[ChuckNorris89]

>Generally I have left out the integration step because it can easily cause instabilities, even with a wind-up preventer.

Funny, in automotive we always left out the derivative component not the integral which IMHO is the most useful component of the controller.

[joeberon]

Yeah I've usually heard that the derivative component is what gets left out, never heard of leaving out the integral

[edge17]

Yea, I built a ball beam balancing device that torqued the beam using electromagnets (instead of the standard 2nd order system with a motor in the center and fast response). The electromagnets can not 'instantly' change the angle of the beams, and the ball's dynamics lead to overall instability as it rolls around and accelerates faster than the system can respond.. Without a derivative term it would have been impossible to control the system. That being said, the project was deliberately contrived in a way where the effects of the P,I,D terms were observable.

[zwieback]

If you have a system without natural dampening and can't tolerate overshoot or oscillation you'd use a bit of D to slow things down.

[rcxdude]

It does depend on the system you're controlling, often there's a natural integral in there and so you effectively 'shift' everything down one (P acts more like I, D acts like P, and I is a double-integral). Like how PD is fine for the quadcopter control until wind is added to the simulation.

[jbay808]

Definitely.

The main price of an integrator is 90 degrees of phase lag; this will harm the stability of many systems but as long as it's kept at a low bandwidth it's usually fine.

The main price of derivative gain is high frequency noise amplification, and so a well designed PID will have a limited bandwidth for the D term as well. For many systems, especially those that are already damped or don't need the extra phase margin, it's not needed or not worth the noise cost.

[dls2016]

A quick intuition for this is: d/dx(e^(iwx)) = iw*e^(iwx)... that is, differentiation amplifies higher frequencies more than lower ones.

[aidenn0]

Right, an integral is a low-pass filter with infinite gain at DC and a derivative is a high-pass filter with gain of 0 (negative infinity dB) at DC; they both have 90 degrees of phase shift.

[silentwanderer]

In high school we nearly always left out the I term because we didn't mathematically verify our controllers, couldn't risk breaking the systems we were controlling with windup, and cared more about smooth and predictable motion than accuracy.

[tnecniv]

Why did you guys drop the derivative part? I've always found that pretty useful.