Anti-windup design for input-coupled double integrator systems with application to quadrotor UAV's

Abstract This paper describes the development of an anti-windup scheme for systems which consist of a parallel set of double integrators preceded by a static coupling element and a saturation nonlinearity. A class of anti-windup compensators are proposed which can guarantee global asymptotic stability of the origin of the closed-loop system. Simple linear-like guidelines for choosing the anti-windup compensator parameters are also given. The anti-windup compensator designs are evaluated on a quadrotor unmanned aerial vehicle. Simulation results and flight tests are presented to demonstrate the effectiveness of this approach.

[1]  A. Saberi,et al.  On the input-to-state stability (ISS) of a double integrator with saturated linear control laws , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[2]  Matthew C. Turner,et al.  Antiwindup for stable linear systems with input saturation: an LMI-based synthesis , 2003, IEEE Trans. Autom. Control..

[3]  Matthew C. Turner,et al.  Decentralized Approaches to Antiwindup Design With Application to Quadrotor Unmanned Aerial Vehicles , 2016, IEEE Transactions on Control Systems Technology.

[4]  Petros A. Ioannou,et al.  Adaptive LQ Control With Anti-Windup Augmentation to Optimize UAV Performance in Autonomous Soaring Applications , 2008, IEEE Transactions on Control Systems Technology.

[5]  Huan Zhang,et al.  A weak L2-gain property for nonlinear systems , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[6]  Manfred Morari,et al.  A unified framework for the study of anti-windup designs , 1994, Autom..

[7]  Dennis S. Bernstein,et al.  Global stabilization of systems containing a double integrator using a saturated linear controller , 1999 .

[8]  Sophie Tarbouriech,et al.  Optimization and implementation of dynamic anti-windup compensators with multiple saturations in flight control systems , 2009 .

[9]  Jorge M. Gonçalves.  λ2-Gain of double integrators with saturation nonlinearity , 2002, IEEE Trans. Autom. Control..

[10]  Adolf Hermann Glattfelder,et al.  Control Systems with Input and Output Constraints , 2003 .

[11]  Randal W. Beard,et al.  Consensus Algorithms for Single-integrator Dynamics , 2008 .

[12]  Jorge Goncalves,et al.  L2-gain of double integrators with saturation nonlinearity , 2002 .

[13]  Christopher Edwards,et al.  An anti-windup scheme with closed-loop stability considerations , 1999, Autom..

[14]  Guido Herrmann,et al.  Discrete-time and sampled-data anti-windup synthesis: stability and performance , 2006, Int. J. Syst. Sci..

[15]  Luca Zaccarian,et al.  Modern Anti-windup Synthesis: Control Augmentation for Actuator Saturation , 2011 .

[16]  Guangming Xie,et al.  Consensus control for a class of networks of dynamic agents , 2007 .

[17]  Roland Siegwart,et al.  Design and control of an indoor micro quadrotor , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[18]  Luca Zaccarian,et al.  A common framework for anti-windup, bumpless transfer and reliable designs , 2002, Autom..

[19]  Guido Herrmann,et al.  Further results on full-order anti-windup synthesis: exploiting the stability multiplier , 2004 .

[20]  Ian Postlethwaite,et al.  Linear conditioning for systems containing saturating actuators , 2000, Autom..

[21]  Guang-Ren Duan,et al.  Global Stabilization of the Double Integrator System With Saturation and Delay in the Input , 2010 .

[22]  Chung-Yao Kao,et al.  On the L2-gain of a double integrator with feedback loop saturation nonlinearity , 2001, IEEE Trans. Autom. Control..

[23]  Roland Siegwart,et al.  Full control of a quadrotor , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[24]  Matthew C. Turner,et al.  Alternative approach to anti-windup synthesis for double integrator systems , 2016, 2016 American Control Conference (ACC).

[25]  Matthew C. Turner,et al.  A tutorial on modern anti-windup design , 2009, 2009 European Control Conference (ECC).

[26]  Isabelle Queinnec,et al.  Stability region enlargement through anti-windup strategy for linear systems with dynamics restricted actuator , 2006, Int. J. Syst. Sci..

[27]  Herbert Werner,et al.  Model Identification and ℋ∞ Attitude Control for Quadrotor MAV's , 2012, ICIRA.

[28]  William P. Heath,et al.  Directionality compensation for linear multivariable anti-windup synthesis† , 2015, Int. J. Control.

[29]  Randal W. Beard,et al.  CLF-based tracking control for UAV kinematic models with saturation constraints , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[30]  Timothy W. McLain,et al.  Quadrotors and Accelerometers: State Estimation with an Improved Dynamic Model , 2014, IEEE Control Systems.

[31]  Matthew C. Turner,et al.  Channel-by-channel anti-windup design for a class of multivariable systems , 2015, 2015 American Control Conference (ACC).

[32]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[33]  Matthew C. Turner,et al.  Anti-windup synthesis using Riccati equations , 2007, Int. J. Control.