The cross-field turbulence-driven particle transport in magnetically confined plasmas can be reduced by adequately shaping the flow profiles. HELCAT (HELicon-CAThode), a linear magnetized plasma device, uses concentric ring electrodes to modify the flow profiles by E×B actuation. As a result, turbulent particle and heat transport can be mitigated by generating a sheared radial electric field through the varying ring voltages. Active control of the turbulent fluctuations, including the associated cross-field particle transport, via manipulation of flow profiles is investigated in this work. Once a desired radial azimuthal velocity profile, and its associated level of turbulent fluctuations, are identified, the challenge of systematically achieving and sustaining it still remains. A model-based feedback controller is proposed to achieve this goal even in the presence of external disturbances, model uncertainties and perturbed initial conditions. A linear-quadratic-integral (LQI) optimal controller is designed to minimize a weighted combination of the tracking error and the control effort. Numerical simulations show the effectiveness of the proposed controller to regulate the radial azimuthal velocity profile around a prescribed desired profile. The proposed control solution has the potential of being used as a systematic tool to elucidate the physics of laboratory plasmas such as those achieved in HELCAT.