CEO: Dr. Bernt Götz • phone +493641/66880 • fax +493641/668866 • www.piezosystem.com
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8.2.3. digital controller
The command for the controller consists of the analog signal applied to the MOD input and the
digital value via commands. The slew rate of the amplifier can be adapted to your system using the
"slew rate" limit or the 4th order low pass filter, i.e. frequencies which might stimulate resonances
can be suppressed before they interfere with the closed loop. The slew rate setting value is
adjustable.
The PID-controller calculates the difference between the setpoint and the value from the
measurement system (pos):
err = setpoint
– pos
setpoint = command
pos = position signal
err = deviation
The proportional term (P-term) amplifies the control deviation without reducing frequency and
drives the controller until the difference between the sensed motion and the command is adjusted.
yp = kp * err
kp = adjustable gain
yp = output of p-term
The P-
controller can’t eliminate the error completely, because it needs a deviation to drive. To
minimize the permanent offset of the P-term, an integral action (I-term) is required. ki is the time
constant governing the time it takes for the output to get to a certain value. For a step input it is the
time taken for the output to equal the input.
yi = 1/ki * err * Ts
Ts = 1/sample frequency (50 kHz)
ki = time constant
yi = output of I-term
In general the differential term (D-term) combats ringing (it adds damping) and increases the
reaction speed of the PI
–controller:
yd = kd * 1/Ts * (err
– err[n-1])
err[n-1] = control deviation previous sample
kd = differential time constant
yd = output of D-term
Be careful when using the D-term, because stochastic errors, like noise, cause extreme reactions.
The sum of these 3 terms generates a PID
–control function. The output of the controller is the set
value for the power amplifier to drive the piezo actuator:
y = yp + yi + yd
y = output of PID-controller
In open loop the PID-controller is bridged and the command input controls the amplifier.
