Linear Stability Analysis of an INDI Pitch-Rate Controller under Model Mismatch for a Tilt-Rotor VTOL UAV

2026-07-17

AI Summary

This study addresses the lack of an analytical characterization of linear stability for the INDI inner-loop controller of tilt-rotor VTOL UAVs under model mismatch. The authors construct a fifth-order closed-loop transfer function encompassing the controller, estimator, actu日消息ator, and airframe dynamics, and perform a parametric stability analysis of the pitch-rate/elevator subchannel using the Routh-Hurwitz criterion. For the first time, the stability boundary of the INDI inner loop is explicitly expressed in terms of system parameters, revealing that control effectiveness mismatch—particularly sign errors—is the most critical destabilizing factor, whereas actuator lag and inertia mismatch exert comparatively weaker effects. Building on these insights, two uncertainty-aware tuning strategies balancing robustness and performance are proposed, accompanied by concrete design guidelines for both conservative and aggressive operational scenarios.

Abstract

Incremental Nonlinear Dynamic Inversion (INDI) is attractive for unmanned aerial vehicle (UAV) flight control because it reduces dependence on a full aerodynamic model while retaining strong disturbance-rejection capability. For a tilt-rotor vertical takeoff and landing (VTOL) architecture, however, the admissible model-mismatch range of the fast inner loop is still not characterized analytically in a parameter-explicit way. This paper isolates the pitch-rate/elevon subchannel of an existing cascaded INDI controller and studies its linear stability under model mismatch. A closed-form fifth-order transfer function is derived for the full controller-estimator-actuator-plant interconnection, and stability is characterized through the Routh-Hurwitz criterion over a parameterized linear model. Two representative three-parameter sweeps produce interpretable stability regions. Based on these feasibility maps, two uncertainty-aware tuning procedures are proposed: a robustness-oriented design that maximizes a weighted worst-case combination of gain margin and phase margin, and a performance-oriented design that maximizes worst-case closed-loop bandwidth subject to margin constraints. The results show that actuator lag and inertia mismatch are comparatively benign at nominal gain, whereas control-effectiveness mismatch, particularly a sign error in the allocation, is the most dangerous destabilizing factor, leading to concrete tuning recommendations for conservative and aggressive operating conditions.

Problem

• model mismatch
• linear stability
• INDI controller
• tilt-rotor VTOL UAV
• pitch-rate control

Innovation

• Incremental Nonlinear Dynamic Inversion (INDI)
• Linear Stability Analysis
• Model Mismatch
• Tilt-Rotor VTOL UAV
• Robust Control Tuning