Pulsafeeder MPC Vector - Manual (Page 66)

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21.2 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 setpoint, 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 setpoint, 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 setpoint is reached.
Derivative Part = Kd * (error – last error)