Integration (was RE: "Twitchie")

[Eetu Pikkarainen 2018-01-18]

Thanks Bruce and specially Martin for answers (below). Because of my missing background in physics and engineering I am still quite unsecure. I was thinking about the
flexible ribbon band from the short hand of Twitchie to its long hand. I must keep on thinking but I would still want to see an example of two simple controllers which were as similar as possible but the one were proportional and the other had a integrator.

···

Eetu

[Martin Taylor 2018.01.18.00.04]

[From Bruce Abbott (2018.01.17.1935 EST)]

[Eetu Pikkarainen 2018-01-17]

[From Rupert Young (2017.01.12 22.50)]

(Bruce Abbott (2018.01.11.2330 EST)]

So here’s a nice test of your understanding – can you explain why the hardware implementation can get away without a leaky integrator in the output of the control system, and why the proper output gain is so much lower.

I’d guess because the integration is taking place in the environment, in the damper, which I think Martin has said already.

Could the (quite) flexible ribbon play also a role in integration?

Martin may have a better answer for this than I do; I would say that It does, by storing/releasing the forces accumulated as the rubber band stretches and relaxes. But I think
the main factor is the inertia inherent is the system’s moving parts.

Bruce

If you want to know whether something is an integrator, think of it as a storage cylinder. If you keep putting things into it does it continue to increase some related variable such as the mass of its contents?
You can use that metaphor quite widely. If you apply a force consistently to a mass in a friction-free environment, it goes faster and faster, so the velocity is the result of integrating the force. If you have a bucket and you pour water into it from a tap,
the water level rises, so the level is the result of integrating the flow rate (the level being a surrogate for the quantity of water in the bucket, that same way a neural current is a surrogate for an averaged neural firing rate). If you keep rubbing on a
fabric, it will become worn and frayed, the wear is an integration of the rubbing.

Lots of things can be integrators. But not all energy storage elements are. A helical spring is not; you supply it with potential energy by pushing or pulling on it, but it only stretches or compresses to the point where its restoration force is exactly the
match of your pushing or pulling force, and when your force is removed, the spring goes back to its original length rather than staying at its stretched length.

I don’t know what flexible ribbon Eetu is referring to, or why its flexibility might affect it’s function (if any) as an integrator. What is being put into it that makes something continue to increase proportionately as a result? With the dashpot, the height
of the piston continues to move as a pushing or pulling force is applied, so the height of the piston is the effect of continuing the applied force. Take the force away and the piston stops moving, so the dashpot is an integrator (If it didn’t leak around
the piston or through some small hole, there would be a level of the piston at which the internal pressure force on the piston matched the ambient air pressure plus the pushing or pulling force, and it wouldn’t be an integrator.)

Maybe this metaphor will help determine whether Eetu’s flexible ribbon is an integrator. What is the input, and what output behaves proportionately to the sum of what has been input?

Martin

[Eetu
Pikkarainen 2018-01-18]

        Thanks Bruce and specially Martin for answers

(below). Because of my missing background in physics and
engineering I am still quite unsecure. I was thinking about
the flexible ribbon band from the short hand of Twitchie to
its long hand. I must keep on thinking but I would still
want to see an example of two simple controllers which were
as similar as possible but the one were proportional and the
other had a integrator.

···

Eetu

[Martin Taylor 2018.01.18.00.04]

[From Bruce Abbott (2018.01.17.1935 EST)]

[Eetu Pikkarainen 2018-01-17]

        [From Rupert Young (2017.01.12

22.50)]

        (Bruce

Abbott (2018.01.11.2330 EST)]

            So

here’s a nice test of your understanding – can you
explain why the hardware implementation can get away
without a leaky integrator in the output of the control
system, and why the proper output gain is so much lower.

        I'd

guess because the integration is taking place in the
environment, in the damper, which I think Martin has said
already.

          Could the (quite) flexible ribbon

play also a role in integration?

          Martin may have a better answer

for this than I do; I would say that It does, by
storing/releasing the forces accumulated as the rubber
band stretches and relaxes. But I think the main factor
is the inertia inherent is the system’s moving parts.

Bruce

      If you want to

know whether something is an integrator, think of it as a
storage cylinder. If you keep putting things into it does it
continue to increase some related variable such as the mass of
its contents? You can use that metaphor quite widely. If you
apply a force consistently to a mass in a friction-free
environment, it goes faster and faster, so the velocity is the
result of integrating the force. If you have a bucket and you
pour water into it from a tap, the water level rises, so the
level is the result of integrating the flow rate (the level
being a surrogate for the quantity of water in the bucket,
that same way a neural current is a surrogate for an averaged
neural firing rate). If you keep rubbing on a fabric, it will
become worn and frayed, the wear is an integration of the
rubbing.

      Lots of things can be integrators. But not all energy storage

elements are. A helical spring is not; you supply it with
potential energy by pushing or pulling on it, but it only
stretches or compresses to the point where its restoration
force is exactly the match of your pushing or pulling force,
and when your force is removed, the spring goes back to its
original length rather than staying at its stretched length.

      I don't know what flexible ribbon Eetu is referring to, or why

its flexibility might affect it’s function (if any) as an
integrator. What is being put into it that makes something
continue to increase proportionately as a result? With the
dashpot, the height of the piston continues to move as a
pushing or pulling force is applied, so the height of the
piston is the effect of continuing the applied force. Take the
force away and the piston stops moving, so the dashpot is an
integrator (If it didn’t leak around the piston or through
some small hole, there would be a level of the piston at which
the internal pressure force on the piston matched the ambient
air pressure plus the pushing or pulling force, and it
wouldn’t be an integrator.)

      Maybe this metaphor will help determine whether Eetu's

flexible ribbon is an integrator. What is the input, and what
output behaves proportionately to the sum of what has been
input?

      Martin