Notes on Relay Based Controller Tuning

This final tuning method is loosely based on the ZN closed loop method. It gives an alternative method of obtaining the Ultimate Gain and Period. The basis of all the closed loop methods is to make the process oscillate. So why not use a control scheme which does this automatically ie. on/off control.

However, restricting the size of change which the controller can produce will restrict the amplitude of the oscillations. These can thus be small enough not to upset the process, or its operators!

This controller has a parameter deadzone, which defines the minimum change in the measured variable required to produce a change in output. The other parameter defines the size of the output of the controller. This is set to be + output/2 when the controller is on and - output/2 when it is off.

The tuning method is outlined below:

The process is controlled using the relay based control algorithm. The input parameters are
- The deadzone of the controller
- The restricted output
This gives a response similar to the one shown below
The period of oscillation is equal to the Ultimate Period as before.
From the graph it is also possible to determine the observed amplitude of the oscillations, a.
The Ultimate Gain is obtained by inserting these values into the formula:

= (4 * output) / ( * a)
Finally once the Ultimate gain and period are known then the same formulae as before are used to obtain the controller settings:

Controller Type Gain Reset Derivative

P /2 - -

PI /2.2 P_u/1.2 -

PID /1.7 P_u/2 P_u/8

Controller Type	Gain	Reset	Derivative
P	/2	-	-
PI	/2.2	P_u/1.2	-
PID	/1.7	P_u/2	P_u/8

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