SPM Fundamentals for the MultiMode
Feedback Gains
32
MultiMode SPM Instruction Manual
Rev. B
2.3.3 Integral Gain
Integral gain is used to correct the cumulative error between a system and its target state. In the case
of the balloon, it is not enough to use only proportional gain. As we have seen, the balloon will
maintain a constant error around the setpoint altitude if it relies on proportional gain alone. It is also
necessary to consider whether the total error between the balloon’s actual altitude and its setpoint
altitude is increasing or decreasing over some interval of time. To correct for cumulative error, our
second balloonist, Irene, utilizes
integral gain
.
Let us assume that Peter announces the balloon’s altitude every 30 seconds from his range
fi
nder.
Irene uses a stopwatch and clipboard to record the amount of error at each measuring interval,
averaging the error over a preceding interval of time (e.g., 3 minutes). Irene
fi
res the burners based
upon her observations: if she notices that the running average error puts the balloon below the
setpoint altitude, she
fi
res the balloon’s burners, if she notices that the average error puts the
balloon above the setpoint, she turns the burners off. The effect of integral gain feedback is to
reduce total error by addressing error over a longer period of time. This tends to smooth out the
short-term,
fl
uctuating effects of proportional gain while narrowing the error closer to the setpoint
value. Unfortunately, if the integral gain is set too high, there is a tendency to overshoot the
setpoint. Therefore, integral gain is highly sensitive and must be used carefully.
2.3.4 LookAhead Gain
Finally, the third balloonist, Larry, employs yet another type of gain to ensure optimal tracking over
the terrain:
LookAhead
gain. For our example, Larry uses a map to anticipate the rise and fall of the
terrain. When his map indicates a mountain, he opens his valve to
fi
re the burners and lift the
balloon. When a valley is indicated on the map, he turns his burner off to lower the balloon. The
effect of LookAhead gain is to keep the balloon within the proper altitude zone so that proportional
and integral gains will perform better by maintaining the balloon closer to its proper setpoint
altitude. When the terrain is comprised of regular rises and falls, the LookAhead balloonist is at his
best, easily anticipating rises and falls. In these instances, LookAhead gain can be maximized.
Conversely, when the terrain is rough and broken, the LookAhead balloonist must struggle with the
balloon’s sluggish response to anticipate every irregular rise and fall, and may actually make
control of the balloon more dif
fi
cult. In these instances, LookAhead gain should be minimized or
turned off.
2.3.5 Completing the Analogy—Feedback Gains in SPM
Feedback gains used to control an SPM’s probe tip are not far removed from those controlling a hot
air balloon. In the case of a probe tip, the objective is quite similar: the operator assigns a setpoint
value corresponding to a certain amount of tip-sample force, then adjusts gains to track the surface
as closely as possible while maintaining the setpoint. Instead of gas-
fi
red burners, however, the Z-
axis piezo crystal uses voltage to retract and lower the probe. In addition, such parameters as
Scan
rate
must be
fi
gured in. Just as a balloonist would
fi
nd it dif
fi
cult to closely track rough terrain in a
fast-moving balloon, the microscopist must frequently adjust
Scan rate
and
Setpoint
to track
samples successfully.
