Three Control Components - Idex Pulsafeeder MPC Vector Installation, Operation & Maintenance Manual

22.2

Three Control Components:

The PID controller has three adjustable internal components, all of which contribute to the final output value; they are
proportional, integral, and derivative.
Proportional Component
The proportional component of the control system (also known as "gain") is concerned with the current error
("current" as in time, not electricity). The component is calculated by multiplying the current error by a proportional
coefficient, commonly known as Kp or proportional gain. Since the proportional component is only concerned with
current error it is able to contribute to initial startup speeds. Think of the proportional gain as the component which
gives a jump start to the pump. Typical values of Kp for this application are in the 0.25 -> 0.7 range.
Proportional Part = Kp * error
Integral Component
The integral component of the control system (also known as "reset") provides a historical memory to the system.
This is accomplished by adding the errors into an error summation. The sum of the errors is then multiplied by an
integral coefficient, Ki which is also called the integral gain. Because the integral component is a historical
component, it can take some time to build "history". The Integral component is used mainly to force the control to
track closer to the desired set point, to eliminate any "offset". Typical values of Ki are in the same range as Kp, 0.25 -
> 0.7.
Integral Part = Ki * error sum
Derivative Component
The derivative component (also known as "rate") provides a predictive element to the system. The derivative
component compares the current error and previous error to calculate the approximate change over the last sample
period. This is then multiplied by the differential coefficient, Kd which is also called the differential gain. When the
flow rate of the pump is rising, the differential component is used to keep it from rising too fast. This is because as
you get closer to the flow set point, the current error will be smaller than the last error. The differential term can be
used to stabilize systems with excessive overshoot, it slows down the response as the set point is reached.
Derivative Part = Kd * (error – last error)
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