The proportional-integral (PI) controller make use of an integrating block to produce a signal which is integral over time of the error signal. The output value of the integrator is zero for beginning.
As long as the input supplied to the integrator is positive, the value of its output rises at a rate depending on the input. When value of E is zero, the input to the integrator is zero and its output will stay at the same level. Its output will fall if we supply a negative voltage to it.
The two plots drew below show us that how the integrator corrects for the output off-set. In our diagram 34.7 the simulated PI controller is in running position with its integrator switched off. It then acts just like a P controller. The control voltage y never reaches the set point and as a result the output has a significant offset.
When we switch the integrator on, the integrator adds its output to y. The output level of integrator rises sharply at earlier stages then rises more slowly. The value of y is enhanced by this so that it reaches the set point. At that point the error E is zero so the integrator output remains fixed. The output goes up more slowly because of the load but finally reaches the set point. The vat is full to the required level, the error signal is zero and the valve is closed. In a regulator system based on a PI controller, the set point is adjusted to a fixed level and stays there. The output reaches the set point slightly later. In a servo system, in which the set point is continually changing, the output may not be able to keep up with the changes.
The plot in Figure 34.10 the right shows what may happen. This is the same simulated system as used in the previous plots, but the set point is now programmed as a triangular wave. This could be the system controlling an oscillating motion like that of the heater-dryer fans in a car-wash. The output changes with the same frequency as the set point, but never catches up with it. The next section shows how the response can be speeded up.
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