Derivative Action - The Good, Bad, and Ugly

by John Gerry, P.E.

Click here to see the complete presentation in more detail as a web-cast.

Derivative has a stabilizing effect The reason to use derivative (or D) is that you can use more Proportional and especially more Integral action. The result can be a much faster reacting control loop. The effect of properly applied D (or derivative) action is most pronounced on second order processes like temperature loops. But, D action can help the response of most loops.

The figure shows the response of a temperature loop to an upset. The blue line is for PI and the red line is with the addition of D action. For easy comparison, both controllers have the same proportional and integral terms. Below this figure is the robustness plot for both systems. A complete tutorial on Robustness plots is the subject of a previous presentation, "Loop Stability - the other half of the PID Tuning Story".

As you can see, by using D action, the response is smoother and the loop is more robust.

Red line shows the stabilizing effect of derivative Red line shows the loop is more robust with addition of derivative

 

Controllers Differ

If set point response is important on this loop, then you need to examine the effects of D on the setpoint. For example, some controllers allow you to remove D action from setpoint changes. The simulation below compares the setpoint response of Honeywell Plantscape A and B algorithms. The blue line is for the B algorithm, with no D action on the setpoint. Notice how the controller output for the A algorithm, or red line, has a huge initial spike.

The Bad

Most processes can be helped by D action. However, on those that are of almost pure dead time you should not use D. These are somewhat rare. An old rule of thumb is to not use D on noisy loops.

There are always trade-offs in process control. If the loop is noisy, D action will make your valve move more, causing more wear on the valve decreasing its life. This is why using just a little bit of D causes harm to the loop: it does little to improve performance and wears out the valve. If you use D, use the full, proper amount. Additional filtering can help counteract the valve wear, if the filter is the right size. A discussion on filters is the subject of a previous presentation, "Choosing the Best Filter".)

The Ugly

Use Derivative only on controllers that limit the derivative gain. Manufacturers implement this limit by applying a first or second order filter to the PV or error signal when the user dials in a number for D. If your manufacturer does not do this, don't use the D action - it will make the controller output smash into your upper or lower limits continually in the presence of any amount of noise as shown by the blue line in the lower plot. This is partly why D gets such a bad rap. The red plot is the same controller with the proper D gain limit.



There is another caution with parallel type controllers. (A discussion on controller types was the subject of a previous presentation, "Differences in PID Algorithms and Units".) On many of these controllers, the D gain limit changes with the dialed in value of controller gain. Dial in a gain of 1, and everything works as expected. Dial in smaller and smaller controller gains, and the D gain limit slowly vanishes. Put in a large controller gain, and the D gain limit is so close to the actual D that it ends up canceling the D action. The bottom line is, do not use D on parallel controllers unless the controller gain is close to 1.

Conclusions

Properly set, Derivative action improves the response of most loops. Even with the proper setting, you should examine the trade-offs in valve wear.

>ExperTune's software lets you compare these trade-offs and gives you the tools to decide what to use in your loop. For ExperTune's full recommendations, on using derivative action see the full presentation as a web-cast.

For more information on ExperTune see their website at: www.expertune.com.

 

© 2002 ExperTune, Inc.

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