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Article

Energy-Based Control and LMI-Based Control for a Quadrotor Transporting a Payload

by
María-Eusebia Guerrero-Sánchez
1,†,
Omar Hernández-González
1,†,
Rogelio Lozano
2,
Carlos-D. García-Beltrán
3,
Guillermo Valencia-Palomo
4,* and
Francisco-R. López-Estrada
5
1
Tecnológico Nacional de México/Instituto Tecnológico Superior de Coatzacoalcos, Carretera Antigua Mina-Coatza, km. 16.5, Col. Reserva Territorial, Coatzacoalcos 96536, Veracruz, Mexico
2
Sorbonne Universités, UTC CNRS UMR 7253 Heudiasyc, 60203 Compiègne, France
3
Tecnológico Nacional de México/Centro Nacional de Investigación y Desarrollo Tecnológico, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca 62490, Morelos, Mexico
4
Tecnológico Nacional de México/Instituto Tecnológico de Hermosillo, Ave. Tecnológico y Periférico Poniente S/N, Hermosillo Sonora 83170, Mexico
5
Tecnológico Nacional de México/Instituto Tecnológico de Tuxtla Gutiérrez, TURIX-Dynamics Diagnosis and Control Group, Carr. Panam. km 1080, A.P. 599, Tuxtla Gutierrez 29050, Mexico
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2019, 7(11), 1090; https://doi.org/10.3390/math7111090
Submission received: 8 October 2019 / Revised: 4 November 2019 / Accepted: 6 November 2019 / Published: 11 November 2019
(This article belongs to the Special Issue Mathematics and Engineering)
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Abstract

This paper presents the control of a quadrotor with a cable-suspended payload. The proposed control structure is a hierarchical scheme consisting of an energy-based control (EBC) to stabilize the vehicle translational dynamics and to attenuate the payload oscillation, together with a nonlinear state feedback controller based on an linear matrix inequality (LMI) to control the quadrotor rotational dynamics. The payload swing control is based on an energy approach and the passivity properties of the system’s translational dynamics. The main advantage of the proposed EBC strategy is that it does not require excessive computations and complex partial differential equations (PDEs) for implementing the control algorithm. We present a new methodology for using an LMI to synthesize the controller gains for Lipschitz nonlinear systems with larger Lipschitz constants than other classical techniques based on LMIs. This theoretical approach is applied to the quadrotor rotational dynamics. Stability proofs based on the Lyapunov theory for the controller design are presented. The designed control scheme allows for the stabilization of the system in all its states for the three-dimensional case. Numerical simulations demonstrating the effectiveness of the controller are provided.
Keywords: energy-based control; payload swing attenuation; linear matrix inequalities; quadrotor; larger Lipschitz constants energy-based control; payload swing attenuation; linear matrix inequalities; quadrotor; larger Lipschitz constants

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MDPI and ACS Style

Guerrero-Sánchez, M.-E.; Hernández-González, O.; Lozano, R.; García-Beltrán, C.-D.; Valencia-Palomo, G.; López-Estrada, F.-R. Energy-Based Control and LMI-Based Control for a Quadrotor Transporting a Payload. Mathematics 2019, 7, 1090. https://doi.org/10.3390/math7111090

AMA Style

Guerrero-Sánchez M-E, Hernández-González O, Lozano R, García-Beltrán C-D, Valencia-Palomo G, López-Estrada F-R. Energy-Based Control and LMI-Based Control for a Quadrotor Transporting a Payload. Mathematics. 2019; 7(11):1090. https://doi.org/10.3390/math7111090

Chicago/Turabian Style

Guerrero-Sánchez, María-Eusebia, Omar Hernández-González, Rogelio Lozano, Carlos-D. García-Beltrán, Guillermo Valencia-Palomo, and Francisco-R. López-Estrada. 2019. "Energy-Based Control and LMI-Based Control for a Quadrotor Transporting a Payload" Mathematics 7, no. 11: 1090. https://doi.org/10.3390/math7111090

APA Style

Guerrero-Sánchez, M.-E., Hernández-González, O., Lozano, R., García-Beltrán, C.-D., Valencia-Palomo, G., & López-Estrada, F.-R. (2019). Energy-Based Control and LMI-Based Control for a Quadrotor Transporting a Payload. Mathematics, 7(11), 1090. https://doi.org/10.3390/math7111090

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