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Fig. 27.9. Proportional controller performance using the Z-N tuning rule

Control engineers do not like oscillations, since they reduce the lifespan of the final control elements. In addition, if an even larger proportional gain is applied, the control system will get unstable with oscillations of growing amplitude. The offset can be eliminated with a smooth control, but we need integral control action for this.

The Z-N tuning rules for proportional-integral control (PI control) suggest that Ti = 0.83-Pu and Kc = 0.45-Ku. Therefore, in this case the tuning is given by Kc = 0.189 and = 0.955. Fig. 27.11 shows the response of the controlled system using these values.

Here, the offset is eliminated. This tuning can be improved even further by trial and error (this is called manual fine tuning), which is always advisable to do in a real plant to adapt the performance of the controller to the process specifications. For example, a lower proportional gain can be tried in this case to get a smooth control action and reduce the overshoot (which is the difference between the maximum value of the process response and the set point), although this will cause a slower response of the controlled process.

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