Stabilisation and altitude tracking of a four-rotor microhelicopter using the lifting operators

The lifting methodology can be used for simplifying the closed-loop stability study of a system in which the measurement data are acquired at different frequencies. This is because the lifting operators allow treating this kind of systems as if there is only one control frequency, which reduces the complexity of the problem in a very important way. The four-rotor microhelicopter designed by the authors, whose control is faced, is a nonlinear plant with sensors operating at two different frequencies. First, the system is linearised cancelling the rotors dynamics. Then, the authors implement a model reference adaptive control structure for identifying the gains of the linear reference plant and performing the adaptive control of the microhelicopter. At this point, the system stability study is carried out by just computing the eigenvalues of the closed-loop states matrix thanks to the lifting operators.

[1]  Dongguang Li,et al.  Analysis of dual-rate inferential control systems , 2002, Autom..

[2]  H. Voos.  Nonlinear and neural network-based control of a small four-rotor aerial robot , 2007, 2007 IEEE/ASME international conference on advanced intelligent mechatronics.

[3]  C.J.B. Macnab,et al.  A New Robust Adaptive-Fuzzy Control Method Applied to Quadrotor Helicopter Stabilization , 2006, NAFIPS 2006 - 2006 Annual Meeting of the North American Fuzzy Information Processing Society.

[4]  Rogelio Lozano,et al.  Real-time stabilization and tracking of a four-rotor mini rotorcraft , 2004, IEEE Transactions on Control Systems Technology.

[5]  Tongwen Chen,et al.  Multirate sampled-data systems: computing fast-rate models , 2004 .

[6]  Boubaker Daachi,et al.  ROBUST FEEDBACK LINEARIZATION AND GH∞ CONTROLLER FOR A QUADROTOR UNMANNED AERIAL VEHICLE , 2005 .

[7]  Leopoldo Acosta,et al.  Determining the stability of a multifrequency large-scale system using lifting operators , 2004 .

[8]  L. Fridman,et al.  Feedback linearization and high order sliding mode observer for a quadrotor UAV , 2006, International Workshop on Variable Structure Systems, 2006. VSS'06..

[9]  Roland Siegwart,et al.  Design and Control of an Indoor Coaxial Helicopter , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[10]  M.O. Efe.  Design of a sliding mode controller for a biochemical process by using an intermediate output variable , 2007, 2007 Mediterranean Conference on Control & Automation.

[11]  D. G. Meyer,et al.  Cost translation and a lifting approach to the multirate LQG problem , 1992 .

[12]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[13]  Camillo J. Taylor,et al.  Quadrotor control using dual camera visual feedback , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[14]  Bengt Lennartson,et al.  State-space solution to the periodic multirate H∞ control problem: a lifting approach , 2000, IEEE Trans. Autom. Control..

[15]  Roland Siegwart,et al.  Backstepping and Sliding-mode Techniques Applied to an Indoor Micro Quadrotor , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[16]  T. Madani,et al.  Sliding Mode Observer and Backstepping Control for a Quadrotor Unmanned Aerial Vehicles , 2007, 2007 American Control Conference.

[17]  Barnes W. McCormick,et al.  Aerodynamics, Aeronautics and Flight Mechanics , 1979 .

[18]  T. Madani,et al.  Backstepping Sliding Mode Control Applied to a Miniature Quadrotor Flying Robot , 2006, IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics.

[19]  P. Castillo,et al.  Stabilization of a mini rotorcraft with four rotors , 2005, IEEE Control Systems.

[20]  Abdelaziz Benallegue,et al.  Backstepping control with exact 2-sliding mode estimation for a quadrotor unmanned aerial vehicle , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[21]  T. Madani,et al.  Control of a Quadrotor Mini-Helicopter via Full State Backstepping Technique , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[22]  R. Lozano,et al.  Robustness with respect to delay uncertainties of a predictor-observer based discrete-time controller , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[23]  Holger Voos.  Nonlinear state-dependent Riccati equation control of a quadrotor UAV , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[24]  Tongwen Chen,et al.  Nonuniform multirate filter banks: analysis and design with an 𝒽∞ performance measure , 1997, IEEE Trans. Signal Process..

[25]  B. Francis,et al.  Input-output stability of sampled-data systems , 1991 .

[26]  R. Lozano,et al.  Simple Real-time Attitude Stabilization of a Quad-rotor Aircraft With Bounded Signals , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[27]  Yuri B. Shtessel,et al.  Control of a Quadrotor Vehicle Using Sliding Mode Disturbance Observer , 2007, ACC.