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A Simple Approach to Regulate a PVTOL System Using Matching Conditions

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Abstract

In this work, based on shaping an energy function, it is introduced an output-feedback regulation control law for a Planar Vertical Takeoff and Landing (PVTOL) aircraft. To this end, a version of the matching control energy method is used to construct the Lyapunov candidate function and the stabilizer controller to regulate the PVTOL aircraft. The non-measurable system velocities are recovered using a suitable exact differentiator observer, achieved through super-twisting based observer. The theorem of LaSalle, together with some tools from the cascade system theory, was used to carry out the closed-loop stability analysis. Using a suitable finite time-varying identificator, the obtained controllers were improved to compensate bounded, smooth, and matching perturbations. Numerical simulations were included to test the effectiveness of the obtained controller.

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Authors and Affiliations

  1. Centro de Investigacion en Computacion, Instituto Politecnico Nacional, Mexico City, Mexico

    Carlos Aguilar-Ibanez, Miguel S. Suarez-Castanon, Jesus Meda-Campaña, Octavio Gutierrez-Frias, Carlos Merlo-Zapata & Jesus A. Martinez-Castro

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  1. Carlos Aguilar-Ibanez
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  2. Miguel S. Suarez-Castanon
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  3. Jesus Meda-Campaña
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  4. Octavio Gutierrez-Frias
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  5. Carlos Merlo-Zapata
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  6. Jesus A. Martinez-Castro
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Correspondence to Carlos Aguilar-Ibanez.

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This research was supported by Secretarí a de Investigación y 20190263 and 20196405.

Appendix

Appendix

Cascade theorem

(see corollary 10.3.3 in [17]): Let us consider the pair of cascade connected subsystems of the form:

$$ \begin{array}{@{}rcl@{}} \overset{.}{x}&=&f(x,z),\\ \overset{.}{z}&=&g(z), \end{array} $$
(54)

where x ∈Rn, z ∈Rm, f(0, 0) = 0, g(0) =0, and f(x,z), g(z) are locally Lipschitz on Rn ×Rm. Suppose the equilibrium x =0 of \(\overset {.}{x}=f(x,0)\) is globally asymptotically stable and the equilibrium z =0 of \(\overset {.}{z}=g(z)\) is globally asymptotically stable. Suppose the integral curves of the composite system are defined for all t =0 and bounded. Then, the equilibrium (x,z) = (0, 0) of (54) is globally asymptotically stable.

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Aguilar-Ibanez, C., Suarez-Castanon, M.S., Meda-Campaña, J. et al. A Simple Approach to Regulate a PVTOL System Using Matching Conditions. J Intell Robot Syst 98, 511–524 (2020). https://doi.org/10.1007/s10846-019-01087-x

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