<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(0.1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0.1</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(3.0~\mathrm {rad/s}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3.0</mn> <mspace width="3.33333pt" /> <mrow> <mi mathvariant="normal">rad</mi> <mo stretchy="false">/</mo> <mi mathvariant="normal">s</mi> </mrow> </mrow> </math></EquationSource> </InlineEquation> and damping ratios near <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(1.0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1.0</mn> </mrow> </math></EquationSource> </InlineEquation>, yields an overshoot below <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(20\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>20</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>. The steady-state time is less than <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(2~\textrm{s}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mspace width="3.33333pt" /> <mtext>s</mtext> </mrow> </math></EquationSource> </InlineEquation> for the attitude variables and less than <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(10~\textrm{s}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>10</mn> <mspace width="3.33333pt" /> <mtext>s</mtext> </mrow> </math></EquationSource> </InlineEquation> 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, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\pm 10\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>±</mo> <mn>10</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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

  • Huascar Mirko Montecinos Cortez,
  • Neusa Maria Franco de Oliveira,
  • Francisco Javier Triveno Vargas

摘要

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 \(0.1\) 0.1 and \(3.0~\mathrm {rad/s}\) 3.0 rad / s and damping ratios near \(1.0\) 1.0 , yields an overshoot below \(20\%\) 20 % . The steady-state time is less than \(2~\textrm{s}\) 2 s for the attitude variables and less than \(10~\textrm{s}\) 10 s 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, \(\pm 10\%\) ± 10 % 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.