LMI-Based Gain Synthesis for Simple Robust Quadrotor Control

In this paper, we present a method for using linear matrix inequalities (LMIs) to synthesize controller gains for a quadrotor system. The controller is based on approximate feedback linearization and is structured to allow for tuning similar to proportional-integral-derivative (PID) controllers. The synthesis procedure generates suboptimal gains with respect to mixed <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">H₂</tex></formula> and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">H∞</tex></formula> performance cost functions and a pole placement region constraint. The basic procedure is extended to account for dynamic external disturbances, inexact nonlinearity cancellation, multiplicative actuator uncertainty, and saturated integrators in the control loop. The controller is tested in a real-world flight using 10 Hz position updates with 2 cm standard deviation noise to approximate GPS or vision-based control scenarios.