In the present work, motivated by the recent inclusion of optical variables in combustion processes, we consider the control of a reduced Hammerstein plant model over an additive white noise (AWN) channel located at the feedback path. For comparison, assuming uncertainty in the knowledge of the static nonlinearity of the Hammerstein plant model, we first propose in a one degree-of-freedom (DOF) scheme, the design of a proportional controller for robust stability We then introduce a PI controller, in a 3 DOF scheme, to achieve not only robust stability, but also AWN channel Signal-to-Noise Ratio (SNR) minimization and setpoint first moment tracking.