Stability and Controllability
In my half century of engineering, the concept of the boundaries between stability vs. controllability has been difficult to define. They apply to aircraft, boats and wheeled vehicles.
Start by imagining a Lincoln
First, when it is laying flat on the playground, it is stable – it will remain as you place it.
Now, stand it up on end, on a firm flat base. In a still wind, this “stick” is stable. Now, at sunset colder air from the dark eastern sky begins to blow gusts toward the west. The pole topples over when the top leans 12 inches to the west, as the center of gravity leans just over than 12 inches. So, the stick was marginally stable.
Well that much is obvious. Now, let’s bury ten feet of the pole vertically in a concrete base. The bottom end is pretty stable, isn’t it? How about the top end? It is whipping back and forth at sunset. Is that stable or unstable?
In my field, it would be described as oscillatory unstable but still controllable. If the wind stops gusting, the stick returns to perfectly upright. What if a wind gust is so strong that it puts a permanent bend in the stick? The thing is still stable when the wind stops, but the top is pointed in a different direction. Remember that for later.
What could you do to prevent that flexing back and forth from bending or breaking the stick? You could put a shock absorber on it, but where would you anchor it? Put a large, heavy ball on top of the pole. The size of the ball would increase the wind drag force so that the pole would bend more. However, the mass would reduce the frequency of oscillation, hopefully to the extent that flexing would not reach the resonate amplification to cause the bending to exceed the yield bending limit of the pole.
That system works in vehicles, too
Recall when I spoke earlier about the free control testing of automobiles at high speed? You would be going at 65 mph with one hand at the top of the steering wheel rim. First you pull the rim quickly to the right and release it. Ideally, the car should snap back to the left, overshoot somewhat, and then come back to the right and stabilize going straight, nearly in the original direction. Less ideal cars might flip left to right several times before becoming steady. That stability is not so good, but adequate.
If the car continued to oscillate left to right without end, that was a failure. If the car snapped so hard that is spun out, that was a not-acceptable disaster.
How could you correct that? Chrysler did it this way. First they increased the mass of the steering wheel rim. They could have added a steering damper to the steering linkage (power steering cars had that and did not fail the test). Some auto companies did that, but it reduced steering feel. Eventually Chrysler settled on changing the self-aligning torque of the tires – thereby increasing the stiffness of the “pole” and raising the resonate frequency. Steering feel got better.
Today? All cars have power steering and nearly all have computer enhanced stability control that operates on a combination of steering and brake inputs. That technique means that a race car can be driven at more than 200 mph with an over steering chassis setup that would be uncontrollable without that high speed correction going on.
By now, you may recognize that everything we have discussed applies to supersonic aircraft, and very powerful speed boats. Well, actually, it applies, period, but below the critical speed a human driver/pilot can handle it.
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