Overcoming Fundamental Control Limitations in Powered Descent Flight through Robust Incremental Nonlinear Dynamic Inversion
This work identifies a fundamental, controller-independent limitation in reusable launch vehicle powered descent: a sudden $180^\circ$ phase transition in the open-loop transfer functions from the control inputs to the lateral drift and drift rate. The transition occurs inside the flight envelope, reverses the effective control direction, and can destabilize the closed loop system under uncertainty. An analytical condition governing this transition is derived, its physical mechanism is established, and its dependence on vehicle mass, aerodynamic properties, and geometry is characterized. An Incremental Nonlinear Dynamic Inversion (INDI)-based control architecture is then developed to inherently address this limitation and is tuned via $\mathcal{H}_\infty$ Closed Loop Shaping to provide local robustness and performance guarantees. The internal dynamics introduced by the INDI inversion are analytically derived and proven to be stable throughout the flight envelope. The proposed controller is compared against a robust gain-scheduled baseline controller through linear stability analysis and an extensive nonlinear Monte Carlo campaign. Both controllers achieve 100% success across the considered Monte Carlo campaign, though the INDI-based controller provides improved tracking performance, superior nominal and dispersed stability margins, requires fewer controller design points, and reduces controller tuning complexity.