ZieglerNichols
Method:

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 steadystate process
gain is positive and the required Proportional control gain, K_{c},
has to be positive as well.

Turn the controller to Ponly mode, i.e. turn both the Integral and Derivative
modes off.

Turn the controller gain, K_{c}, up slowly (more positive
if K_{c} was decided to be so in step 1, otherwise more
negative if K_{c} was found to be negative in step 1) and
observe the output response. Note that this requires changing K_{c}
in step increments and waiting for a steady state in the output, before
another change in K_{c} is implemented.

When a value of K_{c} results in a sustained periodic oscillation
in the output (or close to it), mark this critical value of K_{c}
as K_{u}, the ultimate gain. Also, measure the period of
oscillation, P_{u}, referred to as the ultimate period.
( Hint: for the system A in the PID simulator, K_{u} should
be around 0.7 and 0.8 )

Using the values of the ultimate gain, K_{u}, and the ultimate
period, P_{u}, Ziegler and Nichols prescribes the following
values for K_{c}, t_{I} and t_{D},
depending on which type of controller is desired:
ZieglerNichols Tuning Chart:

K_{c}

t_{I}

t_{D}

P control

K_{u}/2



PI control

K_{u}/2.2

P_{u}/1.2


PID control

K_{u}/1.7

P_{u}/2

P_{u}/8

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.
TyreusLuyben Tuning Chart:

K_{c} 
t_{I} 
t_{D} 
PI control 
K_{u}/3.2 
2.2 P_{u} 

PID control 
K_{u}/2.2 
2.2 P_{u} 
P_{u}/6.3 
( 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 (tbco@mtu.edu).
Last revised 2/13/2004.
Tomas B. Co
Associate Professor
Department of Chemical Engineering
Michigan Technological University
1400 Townsend Avenue
Houghton, MI 499311295
Back to Homepage