Tuning is iterative, not formulaic
There is no universal set of Kp, Ki, and Kd values that works for every system, the right gains depend on the specific mass, friction, actuator strength, and sensor characteristics of whatever you're controlling. In practice, tuning is an empirical, iterative process, an engineer sets initial gains, runs the system, watches how it behaves, adjusts one gain at a time, and repeats. A common starting approach is to bring up Kp alone first, observe the response, then add Ki to remove any steady-state offset, then add Kd to damp out overshoot, checking the behavior after each change rather than guessing all three values at once.
Reading the system's behavior is itself a skill. A response that's sluggish and slow to reach the target usually means the gains, particularly Kp, are too low and need to be raised. A response that overshoots and oscillates repeatedly usually means gains are too high or poorly balanced relative to each other, often Kp or Ki pushing too hard without enough Kd to damp it. A response that gets close to the target quickly but settles with a small, persistent offset that never fully closes points at the integral term needing to be strengthened. These three patterns, sluggish, oscillating, and offset, cover the majority of what practitioners diagnose when tuning by hand.