Autopilot Closed Loop & Gain

Every autopilot channel is the same loop. A command is set, a sensor reports what the aircraft is actually doing, and a comparator subtracts one from the other to produce the error signal. An amplifier turns that error into a servo demand, the servo moves the control surface, the aircraft responds, and the sensor reports the new attitude back to the comparator. When the error reaches zero the servo stops. This is why the feedback path matters as much as the forward path: without it the system has no idea whether it achieved anything.

Gain decides the character of the response. Gain is simply how much servo movement you get per degree of error. Too little and the aircraft creeps towards the commanded attitude and may never quite arrive, leaving a standing error. Too much and the servo drives hard, overshoots, and the loop spends its time correcting its own corrections, giving an oscillation that takes a long time to die away. Push the gain higher still and the oscillation grows instead of decaying, which is instability, and it is why a real system has authority and rate limits in front of the servo.

Rate damping is the fix. A second signal proportional to the rate of change of attitude is subtracted from the demand, so the loop eases off as it approaches the target rather than arriving at full speed. That is what turns an oscillatory response into a smooth one. In a real installation this comes from a rate gyro, and its loss is a classic cause of an autopilot that hunts. Note also that the servo is the only thing physically moving the controls, which is why a runaway is contained by disconnect and by mechanical limits, not by the computer noticing.

• Try this: Drop the gain to its minimum and command a pitch change. Does the aircraft ever reach the commanded attitude, and what is left over?
• Try this: Raise the gain with damping at zero. At what point does the response stop settling, and what would that feel like in the aircraft?
• Try this: With a high gain, bring damping back in. Why does a signal proportional to rate fix an oscillation that more gain cannot?