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

María-Eusebia Guerrero-Sánchez, Omar Hernández-González, Rogelio Lozano, Carlos-D. García-Beltrán, Guillermo Valencia-Palomo and Francisco-R. López-Estrada
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María-Eusebia Guerrero-Sánchez: Tecnológico Nacional de México/Instituto Tecnológico Superior de Coatzacoalcos, Carretera Antigua Mina-Coatza, km. 16.5, Col. Reserva Territorial, Coatzacoalcos 96536, Veracruz, Mexico
Omar Hernández-González: Tecnológico Nacional de México/Instituto Tecnológico Superior de Coatzacoalcos, Carretera Antigua Mina-Coatza, km. 16.5, Col. Reserva Territorial, Coatzacoalcos 96536, Veracruz, Mexico
Rogelio Lozano: Sorbonne Universités, UTC CNRS UMR 7253 Heudiasyc, 60203 Compiègne, France
Carlos-D. García-Beltrán: Tecnológico Nacional de México/Centro Nacional de Investigación y Desarrollo Tecnológico, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca 62490, Morelos, Mexico
Guillermo Valencia-Palomo: Tecnológico Nacional de México/Instituto Tecnológico de Hermosillo, Ave. Tecnológico y Periférico Poniente S/N, Hermosillo Sonora 83170, Mexico
Francisco-R. López-Estrada: 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

Mathematics, 2019, vol. 7, issue 11, 1-21

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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