[Paper Review] Modeling and Optimal Control of Hybrid UAVs with Wind Disturbance

Sunsoo Kim, Niladri Das+1 more|arXiv (Cornell University)|Jun 19, 2020

Adaptive Control of Nonlinear Systems26 references4 citations

TL;DR

This paper presents a hybrid VTOL UAV combining fixed-wing and rotary-wing advantages, with a nonlinear 6-DOF model integrating rigid body dynamics, wing aerodynamics (via VLM), and motor-propeller thrust (via experimental lookup tables). It designs an $θ_{2}$ optimal controller that outperforms PID and LQR in wind disturbance rejection, achieving lower RMS errors and faster response in both hover and level-flight scenarios.

ABSTRACT

This paper addresses modeling and control of a six-degree-of-freedom unmanned aerial vehicle capable of vertical take-off and landing in the presence of wind disturbances. We design a hybrid vehicle that combines the benefits of both the fixed-wing and the rotary-wing UAVs. A non-linear model for the hybrid vehicle is rapidly built, combining rigid body dynamics, aerodynamics of wing, and dynamics of the motor and propeller. Further, we design an H2 optimal controller to make the UAV robust to wind disturbances. We compare its results against that of PID and LQR-based control. Our proposed controller results in better performance in terms of root mean squared errors and time responses during two scenarios: hover and level-flight.

Motivation & Objective

• Develop a hybrid UAV design that enables VTOL and long-range flight by combining rotary-wing vertical takeoff/landing with fixed-wing efficiency.
• Create a high-fidelity nonlinear 6-DOF dynamic model integrating rigid body mechanics, wing aerodynamics (via vortex lattice method), and propulsion dynamics (via experimental thrust/torque lookup tables).
• Design a robust control system capable of effectively rejecting wind disturbances, a critical challenge in real-world UAV operations.
• Compare the performance of $θ_{2}$ optimal control against conventional PID and LQR controllers under wind gusts in both hover and level-flight regimes.
• Demonstrate that $θ_{2}$ control provides superior disturbance attenuation and stability with lower RMS errors and improved transient response.

Proposed method

• Model the hybrid UAV using a flying wing configuration with four rotors for vertical lift and a fixed wing for forward flight, validated through CAD and physical parameters.
• Apply the vortex lattice method (VLM) to compute wing aerodynamic forces and moments, enabling accurate modeling of lift and drag across flight regimes.
• Conduct experimental measurements of motor-propeller pairs to generate lookup tables for thrust and torque as functions of RPM and angle of attack.
• Formulate the full nonlinear 6-DOF equations of motion using Newton-Euler dynamics, incorporating mass, inertia, and aerodynamic forces.
• Linearize the nonlinear model around hover and level-flight trim conditions to enable design of linear controllers (LQR, PID, $θ_{2}$).
• Implement $θ_{2}$ optimal control via Linear Matrix Inequality (LMI) optimization using CVX and MATLAB, minimizing a cost function that includes disturbance energy and state/control penalties.

Experimental results

Research questions

• RQ1 How can a hybrid VTOL UAV be modeled with sufficient accuracy to capture both vertical takeoff/landing and forward flight dynamics?
• RQ2 To what extent does $θ_{2}$ optimal control outperform PID and LQR in rejecting wind disturbances during hover and level flight?
• RQ3 What are the quantitative improvements in RMS error and transient response when using $θ_{2}$ control compared to PID and LQR?
• RQ4 How does the inclusion of wind disturbance in the $θ_{2}$ controller design enhance robustness compared to standard LQR and PID approaches?
• RQ5 Can the $θ_{2}$ controller maintain stability and performance under realistic wind turbulence, as modeled by the Dryden model?

Key findings

• The $θ_{2}$ optimal controller achieved the lowest RMS error in angular velocity tracking during level flight, with a value of 0.0457 rad/sec, outperforming LQR (0.0573) and PID (0.0859).
• In hover flight, the $θ_{2}$ controller reduced RMS error in yaw angle to 0.4370°, significantly lower than LQR (3.0217°) and PID (5.7745°), demonstrating superior disturbance rejection in rotational control.
• The $θ_{2}$ controller exhibited faster time response and lower overshoot compared to both PID and LQR in both hover and level-flight scenarios.
• The controller design explicitly incorporates wind disturbance as a design factor, resulting in inherently better robustness than PID and LQR, which are not disturbance-optimized.
• The simulation results using the Dryden wind turbulence model confirmed that $θ_{2}$ control maintains system stability and performance under realistic atmospheric disturbances.
• The proposed modeling framework, combining VLM, experimental lookup tables, and SimScape-based simulation, enables rapid and accurate dynamic modeling of hybrid UAVs.