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The command for the controller consists of the analog signal applied to the MOD input, the
digital value given by the
encoder “OFFSET” and the digital value from the RS232 interface.
The slew rate of the amplifier can be adapted to your system using the "slew rate" limiter 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 of this set 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
com = command
mes = position signal
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:
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. Ts is the time
constant governing the time it takes for the output to get a certain value. For a step input it is the
time taken for the output to equal the input.
yi = yi + ki * err * Ts
Ts = 1 / sample frequency (50 kHz)
1/ki = time constant
yi = output of i-term
In general, the differential term combats oscillation (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 addition of these 3 terms generates a PID
–controller. 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 mode, the PID-controller is bridged and the command input controls the amplifier.
Using a subsequent steep notch filter the main resonant frequency will be damped by another
order of magnitude. While using open loop you can also switch on the notch filter to reduce the
stimulation of the resonant frequency.
The PID-specific parameters kp, ki, and kd are stored in the actuator
’s ID-chip by default. These
parameters will work for most applications. Depending on your special application and load, the
mechanical response can be optimized.
