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In this study, control over the wake flow of a single square cylinder exercised by a flat plate attached to the rear side of the cylinder is analyzed numerically via the lattice Boltzmann method. The Reynolds number (Re) is fixed at 150, and the length of the plate is varied from 0.1 to 8.5. Three distinct flow modes are observed in this study: unsteady, transient, and steady flow in the cases of plate lengths (L) in the ranges 0.1 ≤L≤ 6.5, 6.75 ≤L≤ 7.5, and 7.75 ≤L≤ 8.5, respectively. The streamlines exhibit different flow structures, termed hairpin-like, ellipse-like, and elongated bubble-like, at different values of L. Complete wake control is achieved at plate lengths beyond 7.75. This study reveals that the drag and lift coefficients exhibit unsteadiness at short plate lengths in early time steps, but as the plate length increases, unsteadiness slows down and eventually disappears, confirming the steady flow pattern. The mean drag coefficient (CDm), Strouhal number (St), and root-mean-square value of drag and lift coefficients (CDrms; CLrms) are reduced by maximums of 23.5%, 100%, 84.6%, and 99.5%, respectively, as a result of the presence of the plate.