Boundary Control of a Quadrotor UAV with a Payload Connected by a Flexible Cable

This paper addresses the problem of boundary control design for a quadrotor UAV with a payload connected by a flexible cable. The extend Hamilton's principle is applied to establish the model of the slung-load system which consists of two nonlinear wave equations. The objective of this paper is to design boundary feedback controllers for the slung-load system via the cable's boundary measurements such that the resulting closed-loop system is exponentially stable. The Lyapunov's direct method is employed to derive the stabilization condition for the system, which is provided in terms of linear matrix inequalities (LMIs). The numerical simulation illustrates the effectiveness of the proposed design method.

[1]  Jwusheng Hu,et al.  VIBRATION ATTENUATION OF AN AXIALLY MOVING STRING VIAACTIVE IN‐DOMAIN CONTROL METHODS , 1999 .

[2]  K. Hong,et al.  Robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension , 2004 .

[3]  M. Krstić.  Boundary Control of PDEs: A Course on Backstepping Designs , 2008 .

[4]  Miroslav Krstic,et al.  On the relationship between the Absolute Vibration Suppression and Back-Stepping methods in control of the wave equation with possibly unstable boundary conditions , 2016, 2016 American Control Conference (ACC).

[5]  Eugene P. Wigner,et al.  Formulas and Theorems for the Special Functions of Mathematical Physics , 1966 .

[6]  Miroslav Krstic,et al.  Lyapunov stability of linear predictor feedback for distributed input delays , 2010, 49th IEEE Conference on Decision and Control (CDC).

[7]  Dongbing Gu,et al.  Quad-rotor lifting-transporting cable-suspended payloads control , 2015, 2015 21st International Conference on Automation and Computing (ICAC).

[8]  Mou Chen,et al.  Antidisturbance Control for a Suspension Cable System of Helicopter Subject to Input Nonlinearities , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[9]  M. Benati,et al.  Formulation of Equations of Motion for a Chain of Flexible Links Using Hamilton’s Principle , 1994 .

[10]  John E. Rijnsdorp,et al.  Advanced process control: W. Harmon Ray , 1982, Autom..

[11]  Costas J. Spanos,et al.  Advanced process control , 1989 .

[12]  Jun-feng Li,et al.  Stabilization analysis of a generalized nonlinear axially moving string by boundary velocity feedback , 2008, Autom..

[13]  K. Hong,et al.  Asymptotic stabilization of a nonlinear axially moving string by adaptive boundary control , 2010 .

[14]  Shuzhi Sam Ge,et al.  Adaptive Boundary Control of a Nonlinear Flexible String System , 2014, IEEE Transactions on Control Systems Technology.

[15]  Hans Zwart,et al.  An Introduction to Infinite-Dimensional Linear Systems Theory , 1995, Texts in Applied Mathematics.

[16]  Vijay Kumar,et al.  Opportunities and challenges with autonomous micro aerial vehicles , 2012, Int. J. Robotics Res..

[17]  J. Wickert.  Non-linear vibration of a traveling tensioned beam , 1992 .

[18]  Miroslav Krstic,et al.  Nonlinear stabilization through wave PDE dynamics with a moving uncontrolled boundary , 2016, Autom..

[19]  Jean-Pierre Corriou,et al.  Distributed Geometric Control of Wave Equation , 2008 .