In textbooks there is
much written about the design methods using Root Locus or Frequency Response,
which all rely on a good model for the process. However, in practice an
engineer will need to adjust a controller to suit the performance
requirements of a system, where little is known about the system dynamics.
Ziegler and Nichols,
developed methods to assist in the estimation of controller settings. There
are two methods based upon simple (perhaps) methods – The Open Loop and the
Closed Loop Methods. The testing is simple to carry out but the
engineer must be aware of some pitfalls.
The Quarter Amplitude
Response
The methods described
aim to achieve the response to an input change that decays in the manner
shown.
If the plant is
operating near its maximum conditions it may not be practical to increase the
output as it may have ramifications on such things as boiler tube life. So,
often one needs to decide to reduce the output.
Another problem is that
most systems have noise (random process variations) on the output variable.
This is especially so in digital systems where signals are sampled and so
become discontinuous.
Open Loop Method
This figure shows a
possible result of an open loop step response test. A line is drawn at
the maximum slope and the parameters, L and T, can be measured from the curve
as well as M and N. The ratio M/N is a measure of the steady state gain K_{p}
of the process.
Again real process
traces tend to be noisy and the drawing of such lines will require several
goes in order to average the results.
From the measurements
the following controller settings can be obtained;

Controller
Gain

Integral
Time

Derivative
Time

Proportional
Control

T/(LxK_{p})



P
+ I Control

0.9T/(
LxK_{p})_{(1)}

l/0.3


P+I+D
Control

1.2T
(LxK_{p})_{(2)}

2L

0.5L_{(3)}

Notes
(1)
The 0.9 is quoted in texts but in practice use 1.0
(2)
The 1.2 is quoted in texts but in practice use 1.0
(3)
Derivative action is difficult to use as it amplifies process noise, so in
practice unless you are using servos where noise free feedback is available,
do not struggle with derivative action.
This test should yield
some approximate values that may be quite good in heavily damped systems. The
test should give results for further manual adjustment.
As an example, the
settings for the control settings can be given by this method for the curve
shown.
The line of the maximum
slope is found and a line tangential to the curve is drawn through it. The
process gain can be seen as 1.0.
From the measurements
the following controller settings can be obtained;

Controller
Gain

Integral
Time in secs

Derivative
Time

Proportional
Control

15



P
+ I Control

13.5

13.3s


P+I+D
Control

18

8

2s

The Closed Loop Method
(The Ultimate Method)
This may be called the
Ultimate Method because it will be the last thing you do before being sacked
for wrecking the plant. This method requires much thought before undertaking
it. It can be nerveracking to carry out on large plant.
The essence of this
method is to determine the gain of the proportional controller to sustain
constant amplitude oscillations and to determine the frequency of the
oscillations. The gain and frequency are used to determine the controller
settings to give the Quarter Amplitude Response.
The procedure is as follows;
1)
Remove the effects of Integral and Derivative action (T_{i} as large
as possible and T_{d} as small as possible)
2)
Set the Proportional term to a low value and introduce a step in the setpoint
and return it after a short time (heave a sigh of relief at this stage if no
oscillations seen)
3)
Increase the gain by a small amount and make the setpoint change. Does
it oscillate and die away? If so heave another sigh.
4)
Repeat the process until the oscillations are of constant amplitude and note
the gain and frequency. (This is difficult to achieve in real power station
systems.)
5)
The Controller Gain K_{u} and period of oscillation T_{u} .
These are called the Ultimate values. The curve B is what you are looking
for, if you find A, panic and abort test. Take a breather and carefully
choose a lower value of Proportional Gain K_{u} . Persevere, but
beware the desk operators are going to swear at you.
6)
Calculate the terms as follows;

Controller
Gain

Integral
Time in secs

Derivative
Time

Proportional
Control

0.5K_{u}



P
+ I Control

0.45K_{u}

T_{u}/1.2


P+I+D
Control

0.6K_{u}

T_{u}/2

T_{u}/8

This method is lengthy to perform and it
will be necessary to observe several cycles (could be minutes).
Also in processes that interact, the
oscillations can be propagated into other systems.
This test sorts the men from the boys.
Advice
1)
Have a written note of all controller settings so that you can get back to a
safe point.
2)
Have a written plan that is approved by Operations staff.
3)
Work out procedures to get back to a safe point, identify conditions where
you abort.
4)
Ideally have paper copies of all traces suitably annotated as evidence. Good
chart recorders are essential even though we are in a digital age.
5)
Tell the Operations staff what could happen. Take them along with you.
6)
Report all your tests.
Special Considerations in Digital Control Systems
1)
Read about the characteristics of the controller software (beware, if it does
not have high frequency roll off as sampled data systems amplify Sampling Noise). Are all the terms Gain, Integral and
Derivative independently settable?
2)
Know the sampling frequency and does this potentially cause problems?
Shannon’s Theorem.
3)
How quickly can you change setting back to the original ones? Have a
plan available to get back to safe settings in the event of problems.
4)
In general terms do not use Derivative action with sampled data systems
5)
Many modern process plants utilise ISE as a performance indicator, which tend
to lead to smaller overshoots then the quarter amplitude response.
6)
Digital techniques allow implementation of modern control methods which can
be very difficult to tune.
Conclusion
1)
Tuning of closed loop systems can be difficult and fraught with problems.
2)
For advice and assistance contact Harrogate Power Associates Ltd
