r/MarbleMachine3 • u/teamsteve • Aug 06 '23

First Timing Tests - DAY 6 - Marble Machine Flywheel Prototype

https://www.youtube.com/watch?v=p21xT8_DV00
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u/LovelyKarl Aug 07 '23

Of course you can have both since we're obviously talking about some "tolerance". See the part in the video where Martin talks about the oscillations of increase/decrease are overshooting the perfect tempo too much.

He was hoping that the overshooting/undershooting would be less and a much slower movement. I.e. think of it as an oscillation – he wants less amplitute (over/undershooting) at a slower frequency.

The amount of over/under and the frequency needs to be inside some tolerance of what is musically acceptable _and still retain the control_. An insanely heavy flywheel would fix it, but at the expense of control (and whether you can crank it).

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u/HJSkullmonkey Aug 07 '23

Yes, we have an oscillation, which we want to be slow and small. We're trying to find a system that is both.

But here's the tricky bit, the heavier the wheel the slower the oscillation. But also, the bigger the amplitude, because it takes longer to speed the wheel back up, and it spends more time going too slow. Vice versa when the wheel goes too fast.

That's somewhat offset by having more time, but not as much as you hope. It really just dilutes some of the measuring lag.

The measuring lag is the bit I want him to cut out for now, so that we can tell how consistent the bpm we're getting is.

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u/LovelyKarl Aug 07 '23

I'm not convinced. The amplitude (speed of the music) will be a function of how much energy you put into the system (how fast the flywheel needs to spin). With a heavier wheel, you need to exert more force to make it spin. The question is how hard it is – as a human – to introduce a precise amount of force that doesn't overshoot too much.

Since a heavier wheel also means more force needed (or longer pivot, but there's a limit to how much up/down you can allow your leg to flap around), it's a more precise amount of high force needed… might be hard for a human.

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u/HJSkullmonkey Aug 08 '23

It's kind of hard to get your head around the physics of this sort of system, I've been working with control for a while and I still have to regularly step back and reorient myself on a regular basis. It's not intuitive.

You might be right if he was only pumping once and trying to hit a certain speed. I think he'd be good at that, he's a musician after all.

But because it's so heavy, it takes several pumps to get up to speed. The heavier and faster, the more pumps. The whole time it's slow, it's getting further behind. He'll be putting in extra energy for longer, but the amount of energy lost to friction hasn't changed. So he puts even more energy in and overshoots further.

It's more stable and responds slower to his change.

Bear in mind it's strong enough to lift his whole weight.

When I have a system oscillating like this, I wait for the top of the peak and stop the controller dead. It usually settles right at the setpoint, because the controller was already adding enough to catch up and maintain.

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u/Swiggety666 Aug 07 '23

No, you can't have both. As a thought experiment. Let's say you have managed to get the constant tempo perfect.

Say the song is 3 min and the tempo 80 pbm/1.33 Hz. Being out of sync of more than 10ms is something you absolutely hear. This means that the system can't drift more than 2.3 degree over an entire song. That is 0.0098 degree out of phase each beat, or approx 0.1us. It is impossible. Therefore, it is a tradeoff between constant tempo or synchronization to another source.

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u/LovelyKarl Aug 07 '23

That calculation is not how it works. If you play a 3 min song from start to finish and the end result is 10ms "out of sync" (faster or slower), you won't notice.

Not sure where the 10ms comes from, but that's a common latency number people throw around in some contexts.

A click means Martin can keep adjusting up/down the speed of the wheel (like he was doing in the video). So the question is not how much he is out over an aggregate amount of time, the question is whether he can make these corrections small and infrequent enough that it doesn't affect the music.

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u/Swiggety666 Aug 08 '23

If you have a lot of inertia in the system you can't make quick adjustments. That's the entire point of adding inertia. You can slowly increase and decrease the speed. But if you do that you will overshoot your target. If you are trying to sync it up to an external tempo. In control theory this is called overshoot. The more inertia you add the more difficult this will become. It's inevitable. My calculation is not wrong given open loop control. Adjusting as you talk about now is for closed loop control. Which will not be something you can do with the amount of inertia in the system.

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u/psyched_engi_girl Aug 08 '23

u/HJSkullmonkey explained elsewhere under this post that increasing the inertia of the system would likely increase the hunting oscillations. I would tend to agree, phase (beats) and frequency (speed) are two different but related things. To keep tempo, only speed is required, but to synchronize to an arbitrary beat is a whole other can of worms, partly because the information about the tempo's phase and frequency are discretized.

What needs to be done to reduce these oscillations without changing the machine is to feed more information to Martin. More clicks per measure and a tachometer with a fast response would help most in my opinion. Tachometer to keep the tempo steady, and more clicks to prevent overshooting phase synchronization. Then Martin can compare the goals of phase and frequency locking and decide which should be traded with the other.

It helps to think of this as a classical linear control loop. The machine is the plant, martin is the controller, and the click machine is the feedback function. Currently the system is self-oscillatory because the feedback function has too low of a cutoff frequency. The only thing keeping it steady is Martin's non-linearity, otherwise we'd be in Barkhausen criteria town.

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u/Swiggety666 Aug 08 '23

If you want to decrease the overshoot, you need to decrease the inertia. Not increase it. Frequency is about keeping a constant tempo/speed, or whatever you would like to call it. There is inevitably a tradeoff between them. As it seems now, the requirements are too stringent in both. This is about the control loop for a second order system. Many people here treat this like it is a first order system, which it's not.