Damping to reduce error signals
For a servo position control loop then using a tacho-generator can reduce the speed at which the motor approaches the optimum demanded position. This means that there is less overshoot because the mass of the &quot;thing&quot; being moved is less likely to significantly overshoot the demand point because it doesn't have as much momentum/energy.
Because a tacho-generator produces an output voltage that is proportional to speed, that output voltage can be used to reduce the error signal and therefore control the speed of approach thus reducing overshoot.
Using R1, R2 and C in the circuit can do the same thing. If the output from the error detector circuit (not a great choice of words IMHO) is rapidly changing then the capacitor's impedance will be lower and the error signal amplitude will be reduced by the effect of the potential divider. For a steady error value, the capacitor will look like an open circuit and there will be no attenuation to the error signal.
Hence, the RC circuit behaves like a tacho-generator used to stop speed getting excessive.

However I found out that it (tacho-generator) may cause velocity lag and error

Both will cause velocity lag but neither will create an error unless the open-loop response is low in gain and there is stiction in the system