page 115
10.1. Adjustment rule for a controller
The adjustment process by Ziegler and Nickols is of advantage
in a closed control loop in the case of controlled systems with
unknown time constant.
Adjustment rule
The controller is first operated as a pure P system. The rate
time TV is set to 0 and the reset time is set to a very high value
(ideally to
∞
) for a slow system. For a fast controlled system a
small TN should be chosen. The proportional-action coefficient
KP is then increased until the system deviation and the variable
deviation at KP = KP
critical
execute constant oscillation at a
constant amplitude. The stability limit has been reached. The
time period T
critical
of the permanent oscillation has to be
determined. Only add a D part if required. TV should be approx.
2 – 10 times smaller than TN and KP = KD.
The ideal controlled system should be set as follows:
Controlling
system
KP = KD TN TV
P 2.0 * KP
critical
--
PI 2.2 * KP
critical
0.83 * T
critical
-
PID 1.7 * KP
critical
0.50 * T
critical
0.125 * T
critical
Please note that the controlled system is not affected by
the oscillation. In sensitive controlled systems KP should
only be increased up to a value at which no oscillation will
occur.
Attenuation of overshooting
The PT1 (low pass filter) function can be used to attenuate
overshooting. The set value XS should be attenuated by PT1
before it is integrated in the controller function. The setting
variable for T1 should be approx. 4 – 5 times bigger than TN (of
the PID or GLR controller).
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