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| chickenHeadKnob:
--- Quote from: GK on April 25, 2013, 02:10:47 pm ---So how many individual integrators will that problem require then? ;D I'm assembling into this computer project 30. I still have a ship load of hardware assembly to complete before I can run anything serious. I currently have this machine ~90% designed and ~5% built. The former has been taking nearly all of my free time over the past several months, but should make way for the latter (construction) in another month or two in a major way. Once this thing is built I'll have all the time in the world to study problems to run. --- End quote --- Well my comment was a sideways query as to how you would implement an FPU simulator, because I don't know how. The original and canonical FPU problem is 64 idealized and simulated spring-mass units connected in a line so I was thinking 64 oscillators of some sort, maybe simple RC's or an array of 74HC14's in a ring oscillator configuration. That would be the first step. Next I would need to add in the non-linear terms in a controlled way, thats the second step. Finally how to display what is happening in the system. Anyway I thought you might have some ideas. |
| GK:
--- Quote from: chickenHeadKnob on April 25, 2013, 09:58:01 pm --- --- Quote from: GK on April 25, 2013, 02:10:47 pm ---So how many individual integrators will that problem require then? ;D I'm assembling into this computer project 30. I still have a ship load of hardware assembly to complete before I can run anything serious. I currently have this machine ~90% designed and ~5% built. The former has been taking nearly all of my free time over the past several months, but should make way for the latter (construction) in another month or two in a major way. Once this thing is built I'll have all the time in the world to study problems to run. --- End quote --- Well my comment was a sideways query as to how you would implement an FPU simulator, because I don't know how. The original and canonical FPU problem is 64 idealized and simulated spring-mass units connected in a line so I was thinking 64 oscillators of some sort, maybe simple RC's or an array of 74HC14's in a ring oscillator configuration. That would be the first step. Next I would need to add in the non-linear terms in a controlled way, thats the second step. Finally how to display what is happening in the system. Anyway I thought you might have some ideas. --- End quote --- OK, basic rule of analog computing - most physical systems can be simulated with enough of rather few building blocks, namely, the integrator, the inverting summer and the function generator. The spring mass problem is rather simple (see attached). in it simplest form it is just a double integration in a loop with damping feedback. It requires two inverting summer and two integrator stages. To simulate 64 (does it have to be 64?) of them I would need 128 integrators and 128 summers. You say they were connect in a line? That makes it a fair bit more complex (much more than just summing outputs as the masses of all of the lower units are hanging on and thus influencing the higher units). Sounds like an interesting problem though. The attached simulation just shows three independent spring mass simulations run simultaneously. Another rule of analog computing; you don't actually need an analog computer as all of its building blocks and be readily simulated and interconnected in SPICE ;D . However, in comparison, that is hardly any fun. EDIT: I don't have the time to search for it right now, but in one of my textbooks a double (series connected) spring mass system is described as part of a car suspension system simulation. From memory the first spring mass represents the weight of the wheel in its entirety and the suspension spring while the second spring mass represents the "spring factor" of the inflated tire and the weight of the tire itself. The solution to the problem you describe could be as simple as expanding upon that problems basic methodology by simply adding to the number of series-connect spring masses. |
| chickenHeadKnob:
--- Quote from: GK on April 26, 2013, 12:55:53 am --- OK, basic rule of analog computing - most physical systems can be simulated with enough of rather few building blocks, namely, the integrator, the inverting summer and the function generator. The spring mass problem is rather simple (see attached). in it simplest form it is just a double integration in a loop with damping feedback. It requires two inverting summer and two integrator stages. To simulate 64 (does it have to be 64?) of them I would need 128 integrators and 128 summers. You say they were connect in a line? That makes it a fair bit more complex (much more than just summing outputs as the masses of all of the lower units are hanging on and thus influencing the higher units). Sounds like an interesting problem though. The attached simulation just shows three independent spring mass simulations run simultaneously. Another rule of analog computing; you don't actually need an analog computer as all of its building blocks and be readily simulated and interconnected in SPICE ;D . However, in comparison, that is hardly any fun. --- End quote --- Thank you for the thoughtful reply. Need to be 64?, well if I want to be true to the original, yes. Enrico Fermi (nobel physics), Stan Ulam mathematician and co-inventer of the hohlraum type of fusion bomb, Pasta a relative nobody computer guy and Mary Tsingou a mathematician/programmer were researching models of heat diffusion in solids and looked for a simplified model to be simulated on an early digital computer. The mass-springs in the model are undamped (frictionless). I see in damping in the double spring model in your png, otherwise its on the right track. What I was hoping for was to be able to simulate the individual mass-springs with a few cheap components, I thought trying to display what is happening would be much more of a challenge. Note that the surprising thing about the FPU simulation is that it never settles down for a broad spectrum of inputs, instead it exhibits chaotic behaviour. I agree spice is no fun, I wanted the tactile experience of real hardware. My brother gave me a "chaotic pendulum" for christmas many years ago, it is just a magnet hanging from a string and some disk magnets you position around the base which cause the pendulum to swing in widely different directions and periods. It is fun to play with and I thought a real FPU simulator would be even better. Sort of a high brow mathematical lava lamp. I am a coder and if I was forced to I probably wouldn't use spice, and instead code it up myself. But I don't have to as multiple implementations are available on the net. Some links: http://www.scholarpedia.org/article/Fermi-Pasta-Ulam_nonlinear_lattice_oscillations http://physics.ucsc.edu/~peter/242/FPU-birth-of-nonlinear-science-Lilienfeld.pdf - this is a good intro pdf of lecture slides |
| GK:
Hmmmm..........Problem is if it is un-damped you somehow have to maintain a loop gain of precisely 1, otherwise the oscillations will either grow until the amplifiers saturate or decay altogether. To do this with a real world analog computer you will then need a level detector controlling a multiplier to act as a servo loop to regulate the amplitude of oscillation. However the feedback contribution of the servo leveling loop(s) may corrupt the experiment (there may also be some serious interaction issues too). At this stage I really don't know. Perhaps this is a reason why they had to hang out until someone had finally developed a digital computer that they could play with? |
| GK:
I just deleted and re-posted revised circuits for the vertical and horizontal deflection coil drivers attached to posts 81 and 84. I ended up modifying the frequency compensation. In the previous iteration(s) I had pole-zero pairs in the coil current-sense negative feedback loop(s) to give greater loop gain at DC, but this compromised the transient response to some degree, producing significant (10%) overshoot to the edges of a full amplitude square wave stimulus due to the zero (a high-pass pole) introduced into the loop response. I have now removed the pole-zero pairs in each amplifier circuit to keep the feedback loops 100% DC coupled. This gives the deflection amplifiers an almost perfect transient response without any overshoot. Now I will have to revise the PCB layouts yet again.......damn. |
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