In earlier work we demonstrated that in the presence of an external periodic force, the rheological parameters of slender rods in simple shear flow vary chaotically for a certain range of parameters. Algorithms are available in the literature to control the chaotic dynamics of these rheological parameters onto periodic solutions. In earlier work, we also showed that upon including hydrodynamic interactions between the particles, we can extend the range of parameters of the suspension in which the rheological parameters vary chaotically. This result suggested that we try to determine the effect of hydrodynamic interactions in the semi-dilute limit on control of chaos in the rheological parameters. We present numerical evidence that inclusion of hydrodynamic interactions in the semi-dilute regime greatly increases the difficulty of control of chaos. This suggests that inclusion of hydrodynamic interactions could lead to considerably different results when compared to dilute suspensions and thus it may be necessary to include these effects in simulations of moderately concentrated suspensions.