Linear Stability Analysis of an INDI Pitch-Rate Controller under Model Mismatch for a Tilt-Rotor VTOL UAV
Robotics
Summary
The authors studied a flight control method called Incremental Nonlinear Dynamic Inversion (INDI) used for UAVs, focusing on how it handles errors in the model for a tilt-rotor VTOL vehicle. They examined the stability of part of the controller that manages pitch rate and control surfaces under different error conditions and derived a precise mathematical description of the system. By analyzing this, they created maps showing when the system remains stable and proposed two ways to tune the controller: one focusing on robustness and one on performance. Their findings indicate that errors in actuator speed and inertia are less risky than errors in control effectiveness, especially if the sign of the control input is wrong, guiding safer tuning choices.
Authors
Lorenzo Schenk, Guillaume Ducard, Christopher Onder
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.