MOGlabs FSC100, Manual

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To suppress that disturbance, a feedback servo should have high gain
at 50 and 60 Hz. Gain has a low-frequency limit usually defined by
the gain-bandwidth limit of the opamps used in the servo controller.
The gain must also fall below unity gain (0 dB) at higher frequencies
to avoid oscillations such as the familiar high-pitched squeal of audio
systems (commonly called “audio feedback”) for frequencies above
the reciprocal of the minimum propagation delay of the combined
laser, frequency discriminator, servo and actuator system. Typically
that limit is dominated by the response time of the actuator and for
laser piezos that is usually of order kHz.
Figure 1.3 is a conceptual plot of gain against Fourier frequency
for the
FSC
. To minimise the laser frequency uncertainty, the area
under the gain plot should be maximised.
PID
(proportional integral
and differential) servo controllers are a common approach, where
the control signal is the sum of three components derived from the
one input error signal. The proportional feedback (P) attempts to
promptly compensate for disturbances, whereas integrator feedback
(I) provides high gain for offsets and slow drifts, and differential
feedback (D) adds extra gain for sudden changes.
When using a single integrator, the gain decreases at 20 dB per
decade of Fourier frequency change, indicating a stronger response
at lower frequencies. Adding a second integrator increases this to
40 dB per decade, reducing the long-term offset between actual and
setpoint frequencies. Increasing the gain too far however, results
in oscillation as the controller “overreacts” to changes in the error
signal. For this reason it is sometimes beneficial to restrict the gain
at low frequencies, such as in the fast servo loop, where a large
response can cause a laser mode-hop.
The differentiator compensates for the finite response time of the
system and has gain that increases at 20 dB per decade. To prevent
oscillation and limit the influence of high-frequency noise, there
is an adjustable gain limit that restricts the differentiator at high
frequencies.