A virtual command protection strategy for pseudo-inverse flight control allocation

• A framework to evaluate control allocation algorithms, covering open-loop metrics and closed-loop impact. • Direction-preserving virtual-command limiter using an ellipsoidal attainable moment set derived via SVD of the effectiveness matrix; closed-form, optimization-free, microsecond runtime, and reuses the pseudo-inverse already computed in the allocator. • Anti-saturation feedback that feeds allocation error into the reference model to remove steady-state allocation error. • The dual-protection mechanism is demonstrated on an eVTOL model: fewer infeasible commands, lower allocation and tracking errors, and reduced rotor saturation. Over-actuated flight systems frequently encounter infeasible virtual commands outside the Attainable Moment Set (AMS), especially during aggressive maneuvers and failures. In such cases, pseudo-inverse-based control allocation can produce large allocation errors in magnitude and direction, degrading closed-loop performance. This paper proposes a dual protection mechanism for these control allocators in the dynamic inversion framework. Firstly, an ellipsoidal virtual command limiter is derived from the singular value decomposition of the control-effectiveness matrix. This limiter projects any infeasible command onto an ellipsoid that tightly approximates the AMS while preserving its original direction. Secondly, an anti-saturation feedback is designed to feed the allocation error into the reference model with a specific gain, removing persistent control allocation errors from the steady-state virtual command. Open-loop evaluations on an eVTOL model indicate that the ellipsoidal virtual command limiter effectively reduces directional allocation error, with significantly less computational complexity than online optimization. Closed-loop simulations demonstrate that the proposed protections reduce allocation error and input saturation, and improve tracking performance among coupled motion axes.