Appendix G. Feedback Modes
This Appendix will discuss the different feedback modes of the R9 Controller. The Feedback controls can
be found on the Z PI hardware item.
G.1. PI Controller Gain Values
There are two different schemes of how to set the gains of a PI controller. Both have advantages and
disadvantages so they are both implemented and the user can decide which one to use.
• Form1: Out = P * err + I * T * Int(err, dt)
• Form2: Out = K * (err + T * π * Itc * Int(err, dt))
Where P = Proportional Gain, I = Integral Gain, K = Gain, Itc = Integral Cutoff Frequency, T =
sample period, and err = error signal.
Important
Do not expose both pairs of PI controls at the same time in either the Dashboard or
Procedure Space. Either use the Proportional Gain and Integral Gain pair, or use the
Gain and Integral Cutoff Frequency pair, but NOT both.
Note
By default, IHLs will be setup to use Form1 for Z feedback. The Proportional Gain is set to
zero and only the Integral Gain is exposed on the Dashboard.
Tip
Form1 is useful for setting up feedback for the Z PI controller. Form2 is used for setting up
the amplitude and frequency feedback in the PLLs.
G.2. Z PI Controller Linearization
In SPM quite often the measured signal decays exponentially over distance. A consequence of this is that
the Z feedback settings depend on distance. Also, the Z controller acts differently on the two sides of the
Setpoint. The Z feedback controller has three different feedback modes that differ in how they resolve this
problem:
• Linear: This is the standard linear mode that is implemented on all PI controllers in the R9 Controller.
The Proportional Gain is set to zero by default. Typical starting values for the Integral Gain range from
1 to 4 km/As for STM. For AFMs that use tuning forks, this is typically on the order of 100 nm/Hz*s to 2
m/Hz*s. The physical unit for the Proportional Gain is OutputUnit / InputUnit. The physical unit for the
Integral Gain is OutputUnit / (InputUnit * s).
The Linear mode subtracts the Input Signal from the Setpoint to generate the error signal.
err = InputSignal - Setpoint
• Logarithmic: This setting is typically used when the response of the probe to sample interaction is
exponential. The Proportional Gain is set to zero by default. Typical starting values for the Integral Gain
range from 50 to 200 m/s. The physical unit for the Proportional Gain is OutputUnit. The physical unit
for the Integral Gain is OutputUnit / s.
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