<p>This paper addresses the control problem of a tilting quadrotor-an unmanned aerial vehicle (UAV) with a reconfigurable structure that enhances flight performance and enables multi-tasking capabilities. To tackle the challenges posed by time-delayed dynamics in altitude and servomotor responses, this work proposes a set of computationally efficient yet robust Proportional-Derivative (PD) control algorithms. These algorithms effectively mitigate such delays. The control design leverages a linearized mathematical model of the longitudinal motion within the <i>x</i>-<i>z</i> plane, derived using the Newton-Euler formalism. To ensure closed-loop stability, the analysis employs a geometric approach to explore the parameter space of the controller gains and delineates stability regions. The design further enforces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11081_2025_9995_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-stability constraints within these regions, guaranteeing rapid and reliable system responses. Subsequently, “optimal” control parameters are determined by solving an optimization problem based on the Chebyshev center of the stability region. Finally, numerical examples are presented to illustrate and validate the proposed control design methodology.</p>

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Stability and optimal control of a fully-actuated tilt-rotor with delayed feedback

  • José-Carmen López-Hernández,
  • César-Fernando Méndez-Barrios,
  • Adrián-Josué Guel-Cortez

摘要

This paper addresses the control problem of a tilting quadrotor-an unmanned aerial vehicle (UAV) with a reconfigurable structure that enhances flight performance and enables multi-tasking capabilities. To tackle the challenges posed by time-delayed dynamics in altitude and servomotor responses, this work proposes a set of computationally efficient yet robust Proportional-Derivative (PD) control algorithms. These algorithms effectively mitigate such delays. The control design leverages a linearized mathematical model of the longitudinal motion within the x-z plane, derived using the Newton-Euler formalism. To ensure closed-loop stability, the analysis employs a geometric approach to explore the parameter space of the controller gains and delineates stability regions. The design further enforces \(\sigma \) σ -stability constraints within these regions, guaranteeing rapid and reliable system responses. Subsequently, “optimal” control parameters are determined by solving an optimization problem based on the Chebyshev center of the stability region. Finally, numerical examples are presented to illustrate and validate the proposed control design methodology.