INDI control for the take-off and landing phases of an eVTOL

Abstract This article presents the development and implementation of incremental nonlinear dynamic inversion (INDI), integrated with a proportional-derivative (PD) controller, to enhance stability and reference tracking during the takeoff, hover, and landing phases of an eVTOL (electric vertical takeoff and landing) vehicle. Simulation results indicate that INDI, combined with a PD controller tuned with natural frequencies between $$0.1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:math> and $$3.0~\mathrm {rad/s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>3.0</mml:mn> <mml:mspace/> <mml:mrow> <mml:mi>rad</mml:mi> <mml:mo>/</mml:mo> <mml:mi>s</mml:mi> </mml:mrow> </mml:mrow> </mml:math> and damping ratios near $$1.0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1.0</mml:mn> </mml:mrow> </mml:math> , yields an overshoot below $$20\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>20</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> . The steady-state time is less than $$2~\textrm{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mspace/> <mml:mtext>s</mml:mtext> </mml:mrow> </mml:math> for the attitude variables and less than $$10~\textrm{s}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>10</mml:mn> <mml:mspace/> <mml:mtext>s</mml:mtext> </mml:mrow> </mml:math> for altitude. The rise time (10–90% of the final value) is consistent with and shorter than the steady-state time, meeting the performance requirements for vehicle operation and ensuring stable behavior during takeoff, hover, and landing. The system also exhibits robustness to parametric uncertainties (in particular, $$\pm 10\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>±</mml:mo> <mml:mn>10</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> variations), maintaining bounded tracking errors within the vertical-flight envelope considered. The study further includes hardware-in-the-loop experiments to evaluate the behavior of the control law implemented on an STM32F4 microcontroller. Finally, a simulation-based stability and robustness analysis confirms that the closed-loop system remains stable provided that model uncertainties remain moderate.