H∞ Loop Shaping for Robust Attitude Control of Launch Vehicles

This paper presents a systematic framework for applying H ∞ Loop Shaping to the design of Thrust Vector Control systems for the atmospheric ascent of rigid launch vehicles. H ∞ Loop Shaping offers a streamlined alternative to the widely used H ∞ Closed Loop Shaping by automatically ensuring robustness at the plant input and output and preventing the need to simultaneously tune multiple closed-loop transfer functions to achieve the desired goals. The proposed methodology simplifes controller synthesis while maintaining robust stability and performance, as demonstrated by stability margin, structured singular value, and worst-case gain analysis. Preliminary findings suggest equivalency between controllers designed using H ∞ Loop Shaping and H ∞ Closed Loop Shaping, with the former offering a more efficient and less complex approach. Future work will extend the guidelines to flexible launch vehicles and attempt to fully demonstrate the equivalence between controllers attained with both methods.