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Perhaps begin by trial-and-error tuning with only P-control (set I and D to zero). Note that this alone will probably be inadequate, due to steady-state error: because, if the error is zeroed out, then the P-control effect (proportional to error) will be zero and the system will deviate again to settle at some equilibrium offset away from the command reference. Of course, if your system oscillates, you probably want to reduce the P-gain.

A little I-control can then be judiciously added to gradually move the system away from this equilibrium, toward zero error. (I-control has traditionally been known as "automatic reset" in some circles, since it effectively "resets" the original set point to counteract the steady-state error.)

Add some D-control (effectively, viscous braking) to stabilize the system.

Of course, these three effects interact. So, rinse and repeat as needed. You'll probably have to back off your original P-control once you've added I and D.

It's up to you if a little damped oscillation is an acceptable trade-off for fast response.