That an overexuberant negative feedback controller can still lead to explosions is one of the interesting results of control theory...
Terminology question: Does “negative feedback” have a precise definition? So if I point at something and say “this is a negative feedback loop”, is that exactly the same as saying “the current state of this thing is stable, or the state is known to be in the neighborhood of an implicitly communicated stable point”? (And conversely for “positive feedback” = “unstable”) I’m considering that a physical explosion will reliably reach a stable state. Or something that pushes a real value in [0,1] towards the nearest bound, but then stops.
Does “negative feedback” have a precise definition?
Yes; the correction applied is in the opposite direction of the error. A positive feedback controller is one where the feedback is in the same direction as the error.
I’m considering that a physical explosion will reliably reach a stable state.
Not really, because stable implies that it will return to that state if disturbed. If you push around some of the ash after an explosion, it doesn’t restore itself. (It is true that explosions stop when they burn through their energy source, and models that take that into account look realistic.)
Thanks for clarifying. I saw a few definitions that were less precise: wikipedia describes negative feedback as ”...when some function of the output of a system...is fed back in a manner that tends to reduce the fluctuations in the output, whether caused by changes in the input or by other disturbances.” I think I was confused by skipping the tends part, and applying the resulting definition to the shower example.
You’re right on the explosion.
So “negative feedback” does not imply “stable point”. Although “stable point” presumably implies “negative feedback” somewhere?
So “negative feedback” does not imply “stable point”. Although “stable point” presumably implies “negative feedback” somewhere?
Yes, with an emphasis on the ‘somewhere.’ (Is it really ‘feedback’ if the restorative force is already inherent in the system? Well, that depends on how you look at things, but I’d generally say yes.)
Terminology question: Does “negative feedback” have a precise definition? So if I point at something and say “this is a negative feedback loop”, is that exactly the same as saying “the current state of this thing is stable, or the state is known to be in the neighborhood of an implicitly communicated stable point”? (And conversely for “positive feedback” = “unstable”) I’m considering that a physical explosion will reliably reach a stable state. Or something that pushes a real value in [0,1] towards the nearest bound, but then stops.
Yes; the correction applied is in the opposite direction of the error. A positive feedback controller is one where the feedback is in the same direction as the error.
Not really, because stable implies that it will return to that state if disturbed. If you push around some of the ash after an explosion, it doesn’t restore itself. (It is true that explosions stop when they burn through their energy source, and models that take that into account look realistic.)
Thanks for clarifying. I saw a few definitions that were less precise: wikipedia describes negative feedback as ”...when some function of the output of a system...is fed back in a manner that tends to reduce the fluctuations in the output, whether caused by changes in the input or by other disturbances.” I think I was confused by skipping the tends part, and applying the resulting definition to the shower example.
You’re right on the explosion.
So “negative feedback” does not imply “stable point”. Although “stable point” presumably implies “negative feedback” somewhere?
Yes, with an emphasis on the ‘somewhere.’ (Is it really ‘feedback’ if the restorative force is already inherent in the system? Well, that depends on how you look at things, but I’d generally say yes.)