Modeling and Control of a Quadcopter Flying in a Wind Field: A Comparison Between LQR and Structured ℋ∞ Control Techniques

Abstract

This article deals with the stationary flight control problem of an Unmanned Aircraft Vehicle (UAV) flying in a wind field. The main objective is to develop a robust control law to stabilize the drone flying under real-life outdoor conditions while maintaining adequate flight performances. To do so, a generic nonlinear dynamic model of the quadcopter is firstly developed; this model is then completed with the modeling of the wind disturbances, which allows the simulation of the proposed control algorithms. Two approaches for the synthesis of the control laws are compared: the first one uses Linear Quadratic Regulator (LQR) synthesis and the second one uses structured ${\cal H}_{\infty }$ synthesis. Simulations are conducted to evaluate the performances of both control laws when subjected to a nominal wind step input varying from 0 to 14 m/s. This particular input choice makes it possible to analyze the performance of the controllers in both transient (wind gust) and steady states (sustained wind). The results show that better performances are obtained with the structured ${\cal H}_{\infty }$ synthesis using the robust control theory than with the LQR synthesis using the optimal control theory. Furthermore, it is shown that the simplicity of use of the Robust Control Toolbox of MATLAB favors the usage of more complex control architectures without impacting the workload of the control engineer.