••••• THE PID CONTROLLER — Part 1
To better understand the integrator, let’s look at a
typical application. Integrators are often found in high
end audio amplifiers. In this application, they are called
DC servos. A typical application is shown in Figure 5.
The purpose of this circuit is to remove the unwanted
DC voltage from the output of the audio amplifier. Any
DC voltage seen on the output of the amplifier will tend
to charge the integrator’s capacitor. The integrator
then changes the bias of the audio amplifier to remove
the DC component. The resistor and capacitor are
selected so that the circuit will not respond to audio
Also, recall that an AC waveform is symmetrical.
The part above 0 tends to charge the capacitor, while
the part below will discharge the capacitor. Therefore,
when you integrate an AC waveform over a large
amount of time, you get 0. Even a small DC voltage will
charge the capacitor over a long period of time, thus
rebiasing the amplifier.
apply a ramp to the differentiator, we get a steady DC output
voltage. Figure 6 illustrates the input/output relationship of
What Is Derivative?
The derivative is a measurement of the rate of change.
The ideal differentiator is shown in Figure 5. This circuit
looks similar to the high pass filters you have seen in other
schematics. Low frequencies are attenuated, while high
frequencies are allowed to pass. The mathematics that
describe the differentiator is:
Vout = -RC * (rate of change)
Rate of change is equivalent to measuring the slope of
a line. Slope is a measure of the change in voltage divided
by the change in time. In mathematical terms, this is referred
to as a delta voltage over delta time or simply dv/dt. If we
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