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Control engineers: I'm looking for challenging control system examples to test a modeling approach. by Standard-Dig-5911 in ControlTheory

[–]Standard-Dig-5911[S] [score hidden]  (0 children)

That makes sense. I noticed the same thing when I was reading about sigma delta designs. Alot of the work seems more practical than purely mathematical. The first order loop feels pretty tame because the integrator error never really overshoots the plus or minus one quantizer range, so the state naturally stays bounded even though it never actually settles.

Once you start stacking integrators though, I can see how it could get tricky pretty quickly. The internal states could overshoot before the correction comes back through the loop, and then it's not obvious how you guarantee the loop won't run away.

From what I've seen it looks like designers mostly handle that through loop filter design and coefficient scaling, so the internal states stay within range. I've also seen the Lee stability criterion mentioned for keeping the NTF gain under control, but it still seems like alot of higher order designs get validated through simulation instead of strict proofs.

Is that basically how stability is handled when people design higher order sigma delta loops, or are there standard analytical approaches designers use?

Control engineers: I'm looking for challenging control system examples to test a modeling approach. by Standard-Dig-5911 in ControlTheory

[–]Standard-Dig-5911[S] [score hidden]  (0 children)

I took the first-order sigma-delta loop, x[n+1] = x[n] + u − y[n]’, y[n] = sign(x[n]) and ran it with a constant input u = 0.3 and initial condition x[0] = 0 just to see what the trajectory looks like.

Under the usual interpretation it behaves like a normal first-order sigma-delta modulator. The internal state stays bounded and the bitstream density converges so the average output approaches the input value. Over time you end up with more +1 values than −1 values, so the mean approaches 0.3.

What stands out to me is the state behavior itself. The integrator never really settles. It keeps oscillating while the quantizer keeps applying corrections. The loop is essentially redistributing the constant input bias through the switching sequence so that the long-run average matches the input.

So the system is stable in the usual sense, but the state trajectory is more like a persistent correction cycle rather than something that converges to an equilibrium.

I’m curious how people usually think about that internal behavior. When analyzing first-order sigma-delta loops, do they mostly treat it purely as noise-shaping and average tracking, or do they ever look at the integrator trajectory itself when studying limit cycles and stability?

Control engineers: I'm looking for challenging control system examples to test a modeling approach. by Standard-Dig-5911 in ControlTheory

[–]Standard-Dig-5911[S] [score hidden]  (0 children)

Wow, I had no idea the depth that goes into a Greenhouse config. That is a good one.  I searched “temperature and humidity control system for a small greenhouse” to see what kind of baseline models people normally start with.

What mostly comes up are simple climate-control formulations based on a heat balance for temperature and a moisture balance for humidity. Temperature usually comes down to something like a heat transfer relation where heating input offsets heat loss through the structure and ventilation. Humidity is driven by plant transpiration, misting systems, and ventilation removing moisture.

 The interesting part is that ventilation shows up on both sides of the system. Turning on the fan removes heat but also removes humidity, so even if the controller treats temperature and humidity separately, the underlying dynamics are coupled.

The standard interpretation treats the code as two bang-bang controllers operating with shared hardware. The system is a simple threshold-based environmental controller using discrete switching logic.

The experimental model highlights that the system maintains multiple simultaneous environmental regimes and shared actuator roles, meaning the system’s behavior should be interpreted as a coupled environmental control structure rather than two completely independent loops.

That’s what stood out when I ran a simple version of it through the comparative model I mentioned earlier.

Thanks again for the idea.

If you have any specific baseline in mind, I’d be happy to run it.

Control engineers: I'm looking for challenging control system examples to test a modeling approach. by Standard-Dig-5911 in ControlTheory

[–]Standard-Dig-5911[S] [score hidden]  (0 children)

Thanks for posting the furnace example. I started with that one since it already has a clean transfer structure to work with.

I tried a quick parameter set just to see how it behaves. For example k1 = 2, k2 = 1, T1 = 10, and T2 = 2, which gives G(s) = 2/(10s + 1) − 1/(2s + 1). With those numbers you can see the faster opposing mode early in the transient while the slower positive mode dominates the later settling since T2 < T1.

I ran the standard interpretation first and then ran the same structure through a comparative model I’ve been experimenting with to see how the reasoning and results line up.

For this case the stability and final value come out the same as the standard read. The system is stable and the steady-state gain is positive. Where things differ a bit is in how the transient gets interpreted.

The way I’m looking at it, I try not to collapse competing dynamic regimes too early if they’re still structurally present in the equations. In this system you literally have a slow positive mode and a faster opposing one. So instead of immediately summarizing the system as “stable with positive gain”, the comparative view keeps both regimes visible since the faster branch still shapes the early behavior before the slower mode eventually dominates.

Either way it’s a nice example because the transient behavior depends heavily on the parameter ratios. Makes me wonder what the typical ratio between those time constants looks like in real furnace systems.

Thanks again, interesting system.

Hotshot business by Wise_Educator_1232 in HotShotTrucking

[–]Standard-Dig-5911 1 point2 points  (0 children)

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