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Most controllers use proportional-only (P-only) or proportional and integral (PI) control. Proportional and derivative (PD) control is generally used in applications where anticipation is required or in motion control applications. An example of motion control would be a dc servomotor that's connected to a ball screw so that a robot arm can move in a horizontal travel to put parts in several bins that are side by side. The ball screw is rotated by the motor and the platform that the robot sits on is moved in front of a conveyor where it can pick up parts and then move quickly to one of the bins in which the parts are dropped.
In this type of motion control application the motor is generally ramped up at some rate until the desired speed is achieved. The figure below shows an example of this type of response. When the motor reaches full speed, the robot moves at this speed until it's in front of the bin in which the part is to be dropped. When the rob reaches the point where it's to stop, the speed of the motor is ramped down rather abruptly so the ball screw stops the robot directly in front of the bin. The PD controller is useful in these types of applications because it allows the motor to ramp up and reach full speed rapidly and then move at high speed and ramp down quickly as it reaches the SP where the robot should stop and drop off the parts.
Since the PD control can respond quickly, it becomes a detriment
in some process systems like controlling steam valves where this type
of control may cause the valve to fluctuate too much, making it wear
out.
Above: An example of proportional and derivative (PD) control.
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Additional Resources:
PID Tutorial from University of Michigan -- Designed for engineering students, this is a more technical (mathematical) discussion of PID. Consider is reference-grade reading.
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