According to the following text from the pid for dummies, it is not important to have derivative.

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Derivative Action – predicting the future

OK, so the combination of P and I action seems to cover all the bases and do a pretty good job of controlling our system. That is the reason that PI controllers are the most prevalent. They do the job well enough and keep things simple. Great.

But engineers being engineers are always looking to tweak performance.

They do this in a PID loop by adding the final ingredient: Derivative Action.

So adding derivative action can allow you to have bigger P and I gains and still keep the loop stable, giving you a faster response and better loop performance.

If you think about it, Derivative action improves the controller action because it predicts what is yet to happen by projecting the current rate of change into the future. This means that it is not using the current measured value, but a future measured value.

The units used for derivative action describe how far into the future you want to look. i.e. If derivative action is 20 seconds, the derivative term will project the current rate of change 20 seconds into the future.

The big problem with D control is that if you have noise on your signal (which looks like a bunch of spikes with steep sides) this confuses the hell out of the algorithm. It looks at the slope of the noise-spike and thinks:

“Holy crap! This process is changing quickly, lets pile on the D Action!!!”

And your control output jumps all over the place, messing up your control.

Of course you can try and filter the noise out, but my advice is that, unless PI control is really slow, don’t worry about switching D on.