11.3.3 The Resolution of the Integration Term

The integration term is important because it allows a system to reach the reference. Without the integration term, a PID loop can never achieve the reference signal.

The integral term relies on the summation of errors. This sum can become much larger than the error term itself. It is advisable to put limits on this term (caps). The range of the integral term should be about 20 times that of the range of the error term. Due to the magnitude of the error term, there is no problem with resolution in the integration term.

Because the integration is a large number to start with, the coefficient $K_{i}$ must be a small fraction. This is easily done by assuming the binary point to the to the left of the most significant bit of the binary integer representing $K_{i}$. The trouble, however, is that we now have a large number multiplied by another large number. This can take a bit of time for an 8-bit system. As a result, some control systems choose to ignore some of the less significant digits to speed up computation.