We consider the problem of the absorption of 2D water waves by the horizontal motions of a vertical plane in response to the hydrodynamical force it experiences. The solution of this problem is straightforward in the frequency domain. Unfortunately, the transposition of the frequency domain solution to the time domain by inverse Fourier transforming leads to a non-causal impulse response function. Thus it cannot be used just as it is, neither as a control loop for physical absorbing devices nor as a non radiating boundary condition (NRBC) in numerical modeling. In this paper, we propose a method to derive causal approximations of this ideal controller. Two time-domain absorbing relations are proposed, differing in whether or not one knows a dominant frequency of the incident wave train to be absorbed. Their performances are compared with the absorption efficiency of the low frequency asymptotic Sommerfeld relation which simply reads, for such a piston device: U(t)=F(t).