Definition Of "I" (Integral Gain) - Baldor 29M Installation And Operating Manual

Section 1
General Information

Definition of "I" (Integral gain)

Summing Junction
(error detector)
Error
Signal
S
Output
Input
e
Command
Feedback
Input
MN1230
Integral gain (like proportional gain) is amplification of the process error signal, but is time
dependent. If a steady state error exists for long periods of time, it is known as an offset.
Integral gain compensates for this long term error or offset. Generally speaking, if you
were to use only proportional control in a process, the control output would never get the
controlled variable exactly equal to the input command. You would always have some
small amount of error. This is often called offset. The Integral term senses this long term
offset, and corrects the control output to reduce the effect of offset.
Integral gain is mathematically defined as:
out
Where A = Controller output
out
K = Integral gain
i
= Integrator symbol
e
= Process error signal = (setpoint - feedback)
t = Change in time
This formula states that a given control output (A
multiplied by the integral (
What all of this says is simply that in an Integrator loop is used and error is accumulated
over time (or integrated), and integral gain is used to reduce long term error. Figure 6-3
shows this process.
Figure 6-3
Block Diagram of the I Element
K e t
out
i
K e t
i
) is equal to integral gain (K
out
e
) of the error ( ), multiplied by the change ( ) in time (t).
Power Input
Control
Feedback
Measuring
Means
Manually Tuning the Series 29M Control 6-3
),
i
Load Disturbance
Controlled
Variable
Motor
Controlled Variable