Originally Posted by

**panzerwagon**
Although the concepts are similar, the stability of an electronic feedback loop is much easier to quantify and analytically examine due to the inherent closed system it encompasses. For example, an electrical current only passes through a conductor, so it's easy to trace and map out and quantify all sources of stimuli into the feedback loop.

true.. if the loop is completely electronic with well quantified components, then it's just a matter of knowing control theory and doing the math. In other cases, such as thermal control, there is the need to characterize the device being heated, the heater itself, etc. The goal is usually to come up with some simple linear model of the device and heater, so as to make suitable for analysis. There will still be a need to run some tests and see how it turned out, and possibly tune the control loop parameters afterwards.

Originally Posted by

**panzerwagon**
On a bicycle, in addition to the dynamics of the frame, we have a rider of unknown mass, dimensions, weight distribution, strength in each active body part, velocity, tyre size, road surface friction, gradient, not to mention wind velocity and direction. I'd imagine that in order to compute metrics like gain/phase margins, each component would need to get modeled analytically and approximated, as many of them are nonlinear. Even if the equations were tractable, the variables are so many that the loop order would be too high to meaningfully glean these metrics.

The frame, wheels, bar & stem, etc. do act as one or more springs. The rider would be considered the primary mass of interest, and might even add a bit of damping. I think it's too early to say how difficult it would be to model, since we haven't even defined what "stability" means yet.

As for variables such as velocity, tire size, road surface roughness, etc., it's good to be thinking of those things. I imagine that it would be best to start with some standard values for a nominal case. If there is a desire to characterize over a range of one of the variables, that could be done too. There would certainly be value in knowing how each of the variables affects stability, since there may be a desire to change one variable without changing overall stability, so you'd want to change another variable to compensate. An example would be changing tire width in order to compensate for a change of frame stiffness.

Originally Posted by

**panzerwagon**
More importantly, would it actually yield anything practically useful? I suspect most frames are created with ample margin of stability for most real-world cases, through an empirical process. Having two different (positive) phase margin numbers for a couple frames would not necessarily point to superiority of one over the other, and differences would likely be dominated by other qualities.

We've had people discussing "stability" for decades without being able to define or measure what they mean by that term. Bike manufacturers are designing bikes mainly by sticking to what has worked in the past. Does this work? Maybe?? I know that when I started riding recumbents, it took about 1000 miles to feel reasonably proficient handling them, which suggests that the standard for stability or handling is much different from upright bikes.

As I mentioned earlier, there are metrics beyond phase margin for evaluating stability in electronics. The response to a transient can indicate whether it is overdamped or under-damped, suggesting how close it lies to a neutral stability point or how close it is to breaking out into oscillations. I've used this informally to evaluate a bike's tendency to shimmy.

But... the first hurdle is to figure out what the desired characteristics are, and then how to quantify them and measure them. Without this first step, the rest has no meaning.

Steve in Peoria