Ziegler Nichols Method for PID Controller Tuning

Ziegler Nichols Method for PID Controller Tuning

1. Dr. Mohamed Sultan bin Mohamed Ali
Department of Electrical Engineering
College of Engineering
Qatar University
Control Systems
MECE 352
Lecture 13
PID Tuning Method

2. 2
Tuning of PID Controller
The PID controller is widely used in the industries in which the
K
p, K
iand K
dparameters can often be easily adjusted.
The root locus is one of the techniques to obtain the PID
gains.
There are several other methods for tuning a PID controller.
The tuning generally involve the choosing of parameters K
p, K
i
and K
d
The methods can be divided into open- loop and closed- loop
approaches.
Closed loop:
•Ziegler-Nichols, Tyreus-Luyben, Damped oscillation
methods
Open- loop:
•Ziegler-Nichols, Cohen Coon, Fertik, Minimum error
criteria

3. •The following table summarizes the advantages and
disadvantages of using several tuning methods
3
Method Advantages Disadvantages
Manual
tuning
No math required; onlineRequires experienced
personnel
Ziegler-
Nichols
(1942)
Proven method; online Process upset, some trial-
and-error, very aggressive
tuning
Software
tools
Consistent tuning; online
or offline; various
techniques
Some cost or training
involved
Cohen- Coon
(1953)
Goodprocess models Some math; offline; good for
first-order processes
Tuning of PID Controller

4. •The following table summarizes the effects when
the parameters are tuned manually
Effects of increasing a parameter ‘independently’
4
Manual Tuning
ParameterRise time
Settling
time
%OS E
ss Stability
K
p Decrease
Small
change
IncreaseDecrease Degrade
K
i DecreaseIncreaseIncreaseEliminateDegrade
K
d
Minor
change
DecreaseDecrease
No effect
in theory
Improve if
K
dis small
Tuning of PID Controller

5. 5
•Thismethodisusefulwhenmathematicalmodelofaplant
cannotbeeasilyobtainedornotknown.
•Themethodusesexperimentalapproachestotunethe
PIDcontrollers.
•However,theresultingsystemmayexhibitalarge
maximumovershootinthestepresponse,whichis
unacceptable. Thenaseriesoffinetuningtoobtain
acceptableresultsisneeded.
•TheZ-Ntuningrulesgivesaneducatedguessforthe
parametervalues,andprovideastartingpointforfine
tuning,notafinalparametervalues.
•TherearetwomethodscalledZ-Ntuningrules:Open- loop
andclosed- loop.
Ziegler-Nichols MethodTuning of PID Controller

6. 6
S-shaped response curve.
Obtain delay time, Land time constant, T
This is an open loop
technique where we
obtain a system
step response by
experiments.
The PID parameters can be calculated
using a formula in the next slide.
Ziegler-Nichols -First Method (Open-loop)

7. 7
Ziegler-Nichols -First Method (Open-loop)

8. 8
Function C(s)/R(s) may then be
approximated by a first-order system
with a transport lag as follows:
The PID controller tuned by the
first method of Ziegler–Nichols
rules gives ;
PID controller has a pole at the origin and double zeros at s=–1/L
????????????(????????????)
????????????(????????????)
=
????????????????????????
−????????????????????????
????????????????????????+1
Ziegler-Nichols -First Method (Open-loop)

9. 1.Set K
D= K
I = 0(to minimise the effect of derivation and
integration)-, set ????????????
????????????=∞,????????????
????????????=0
2.Increase the K
Pgain until the system reach the critically
stableand oscillate (i.e. when the closed-loop poles located
at the imaginary axis). Obtain the gain, K
u and the oscillation
frequency, ω
uin rad/sor period, T
u, on that time.
9
Ziegler-Nichols -Second Method (Closed-loop)
The Ultimate Cycle Method
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????????????????????????
????????????
????????????(????????????)????????????
????????????
????????????
????????????
????????????

10. 10
3. Calculate the K
P gain that is supposedly needed using
formula in the table.
4. Based on the required type of controller, calculate the
necessary gain using formulas in the table.
Ziegler-Nichols -Second Method (Closed-loop)
????????????
????????????????????????????????????????????????=????????????
????????????1+
1
????????????
????????????????????????
+????????????
????????????????????????

11. Example 1
•Design a PID controller using Ziegler-Nichols tuning method
for unity feedback system with the open loop system which
is given as:
11

12. Final Exam Question
13
A unity feedback system is shown in Figure 1. The rootlocusplot from the system
is given in Figure 2. Figure 3 shows the output at a particular gain value, K.
Figure 1
Figure 2
Figure 3