Resonant Doppler flow imaging based on optical coherence tomography (OCT) is a recently developed imaging modality that provides, besides the structural information, dynamic blood flow information. We show that this method can be applied to a common path OCT system by mounting the mirror in the reference arm on a small piezo actor leading to a simpler and more stable system design. Besides the known 3 state cycle, we describe other cycles with any number of states leading to higher measurement speed or larger velocity range. The hysteresis of the piezo actor is compensated by applying an optimized electrical signal. Two different approaches, one using a Levenberg-Marquardt optimization, the other using the Prandtl-Ishlinskii model for compensation of hysteresis, are applied to generate the optimized control signal. Besides providing an analytical formula for the calculation of the axial velocity for cycles having certain spacings in the reference velocity, we describe deviations from the signal degradation caused by the transversal part of the motion causing errors in the velocity estimation. The performance of the system with two and three states is first evaluated with a mirror on a loud speaker. Measurements with a flow phantom consisting of 1 % Intralipid dilution flowing through small diameter capillaries show the suitability of the system and the expected deviations at high velocities.