ZIEGLER - NICHOLS PID TUNING
To address an FAQ we present here a brief overview of
the Ziegler-Nichols (short: Z-N) tuning methods
Ziegler and Nichols have developed PID tuning methods
back in the early forties based on open loop tests (less known than for example
the Cohen-Coon formulas) and also based on a closed loop test, which is maybe
their most widely known achievement.
The open
loop method allows to calculate
PID parameters from the process parameters. The procedure:
·
· Step 1: Make an open loop plant test (e.g. a
step test)
·
· Step 2: Determine the process parameters:
Process gain, deadtime, time constant (see below: draw a tangent through the
inflection point and measure L and T as shown. By the way: Today we have better
and easier methods).
·
· Step 3: Calculate the parameters according to
the following formulas:
K = time constant / (process gain * deadtime)
PI: Proportional gain = 0.9 * K, integral time = 3.3 *
deadtime
PID: Proportional gain = 1.2 * K, integral time = 2 *
deadtime, derivative time = 0.5 * deadtime
Process gain = dPV / dOP, deadtime = L, time constant = T
The closed
loop method prescribes the following procedure:
·
· Step 1: Disable any D and
I action of the controller (--> pure P-controller)
·
· Step 2: Make a setpoint
step test and observe the response
·
· Step 3: Repeat the SP
test with increased / decreased controller gain until a stable oscillation is
achieved. This gain is called the "ultimate gain" Ku.
·
· Step 4: Read the
oscillation period Pu.
·
· Step 5: Calculate the
parameters according to the following formulas:
PI: Proportional gain = 0.45 * Ku, integral time =Pu / 1.2
PID: Proportional gain = 0.6 * Ku, integral time =Pu / 2, derivative time = Pu / 8
Characterization:
·
· Both methods give a good starting point
but require further fine-tuning.
·
· The open loop method is based on a
measurement range of 0-100 and continuous control. This requires adjustments
for other measurement ranges and for the control interval in digital systems
(the method was developed in the times when only analog controllers existed).
·
· The
closed loop methods does not require adjustments, a big advantage, since both
process and controller are part of the test, but suffers from one major
disadvantage: Bringing the loop into stable, sustained oscillation is simply out
of the question for industrial processes.
·
· Both methods do not distinguish between
setpoint and load tuning and are for self- regulating processes only, not for
integrating processes like liquid level.
Today's technology:
In our PC tool TOPAS a refined Z-N methods is used:
A) Closed loop test: The basic approach is the same as
with the original Z-N but with one
major improvement: Stable oscillation is not required any more.
In addition, the tools not only calculate the PID constants but also the
process parameters- just from one setpoint test - and just by taking 5 data
points!
B) Open loop test: TOPAS provides several methods to calculate the process parameters from a step
or a relay test. Once the process parameters are known you can calculate
refined PID constants (less overshoot, smoother approach than Z-N) for both setpoint tuning and load tuning
(P-action on error or PV) using ACT's
proprietary methods. And you can calculate tuning constants for tight and average level control - to your
specification.
For the more curious: Since the
process parameters are known you can also compare (and measure the performance
of) the PID with model based control right away - without any prior knowledge.
ACT - D.I. Hans H. Eder
Wienerstr. 10, 3443
Int. office: Madeliefjeslaan 13, 3080
Phone ++32-(0)2-767-0895, e-mail: actgmbh@compuserve.com