3

I'm interested in chaotic circuits; and while many circuits that model attractors like Chua's Circuit, Lorenz Attractor, and RC phase shift networks are available, I would really like to model the behaviour of a double pendulum using op-amps.

I've seen a few references to the possibility of computing the differential equations describing the motion of a double pendulum; but no concrete implementations. How could I go about modeling this behaviour using op-amps?

sehrgut
  • 139
  • 3
  • Chua Chaotic cct http://tinyurl.com/y8lddwhb – Tony Stewart EE75 Aug 01 '18 at 02:57
  • I'm aware of Chua's Circuit, as I stated in my question. The question is not how to generate ANY chaotic dynamical system, but specifically how to model a double pendulum. – sehrgut Aug 01 '18 at 04:31
  • This is a 50 yr old grad thesis topic of a double inverted pendulum easily found on web. You need some understanding of control theory. Do they still do this one? here's another Chaos circuit http://tinyurl.com/yap3x3rf – Tony Stewart EE75 Aug 01 '18 at 04:52
  • seems pretty hairy, involving conversions between cartesian and polar cordinates... – Jasen Слава Україні Aug 01 '18 at 05:56
  • @Jasen it will be a learning experience for the OP .... – Solar Mike Aug 01 '18 at 06:26
  • 1
    Begin with the equation. Then decide how you will output a one dimensional signal (a voltage) that represents a one-dimensional value from the pendulum. Then come back and modify your question with this detail. – Andy aka Aug 01 '18 at 09:52
  • @TonyEErocketscientist I'd appreciate you providing links instead of sarcasm. I've read a lot of those papers, and the one you seem to be referring to is not a model of a double inverted pendulum, but a control circuit that uses feedback loops to balance a physical double inverted pendulum. These circuits are all over the literature, and they don't have any relation to this question. And yes, I know about those other chaos circuits: I'm NOT trying to build yet another attractor, I'm trying to model a specific system. – sehrgut Aug 03 '18 at 15:58
  • Your question lacked specs to a recurring thesis topic was my objection. I’m not sure what your problem is. http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum&section=SimulinkModeling – Tony Stewart EE75 Aug 03 '18 at 21:35
  • Do you want a model or know how to convert a model to transfer functions including non-linear stiction. – Tony Stewart EE75 Aug 03 '18 at 21:42
  • 4
    The fundamental Physics Model must be defined before it's realization in Analog Electronics. Learn to articulate the characteristics to make this question worthy of an answer. – Tony Stewart EE75 Apr 21 '19 at 16:34
  • https://diego.assencio.com/?index=1500c66ae7ab27bb0106467c68feebc6 – Tony Stewart EE75 Apr 21 '19 at 16:42

1 Answers1

0

Part of the problem of the double pendulum is that the behaviour is non-linear except at the limit of very small excursions. It follows that you need non-linear elements in your analog computer. For the double pendulum, the non-linear elements are sin/cosine calculators. You can implement the sinusoid elements with multiplier chips and a Taylor expansion, or with ADC/DAC converters and a ROM block. If you calculate an equivalent expansion using exponentials instead of a power series, you can use diodes instead of multiplier chips.

david
  • 4,364
  • 15
  • 30