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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 Kp 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




P + I Control

0.9T/( LxKp)(1)



P+I+D Control

1.2T (LxKp)(2)





(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




P + I Control




P+I+D Control






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 nerve-racking 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 (Ti as large as possible and Td 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 Ku and period of oscillation Tu . 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 Ku . 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




P + I Control




P+I+D Control





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.


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.



1)      Tuning of closed loop systems can be difficult and fraught with problems.

2)    For advice and assistance contact Harrogate Power Associates Ltd