Periodic motion planning and nonlinear ℋ∞ tracking control of a 3-DOF underactuated helicopter

Nonlinear ℋ∞ synthesis is developed to solve the tracking control problem into a 3-DOF helicopter prototype. Planning of periodic motions under a virtual constraints approach is considered prior the controller design in order to achieve our goal. A local ℋ∞ controller is derived by means of a certain perturbation of the differential Riccati equations that appear while solving the corresponding ℋ∞ control problem for the linearised system. Stabilisability and detectability properties of the control system are thus ensured by the existence of the proper solutions of the unperturbed differential Riccati equations, and hence the proposed synthesis procedure obviates an extra verification work of these properties. Due to the nature of the approach, the resulting controller additionally yields the desired robustness properties against unknown but bounded external disturbances. Convergence and robustness of the proposed design are supported by simulation results.

[1]  Y. Orlova,et al.  Nonlinear H ∞-control of nonsmooth time-varying systems with application to friction mechanical manipulators , 2003 .

[2]  Van,et al.  L2-Gain Analysis of Nonlinear Systems and Nonlinear State Feedback H∞ Control , 2004 .

[3]  Alexander L. Fradkov,et al.  Adaptive Control of 3DOF Motion for LAAS Helicopter Benchmark: Design and Experiments , 2007, 2007 American Control Conference.

[4]  A. Schaft.  L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control , 1992 .

[5]  Roberto Kawakami Harrop Galvão,et al.  Modelling and constrained predictive control of a 3DOF helicopter , 2006 .

[6]  Selcuk Bayraktar,et al.  Aggressive landing maneuvers for unmanned aerial vehicles , 2006 .

[7]  Ümit Özgüner,et al.  Sliding Mode Control of a Quadrotor Helicopter , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[8]  T. Basar,et al.  H∞-0ptimal Control and Related Minimax Design Problems: A Dynamic Game Approach , 1996, IEEE Trans. Autom. Control..

[9]  Mariya A. Ishutkina,et al.  Design and implimentation of a supervisory safety controller for a 3DOF helicopter , 2004 .

[10]  Yury Orlov,et al.  Nonlinear Hinfinity-control of nonsmooth time-varying systems with application to friction mechanical manipulators , 2003, Autom..

[11]  Rogelio Lozano,et al.  Adaptive control for a radio‐controlled helicopter in a vertical flying stand , 2004 .

[12]  Lorenzo Marconi,et al.  Robust nonlinear motion control of a helicopter , 2003, IEEE Trans. Autom. Control..

[13]  Ian R. Manchester,et al.  Can we make a robot ballerina perform a pirouette? Orbital stabilization of periodic motions of underactuated mechanical systems , 2008, Annu. Rev. Control..

[14]  Bernard Brogliato,et al.  Nonlinear modelling and control of helicopters , 2003, Autom..

[15]  A. Isidori,et al.  Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems , 1992 .

[16]  A. Bogmér,et al.  On control problems , 1989 .

[17]  P. Khargonekar,et al.  State-space solutions to standard H/sub 2/ and H/sub infinity / control problems , 1989 .

[18]  P. Khargonekar,et al.  H ∞ control of linear time-varying systems: a state-space approach , 1991 .

[19]  Claire J. Tomlin,et al.  Quadrotor Helicopter Flight Dynamics and Control: Theory and Experiment , 2007 .

[20]  Christopher Edwards,et al.  Robust model reference control using a sliding mode controller/observer scheme with application to a helicopter problem , 1996, Proceedings. 1996 IEEE International Workshop on Variable Structure Systems. - VSS'96 -.

[21]  Carlos Canudas-de-Wit,et al.  Constructive tool for orbital stabilization of underactuated nonlinear systems: virtual constraints approach , 2005, IEEE Transactions on Automatic Control.

[22]  A. Shiriaev,et al.  Periodic motion planning for virtually constrained Euler-Lagrange systems , 2006, Syst. Control. Lett..

[23]  Mario Garcia-Sanz,et al.  Control del Ángulo de Cabeceo de un Helicóptero Como Benchmark de Diseño de Controladores , 2006 .

[24]  Leonardo Acho,et al.  Nonlinear H/sub /spl infin//-control of time-varying systems , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).