9. Notes on Feedback Control Loops with the DigiLock 110
Page 43
Status: 5.12.17
reference. A simple parameter adjustment is obtained in an iterative process:
1. Set the integral gain K
I
to a finite value (all others to zero) and increase the overall gain until the
system locks.
2. Alternate between increasing the proportional K
P
and the integral gain K
I
(and K
p
) each until the
feedback loop oscillates, then reduce the gains until the oscillation definitely stops. Standard opti-
mization procedures set the proportional K
P
gain to about half the value at which oscillation starts.
3. Alternate between increasing the differential K
D
and the integral K
I
(and K
p
) gain each until the
feedback loop just oscillates, increase one and the other until the oscillation will not stop by further
increase. At that point reduce the gain until the oscillation definitely stops.
7
Note that the optimized parameters depend on the slope of the error signal at the current lock point and
the actuator response. Therefore there is usually a trade-off between a good locking result and a reason-
able robustness against oscillations due to additional external disturbance and variations in the overall
response.
The DigiLock 110 features a build in network analyzer (see section 8.2.3) which can be used to analyze
the frequency dependent amplitude and phase response of the actuators and control loop elements. In
particular, it can be used to do an in-loop analysis of the stability of the closed lock.
In addition the frequency response of the controller can be analyzed using the Simulation function
(see section 8.2.2). This allows to identify reasonable relative gains for the different contributions, in partic-
ular an advantageous influence of the D part on the phase at higher frequencies.
9.4 Identification of Signal Polarity and Slope
To support the AutoLock features, the DigiLock User Interface (DUI) takes a consistent approach to the
definition of the signal polarity of each controller and the slope of the error signal.
The polarity of the controller is used to match the action of the corresponding output to the direction
of the scan. It should be chosen such that an increased controller output acts in the same direction as an
increase of the Scan module output. Hence, if the output of the controller is identical to the Scan module
output the polarity is positive. Otherwise the direction has to be determined for the particular actuator
used. For example, if the DigiLock 110 Scan module scans the laser via the Scan Control SC 110 and the
output of PID 2 is also chosen to be the SC 110, its polarity is trivially positive. If the output of PID 1 is then
directed to the current of the laser diode, the polarity of the controller will depend on the polarity of the
laser diode as defined by the DCC 110 current control (see Sys DC 110 manual for details). In this case
the polarity of PID 1 has to be opposite to the polarity of the laser diode.
The polarity of the controller output, for any actuator, can be figured out by comparing the signals of
the regular Scan module output, e.g. SC 110 out, with the signal observed while scanning the controller
output. To determine the directionality of the resulting effect, one can look at a characteristic part of the
error signal, e.g. close to the lock point, or use the wavemeter reading if available.
The slope is defined by the displayed graph at the lock point during the scan. It is automatically cho-
sen in AutoLock mode. If the controller is used in manual mode the user can define the lock point by
selecting the corresponding slope direction.
A general method to verify the correct overall polarity
8
is to compare the signals during scan with the
controller switched on and off while using just the proportional part. To do so, only activate the PID con-
troller in question. Set the integrator and differentiator parts to zero and the P part and overall gain to
some finite value (e.g. 10). Use the System input offset (see section 8.2.4) to center the signal around zero.
Switch on the PID controller while scanning across the characteristic lock point. Increase the proportional
part and/or overall gain until you see a significant distortion of the signal. To check the observed effect,
you can compare with the cases of the other polarity as well as the controller being switched off. The
cases of side of fringe locking and locking to a lamb dip of saturated absorption signal are illustrated in
Figure 32 and Figure 33, respectively.
7. Alternatively, there are several optimization methods for PID controllers which mostly originate from slow (temperature type) controller
applications. The Ziegler–Nichols method gives rule of thumb values derived from the proportional gain K
P, o s c
where oscillation of fre-
quency ν
osc
starts: K
P
= 0.6
×
K
P, o s c
; K
I
= 2 K
P,o s c
/ ν
osc
; K
I
= (K
P, o s c
×
ν
osc
)/ 8
8. The overall polarity is given by the product of the PID controller polarity and the sign of the slope.
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