Chaos In Control Loops

Limit cycles caused by nonlinearity or discontinuity; that could be either computational or the property of the plant, or both. Very typical for (improperly designed) feedback loops.

Parrots could remember many buzzwords; although they don't understand what those words mean.

Vladimir Vassilevsky DSP and Mixed Signal Consultant

Sometimes one intentionally allows some residual, low-level oscillation, if it's not going to cause enough harm to justify the effort or expense to eliminate it.

But if it's harmful and it comes as a surprise, then yes, the control loop is improperly designed.

Or it could be the simulator. Change the max timestep and see if the "regularity" changes. ...Jim Thompson

It can be very difficult to simulate long-term values accurately (setting smaller tolerances, usually RELTOL first, will cause it to make finer timesteps -- note the simulation will slow down proportionally).

I once tried simulating a theremin (on the transistor level); it works, but the lowest reasonable beat frequency I can seem to simulate is on the order of 2kHz (out of ~1MHz); less and the phase shift slowly rolls around without a well defined waveform (if it were phase locking due to injection, the waveform would be humpy).

Some circuits are, by nature, chaotic. You can, of course, implement the logistic function with samplers and multipliers; anything from the van der Pol oscillator to Lorentz attractors and beyond can be built from analog and calculus function blocks.

People don't always appreciate that peak-current-mode SMPS controllers are inherently chaotic: the graph of duty cycle(s) vs. setpoint has precisely the same form as varying the "r" parameter in the logistic equation. That is, it exhibits a logistic map behavior, and limit cycles. This can be improved, but cannot be eliminated, with slope compensation and feedback. Such circuits whine and hiss when driven into overload.

Tim

Yet some parrots manage to get college degrees & practice law, or design electronics. You can tell that they are parrots, because they do the same things over & over.

Funny, my kids used to do that too. ;)

Cheers

Phil Hobbs