Two things likely at play here - one is that the servo position sensor itself has some mechanical lag internal to the device (slop in the mechanism) before it starts reversing; the other would be that the displaying device (you didn't say if it was Ray Allen or EFIS) might have a "smoothing" algorithm that takes a few seconds to bring the display to the new value to avoid jittery data.
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Greg Niehues - SEL, IFR, Repairman Cert.
Garden City, TX VAF 2020 dues paid 
N16GN flying 700 hrs and counting; IO360, SDS, WWRV200, Dynon HDX, 430W
Built an off-plan RV9A with too much fuel and too much HP. Should drop dead any minute now.
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