Why should we attempt to remove integrators from the control loop?

Question

I am working on a robotics research project in its very early stages (we do not have a system model yet). A colleague suggested we attempt to remove all integrators in the control loop. If anyone could explain why we would want to do this, and possibly point me towards relevant textbook sections/ journal articles, it would be greatly appreciated!

I did find this journal article, but I am not sure if it is relevant (or even that good): "On overshoot and integrators", Bo Zhu, School of Aeronautics and Astronautics, University of Electronic Science and Technology of China.

I would like to add, from a classical/s-domain perspective, I realise the importance of using integrators to eliminate or minimise the steady-state error. I also realise, again in a classical sense, that having too many integrators may modify the transfer function and cause the system to be unstable. Additionally, systems with more integrators are more complex and may have slower transient responses. I'm not trying to answer my own question, just wanted to provide some perspective of what I think I am aware of.

Answer 1

Integrators increase the low-frequency gain - this is what makes them useful to eliminate steady-state errors.

On the other hand integrators add phase to the Bode plot. This leads to lower margins, oscillations, and possible instability. The best way of seeing this is using Bode plots and the Nyquist criterion; Evans' root locus diagram is also helpful. Additionally, integrators are open-loop unstable, which may bring about practical problems with systems that deviate from the idealized assumptions - integral-windup as mentioned above is just one of the most evident ones.

All of these advantages and disadvantages of integral control become most evident using classic frequency-domain reasoning, however the intuition applies to MIMO, nonlinear, and time-varying systems.

As a reference I suggest you consult one of the many excellent control systems textbooks, such Franklin and Powell, rather then jumping straight to randomly chosen articles in unnamed journals.

Answer 2

First of I assume that you have system that can be approximated well by a linear time invariant model. And since you are talking about integrators I assume that you are controlling from a frequency domain perspective, so the system is SISO, or at least sufficiently decoupled. If you do not have sufficient understanding of loopshaping, then adding integrators can make the closed loop unstable.

Adding integrators can help reduce the steady error. For example when controlling a mass with a force then if you have a reference which has a constant velocity or even acceleration then one or more integrators can be used to reduce the steady state error. However this steady state error due to constant velocity or acceleration when using a controller without integrators can be used to tune feed-forward.

The biggest downside to my knowledge of integrators are integral-windup. Especially when you are dealing with input saturation. There are ways of preventing this, but this does add more complexity to the control logic.