Robust Attitude Control of Nonlinear Multi-Rotor Dynamics with LFT Models and $\mathcal{H}_\infty$ Performance

TL;DR

The paper tackles robust attitude control for nonlinear multi-rotor UAVs operating under wind disturbances and gyroscope noise. It develops an LPV-LFT modeling approach to represent trigonometric nonlinearities and parameter variations as structured uncertainties and synthesizes a robust $\mathcal{H}_\infty$ controller that relies on gyroscope measurements with frequency-weighted noise. The authors demonstrate three contributions: (i) a systematic LFT representation of nonlinear rotor dynamics, (ii) a nine-state $\mathcal{H}_\infty$ controller that outperforms a cascaded PID, and (iii) a comparative analysis under wind disturbances showing substantial improvements in disturbance rejection. Simulation results under Dryden turbulence yield a peak attitude error of $7.12^\circ$ and RMSE of $1.35^\circ$ with $\gamma_0=0.25$, validating formal robustness and practical applicability for urban VTOL and payload-delivery missions.

Abstract

Attitude stabilization of unmanned aerial vehicles in uncertain environments presents significant challenges due to nonlinear dynamics, parameter variations, and sensor limitations. This paper presents a comparative study of $\mathcal{H}_\infty$ and classical PID controllers for multi-rotor attitude regulation in the presence of wind disturbances and gyroscope noise. The flight dynamics are modeled using a linear parameter-varying (LPV) framework, where nonlinearities and parameter variations are systematically represented as structured uncertainties within a linear fractional transformation formulation. A robust controller based on $\mathcal{H}_\infty$ formulation is designed using only gyroscope measurements to ensure guaranteed performance bounds. Nonlinear simulation results demonstrate the effectiveness of the robust controllers compared to classical PID control, showing significant improvement in attitude regulation under severe wind disturbances.

Figures (6)

• Figure 1: System interconnection for designing and implementing proposed controllers.
• Figure 2: LFT interconnection for designing robust controllers.
• Figure 3: Disturbance moments generated by wind gust and turbulence
• Figure 4: Euler angles (attitude) of the multi-rotor
• Figure 5: Rotational rates of the multi-rotor