# Why isn't derivative control used without proportional or integral control?

Why isn't derivative control used separately in industrial controller designs?

One answer I read online was that derivative control is not used separately, i.e., without proportional (P) and integral (I) control, in a closed-loop system because:

If the error is constant and non-zero, then the output of the derivative controller is zero. So it won't work satisfactorily.

Is this the only reason?

• I can't think of another. (Isn't one enough?) Commented Dec 5, 2017 at 14:11
• One is enough but the question is for a coursework, so the more the merrier! Commented Dec 5, 2017 at 14:14
• This answer is effectively telling "It will just never work as a setpoint controller". I think this reason should be very sufficient. Commented Dec 5, 2017 at 14:48
• The only other reason I can think of is noise- The derivative's gain increases with frequency so it tends to amplify any noise in the system. So too much derivative can be a problem. But of course the primary reason is obvious. Commented Dec 5, 2017 at 15:11
• More that that - it is simply not possible to realize an ideal d-controller. It always has a proportional part.
– LvW
Commented Dec 6, 2017 at 15:39

The reason is simply that it is hard to find a process that can benefit from the properties of D-only controller. Let's review those properties.

Derivative control function can be written as U(t) = Kd x de(t) / dt. Which means the control function is proportional to change of an error in the given time.

• If there is no change in a process (i.e. error does not change) then the control function is zero (i.e. "do nothing"). This could be useful, however this also means that D-controller alone cannot bring the system to its target (setpoint).

• If the error changes the control function acts to reverse the change. Furthermore, the faster we approaching our target the stronger derivative action opposes the change. This "slow down" command is very useful. If your target is a wall and you are in a car then you probably want to slow down if you want to stop in time.

So, from the above you can see that D-controller provides damping effect when something changes and no effect whatsoever if nothing changes. You can find applications for this, but not many. Unfortunately, usability of derivative control further reduced by its other properties.

• D-controller is very sensitive to noise in a system. For example, let's say your GPS sensor has 1 m resolution. In reality it means that even if you stay still the consecutive position readings can differ by ±1 m (this would be a "noise" in a system). Now, assuming you are moving 10 km/h and reading position every second (this would be your dt time constant), the distance to your target (an "error") changes about 2.8 m each second. As you can see, the noise amounts to more than 35% of the de(t) part of the equation. If you attempt to use D-controller to stabilize your movement in these conditions it might instead cause instability.

• Derivative term is affected by setpoint change, something called "derivative kick". If we take previous example and change your destination by 100 m then the consecutive calculated distance (error) will change in the middle, e.g. 50, 47, 45, 142, 139, 137 etc. Now, the de(t) will look like this: -3, -2, 97, -3, -2. Note that huge jump in derivative, not only exceeding many times the magnitude of position change, but also having opposite sign.

If you can find a process that can be controlled with logic described above then you can use pure derivative controller. I doubt there are many industrial processes like that, however.