Industrial controllers , basic theory

Derivative Action

The third response found on controllers is the derivative mode. Whereas proportional response responds to the size of the error and reset responds to the size and time duration of the error, the derivative mode responds to how quickly the error is changing. In figure 12, two derivative responses are shown.

The first is a response to a stop change of the measurement away from the set point. For a step, the measurement is changing infinitely fast, and the derivative mode in the controller causes a very large change in the output, or spike, which dies immediately because the measurement has stopped changing after the step. The second response shows the response of the derivative mode to a measurement which is changing at a constant rate. The derivative output is proportional to the rate of change of this error. The greater the rate of change, the greater the output due to derivative. The derivative holds this output so long as the measurement is changing. As soon as the measurement stops changing, whether or not it is at the set point, above or below it, the response due to derivative will cease. Among all brands of controllers, derivative response is commonly measured in minutes as indicated in figure 13.

 

The derivative time in minutes is the time that the open loop proportional plus derivative response is ahead of the response due to proportional alone. Thus, the greater the derivative number the greater the derivative response. Changes in the error are the result of changes in either the set point, or the measurement, or both. To avoid a large output spike caused by step changes in the set point, most modern controllers apply derivative action only to changes in the measurement. Derivative action in controllers helps to control processes with especially large time constants and significant dead time; derivative is unnecessary on those processes which respond fairly quickly to valve motion, and cannot be used at all on process with noise in the measurement signal, such as flow, since the derivative in the controller will respond to the very rapid changes in measurement which it sees in the noise. This will cause large and rapid variations in the controller output, which will keep the valve constantly moving up and down, wearing the valve and causing the measurement to cycle.

Figure 14 shows the combined proportional, reset, and derivative response to a simulated heat exchanger temperature measurement which deviates from the set point due to a load change. When the measurement begins to deviate from the set point, the first response from the controller is a derivative response proportional to the rate of change of measurement which opposes the movement of the measurement away from the set point. This derivative response is combined with the proportional response, and-in addition, as the reset in the controller sees the error increase, it drives the valve farther still. This action continues until the measurement stops changing, when derivative response ceases. Since there is still an error, the measurement continues to change due to reset, until the measurement begins to move back towards the set point. As soon as the measurement begins to move back toward the set point, there is a derivative response proportional to the rate of change in the measurement opposing the return of the measurement toward the set point. The reset response continues because there is still error, although its contribution decreases with the error. Also, the output due to proportional is changing. Thus, the measurement comes back towards the set point. As soon as the measurement reaches the set point and-stops changing, derivative response again ceases and the proportional output is back to 50%. With the measurement back at the set point, there is no longer any changing response due to reset. However, the output is at a new value. This new value is the result of the reset action during the time that the measurement was away from the set point, and compensates for the load change which caused the original upset.

CONCLUSION

This web article has described the responses of a three mode controller when it is used in the feedback control of industrial measurements. The reader should have a clear understanding of the following points.

1. In order to achieve automatic control, the control loop must be closed. -
2. In order to have a stable feedback control loop, the most important adjustment to the controller is the selection of the proper action, either reverse or direct, on the controller. Improper selection of this action will always cause the controller to be unstable. Proper selection of this action will cause the controller output to change in such a way that the movement of the valve will oppose any change in the measurement seen by the controller.

3. The proper value of the settings of proportional band, reset, and derivative time depend on the characteristics of the process. Proportional band is the basic tuning adjustment on the controller. The more narrow the proportional band, the more the controller reacts to changes in the measurement. If too narrow a proportional band is used, the measurement cycles excessively. If too wide a proportional band is used, the measurement will wander and the offset will be too large.

4. The function of the reset mode is to eliminate offset. If too much reset is used, the result will be an oscillation of the measurement as the controller drives the valve from one extreme to the other. If too little reset action is used, the result will be that the measurement returns to the set point more slowly than possible.

5. The derivative mode opposes any change in the measurement. Too little derivative action has no significant effect. Too much derivative action causes excessive response of the controller and cycling in the measurement.
3. The proper value of the settings of proportional band, reset, and derivative time depend on the characteristics of the process. Proportional band is the basic tuning adjustment on the controller. The more narrow the proportional band, the more the controller reacts to changes in the measurement. If too narrow a proportional band is used, the measurement cycles excessively. If too wide a proportional band is used, the measurement will wander and the offset will be too large.

4. The function of the reset mode is to eliminate offset. If too much reset is used, the result will be an oscillation of the measurement as the controller drives the valve from one extreme to the other. If too little reset action is used, the result will be that the measurement returns to the set point more slowly than possible.

5. The derivative mode opposes any change in the measurement. Too little derivative action has no significant effect. Too much derivative action causes excessive response of the controller and cycling in the measurement.

 

 

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Function of automatic control .  - The feedback loop. - The measurement .  - The process .  

 The automatic controller .  -  Controlling the process .  -  Selecting controller action - Upsets . 

 Process characteristics and controllability . - Controller responses . - Proportional action . - Integral action (reset ).

 Derivative action . - Conclusion .