This paper deals with the design of feeding rates for dual-substrate fed-batch processes where the main control objective is the regulation of the microbial growth rate. To this end, feedback of the growth rate error is incorporated to a biomass proportional dual feeding law. A second-order sliding mode observer is used to estimate the growth rate, so that no additional sensors are required. Stability conditions are derived and robustness against several disturbances such as yield uncertainty, measurement errors and kinetic model mismatch is analytically and numerically evaluated. The advantages of the proposal include: minimal measurement requirements, regulation with fast convergence to the desired growth rate and reduced regulation error in the presence of disturbances.