SPM Fundamentals for the MultiMode
Feedback Gains
30
MultiMode SPM Instruction Manual
Rev. B
2.3
Feedback Gains
The feedback system used to control tip-sample interactions and render images must be optimized
for each new sample. This is accomplished by adjusting various gains in the SPM’s feedback
circuit. This section discusses gains and how they are used to obtain images.
2.3.1 Proportional and Integral Gain—An Analogy
To better understand gains and how they control SPM probes, consider the analogy of a hot air
balloon carrying three balloonists. Each rider controls a separate valve on the balloon’s gas burner.
The valves are mounted in parallel, such that if any one valve is open, gas
fl
ows to the burners,
causing the balloon to rise. Similarly, each balloonist may turn their burner off to reduce altitude.
Mounted beneath the balloon’s gondola is a camera, which automatically takes a photograph of the
ground below. The balloon’s objective is to obtain detailed photographs of the surface. To obtain
the highest resolution images, the balloon must track the surface as closely as possible without
crashing into it. This poses a dilemma to the balloonists: how to tightly control the balloon’s
position relative to the ground.
Because the balloon will drift slightly up and down due to the effects of wind and temperature, the
balloonists must establish some minimum altitude as a safety zone. Let us call this the “setpoint”
altitude, and let us assume that it is set at an altitude of 100m.
Note:
For the sake of simplicity, “setpoint” in this analogy applies to the balloon’s
altitude; however, setpoint in SPM is applied to tip-sample forces,
not
the tip’s
height above the surface
When the terrain is
fl
at, the problem is simpli
fi
ed. The balloonists need only ensure a constant
supply of gas is supplied to the balloon’s burners to keep the balloon aloft. As the terrain becomes
hilly, the task becomes more complex. If the terrain rises, the balloonists must respond by
fi
ring the
burners to lift the balloon. As the balloon clears the hill and terrain drops away, the balloonists must
turn the burners off to reduce height and continue tracking the terrain. The type and intensity of the
balloonists’ responses to terrain can be modeled in terms of three types of feedback:
proportional
,
integral
and
LookAhead
.
setpoint altitude
100 meters