I beg to integrate

Conspicuously absent from this discussion of manual tuning methods is Ki, the integral gain. In general, we want to keep the integral term as small as possible, because it is a direct contributor to servo instability — or as it is expressed in servo analysis terms, to a loss of phase margin. Typically, in manual tuning methods, Ki is the last parameters set, and is used to offset DC biases on the load such as gravity, or to bring final position errors to a very small value, or to reduce position errors at higher velocities.

At this point it is important to discuss the idea of tuning your parameters toward a certain goal. It is a fallacy to believe that one set of PID parameters are optimized for all uses of a motion system. Some systems must have very safe, conservative servo parameters. Others can have aggressive parameters which optimize a specific characteristics such as point-to-point transfer time. Others emphasize having a very small errors during the move, etc.

Remember that what you are optimizing is an important factor in determining the best servo parameters. This fact, although obvious, is often overlooked both by motion control end-users, and vendors that provide auto-tuning programs for determining the “best” values.