••••• THE PID CONTROLLER — Part 2
proportional term is proportional to the system error.
Therein lies the problem with proportional control.
This one took a while for me to understand, but it
makes sense when you think about it. The error cannot be
eliminated. If the error was zero, the proportional drive
would be zero, and the weight would fall. Therefore, in a set-up
such as that in Figure 8, there will always be an error. The
blue and red lines can never converge. In Figure 9, we see
how the integral component can improve the steady state
error of our servo motor system. Recall that the integral
accumulates the error over a period of time. In Figure 9, we
see that the servo motor has overshot the set point, just like
in Figure 7. Since the error is not zero, the integrator will
start to accumulate the error. After a period of time, the
integrator output is high enough to move the motor, as seen
in Figure 8. The steady state error is, therefore, reduced.
To better understand the integral, let’s look at what
happens when we increase the integral gain. As you can
see from Figure 10, things can get ugly. There are two
problems with this system: overshoot and oscillation.
The overshoot is caused by the rapid accumulation of
error. A large error exists for a period of time when the
motor is commanded to move. This large error is accumulated by the integrator. This is called “integral wind-up.” If
we were to look at the output of the integrator with an
1S / div
1V / div
FIGURE 9. Proportional plus integral plus differential control under
heavy load. The servo returns to the set point with time:
blue = set point; red = feedback from resistor.
oscilloscope, we would see that the capacitor is fully
charged, i.e., the integrator has saturated. This is not a
good thing! Recall that the capacitor will not discharge until
the error has changed signs. This means that the servo
Circle #32 on the Reader Service Card.