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An internal model control with conditional integrator is proposed for the robust output regulation of single-switch quadratic buck converters. The output regulation problem of a quadratic buck converter is converted to the stabilisation of an augmented system consisting of the buck converter and the internal model. The design procedures include the design of an internal model with conditional integrator and a robust state feedback stabiliser with saturation behaviour. The closed-loop stability of the converter will be theoretically analysed. Finally, the effectiveness of the proposed control scheme for large load and supply variations are also tested. The design of the controller does not require the exact circuit parameters and the stability proof demonstrates the robustness against parameter uncertainties.