piezosystemjena d-Drive Bedienungsanleitung Seite 54

The command for the controller consists of the analog signal applied to the MOD input, the digital
value given by the OFFSET potentiometer, and the digital value from the EDS2 via CAN-Bus. 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 (err) between this input (com) and the value from the
measurement system (mes):
err = com – mes
The proportional term (kp) 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
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
In general the differential term combats ringing (it adds damping) and increases the reaction speed
of the PI–controller:
yd = kd * 1/Ts * (err – err[n-1])
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
In open loop the PID-controller is bridged and the command input controls the amplifier.
Geschäftsführer: Dr. Bernt Götz • Telefon 03641/66880 • Fax 03641/668866 • www.piezojena.com
54
com = command
mes = position signal
kp = adjustable gain
yp = output of p-term
Ts = 1 / sample frequency (50 kHz)
ki = time constant
yi = output of i-term
err[n-1] = control deviation previous sample
kd = differential time constant
yd = output of d-term
y = output of PID-controller