----- Original Message -----
From: Fergus Kyle <VE3LVO@rac.ca>
> Perhaps for tyhose of us less educated, you could "animate" the internal
> circuitry of the NavAid device...? I used to instruct aviators, from
> ab-initio to advanced and always found that if they understood how any
> device "thinks" they could better operate it. I can see how the Derivative
> portion might mitigate the Proportional segment, but the overall effect
> escapes me (and perhaps others).
Ferg,
Lacking a response from Kenneth Whiteley, I'll take a shot at explaining
this. But first, let me thank those who have offered suggestions on our
pitch oscillation problem. We reprofiled the Flettner strips to make them
narrower, which seemed to help pitch stability somewhat at low speed, but
not much at cruise.
Before too much confusion gets propagated here, I should clarify that the
Navaid autopilot is a single axis system, controlling roll only. While it
could conceivably affect pitch by large aileron inputs, the problem we see
exists even when roll is rock steady. The only way the autopilot is
involved is to take the pilot's hand off of the stick, so he isn't making
small pitch inputs to hold speed, perhaps without even noticing.
Proportional-Integral-Derivative (or PID) controllers are are widely used
for control systems. Start with a pure proportional system, in which the
amount of, say, right aileron is proportional to the magnitude of the bank
angle (to the left). As the bank angle reaches zero, the aileron input hits
zero also, but the rolling momentum of the airplane carries it past level
into a right bank. To avoid this, add a derivative term, which subtracts an
amount from the right aileron input that is proportional to the speed at
which the airplane is rolling to the right. The controller "anticipates"
where the airplane is going, and can manage a quick correction without
overshoot, by setting the values of the proportional and derivative terms
optimally.
While this system has good dynamic behavior, it suffers from steady-state
error. If there is a heavy pilot, with no passenger, the airplane will
require continuous right aileron to maintain level flight. Unfortunately,
the controller will apply right aileron only when the airplane is banked to
the left, so it cannot remain level in this case. The Integral term adds a
correction to the aileron input that is proportional to the sum of all of
the past errors, so that the long-term average error is driven to zero. As
long as there is any bank error at all, the sum term keeps increasing,
adding to the aileron correction. The integral is thus a kind of "memory"
term, which remembers what inputs have been required in the past to get the
desired response, in contrast to the anticipation of the future position
that is provided by the derivative.
Dave DeFord
N135TD
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