The high efficiency performance of the Edinburgh Duck wave energy converter (WEC) in 2D regular wave tests makes it a promising wave energy conversion scheme. A solo Duck WEC will be able to apply the point absorber effect to further enhance its performance. Since released degree of freedom will decrease the efficiency, a Duck WEC with fixed pitching axis will be a better option. However, for fixed supported WECs, tide is a non-ignorable consideration. In this paper, a movable mass method is utilized in the whole tidal range to not only balance the Duck to appropriate beak angles, but also follow the variation of hydrodynamic coefficients to keep cancelling the reactance of the system impedance so that complex conjugate control can be realized to optimize the power capture performance of the Duck WEC in tide. Results show that the beak angle should be adjusted to as large a value as possible so that the response amplitude of the Duck at maximum relative capture width will be reasonable small, and the lowest weight of the movable mass is found when its designed position locates at the center of the Duck profile.