SPM Fundamentals for the MultiMode
Feedback Gains
Rev. B
MultiMode SPM Instruction Manual
31
2.3.2 Proportional Gain
Proportional
gain means that something is done proportionally in response to something else. In
the case of our
fi
rst balloonist, Peter, this means producing hot air in proportion to the balloon’s
altitude above the terrain: where the terrain rises sharply, Peter uses large amounts of gas to lift the
balloon; where the terrain is relatively
fl
at, Peter supplies a small, steady amount of gas to maintain
the setpoint altitude above the surface.
A simple feedback loop emerges in this analogy: let us say Peter uses a range
fi
nder every 30
seconds to determine the distance between the balloon and ground. If the balloon is below its
setpoint altitude, he
fi
res the burners. If the balloon is above its setpoint altitude, he turns off the
burners to lower the balloon. The higher the proportional gain, the more Peter reacts to changes in
altitude. For example, at a proportional gain of
1
, if the balloon is 25 meters too low, he opens his
valve at 10 liters per second; if the balloon is 50 meters too low, he opens his valve at 20 liters per
second. The proportional gain value serves as a multiplier such that at a proportional gain of
2
, the
gas
fl
ow rates are doubled from a proportional gain of
1
, and so on. Although this sort of feedback
gain works well for simple, linear models, it does not function as well for nonlinear models. There
remains always some residual error which causes the system to approach, but not quite reach, the
target state.
Assuming that the balloonists wants to get as close as possible without crashing, the response will
depend upon, among other things, the balloon’s speed over the terrain. When the balloon is being
carried swiftly, it is necessary to apply feedback earlier to compensate. (That is, more gas must be
used earlier.) On the other hand, if there is little or no wind, the balloon may achieve a closer
tracking of the terrain. There may also be suf
fi
cient knowledge of the terrain to anticipate its rises
and falls. In order to compensate for these effects,
integral
and
LookAhead
gain feedbacks may also
be employed. These are discussed next.
If altitude < 100 meters,
fire burners.
If altitude > 100 meters,
turn burners off.
range finder
