Notes on Damped Oscillation

This fourth tuning method is based on the ZN closed loop method. The main disadvantage with the ZN closed loop method is that the plant conditions have to oscillate to obtain the parameters. However this method allows a damped oscillation which dies away as the process approaches a setpoint under control with nonoptimal, but known controller settings.

The method is outlined below:

Using proportional only control find controller settings which give a response like the one shown below - the response is kept within reasonable limits and reaches steady state.
The gain required to do this is called , the damped gain.
Evaluate the period of the oscillations, Pd.
To relate to it is necessary to estimate the increase in gain required to cause the system to oscillate continuously as in the ZN closed loop method. This is done by looking at the ratio of the peak-to-trough and following trough-to-peak distances.

= * first peak to trough distance / following trough to peak distance
Also Pu = Pd * 0.95
Once and Pu are obtained these are inserted into the table below as before:

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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