Gain-Scheduled Control of a Quadcopter UAV

In this thesis we develop a gain-scheduled control law for the quadcopter unmanned aerial vehicle (UAV). Techniques from linear control theory are introduced and used to construct adaptive proportional and proportional-integral control laws for use with both state and observer-based output feedback. The controller monitors the yaw angle of the quadcopter and updates a gain matrix as the system evolves through operating points. To demonstrate the effectiveness of the gain-scheduled controller, trajectories involving significant variation in the yaw angle are tracked by the quadcopter, including a helix and Lissajous curve. We consider physical implementation of the controller, and offer suggestions for improvement and future work.

[1]  Sophie Tarbouriech,et al.  Control of linear systems subject to input constraints: a polynomial approach , 2001, Autom..

[2]  Youmin Zhang,et al.  Flatness-Based Trajectory Planning/Replanning for a Quadrotor Unmanned Aerial Vehicle , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[3]  Wilson J. Rugh,et al.  Interpolation of observer state feedback controllers for gain scheduling , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[4]  R. T. Reichert Dynamic scheduling of modern-robust-control autopilot designs for missiles , 1992 .

[5]  Eugênio B. Castelan,et al.  A reduced-order framework applied to linear systems with constrained controls , 1996, IEEE Trans. Autom. Control..

[6]  R. E. Kalman,et al.  New Results in Linear Filtering and Prediction Theory , 1961 .

[7]  A. Papachristodoulou,et al.  On the construction of Lyapunov functions using the sum of squares decomposition , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[8]  Sigurdur Hafstein,et al.  A CONSTRUCTIVE CONVERSE LYAPUNOV THEOREM ON EXPONENTIAL STABILITY , 2004 .

[9]  Sophie Tarbouriech,et al.  Robust stability of uncertain polytopic linear time-delay systems with saturating inputs: an LMI approach , 2002, Comput. Electr. Eng..

[10]  N. Nichols,et al.  Robust pole assignment in linear state feedback , 1985 .

[11]  Wilson J. Rugh,et al.  Gain scheduling for H-infinity controllers: a flight control example , 1993, IEEE Trans. Control. Syst. Technol..

[12]  Peter Giesl,et al.  Construction of a local and global Lyapunov function using radial basis functions , 2008 .

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

[14]  Robert E. Mahony,et al.  Control of a quadrotor helicopter using visual feedback , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[15]  Pablo A. Parrilo,et al.  Semidefinite Programming Relaxations and Algebraic Optimization in Control , 2003, Eur. J. Control.

[16]  Stefan Ratschan,et al.  Providing a Basin of Attraction to a Target Region of Polynomial Systems by Computation of Lyapunov-Like Functions , 2010, SIAM J. Control. Optim..

[17]  P. Veronesi Classical Dynamics of Particles and Systems , 1971 .

[18]  Alexander Graham,et al.  Introduction to Control Theory, Including Optimal Control , 1980 .

[19]  Wilson J. Rugh,et al.  Gain scheduling dynamic linear controllers for a nonlinear plant , 1995, Autom..

[20]  Wilson J. Rugh,et al.  Research on gain scheduling , 2000, Autom..

[21]  Bernard Friedland,et al.  Control System Design: An Introduction to State-Space Methods , 1987 .

[22]  D. Luenberger Observing the State of a Linear System , 1964, IEEE Transactions on Military Electronics.

[23]  Keith Glover,et al.  The application of scheduled H∞ controllers to a VSTOL aircraft , 1993, IEEE Trans. Autom. Control..

[24]  Wilson J. Rugh,et al.  Interpolation methods for gain scheduling , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[25]  Wilson J. Rugh,et al.  Analytical Framework for Gain Scheduling , 1990, 1990 American Control Conference.

[26]  R. Kálmán On the general theory of control systems , 1959 .