. turn both the Integral and Derivative
Turn the controller gain, Kc, up slowly (more positive
if Kc was decided to be so in step 1, otherwise more
negative if Kc was found to be negative in step 1) and
observe the output response. Note that this requires changing Kc
in step increments and waiting for a steady state in the output, before
another change in Kc is implemented.
When a value of Kc results in a sustained periodic oscillation
in the output (or close to it), mark this critical value of Kc
as Ku, the ultimate gain. Also, measure the period of
oscillation, Pu, referred to as the ultimate period.
( Hint: for the system A in the PID simulator, Ku should
be around 0.7 and 0.8 )
Using the values of the ultimate gain, Ku, and the ultimate
period, Pu, Ziegler and Nichols prescribes the following
values for Kc, tI and tD,
depending on which type of controller is desired:
Ziegler-Nichols Tuning Chart:
As an alternative to the table above, another set of tuning
values have been determined by Tyreus and Luyblen for PI and PID,
often called the TLC tuning rules. These values tend to reduce oscillatory
effects and improves robustness.
Tyreus-Luyben Tuning Chart:
( Use the BACK button of your browser to return to a currently
running PID tuning simulation, otherwise click
here to initiate a PID tuning simulation.)
This page is maintained by Tomas B. Co (firstname.lastname@example.org).
Last revised 2/13/2004.
Tomas B. Co
Department of Chemical Engineering
Michigan Technological University
1400 Townsend Avenue
Houghton, MI 49931-1295
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