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We investigate the exact ac control of two periodically driven and weakly coupled Bose-Einstein condensates in a double-well trap.By employing two balance conditions we construct new exact Floquet solutions with the degenerate Floquet energy, and give the balance region on the parameter space.It is revealed that for some different parameters in the balance region the Floquet solutions exactly describe the macroscopic quantum self-trapping, nonlinear coherent construction and destruction of quantum tunneling, respectively.Therefore, we can accurately perform the coherent control by suitably adjusting the system parameters.