Adaptive vibration control of a flexible marine riser via the backstepping technique and disturbance adaptation

This paper proposes an adaptive boundary control for vibration suppression of a flexible marine riser system. The dynamic model of the riser system is described in the form of a nonlinear nonhomogeneous hyperbolic partial differential equation and four ordinary differential equations. In a proper mathematical manner, the backstepping technique, Lyapunov’s direct method, and the adaptive technique are utilized to design an adaptive boundary control for the vibration suppression of the riser system, and also for the global stabilization of the riser within a small neighbourhood of its original position. In addition, a parameter adaptive law is designed to compensate for the system parametric uncertainties and a disturbance adaptation law is proposed to eliminate the effects of boundary disturbance. The uniformly bounded stability of the closed-loop riser system is achieved through rigorous Lyapunov analysis with no discretization or simplification of the partial differential equation dynamics model of the system. Simulation results are presented to illustrate the effectiveness of the proposed control.

[1]  Shuzhi Sam Ge,et al.  Top Tension Control of a Flexible Marine Riser by Using Integral-Barrier Lyapunov Function , 2015, IEEE/ASME Transactions on Mechatronics.

[2]  Shuzhi Sam Ge,et al.  Robust adaptive control of a thruster assisted position mooring system , 2014, Autom..

[3]  Shuzhi Sam Ge,et al.  Vibration Control of a Flexible Beam With Output Constraint , 2015, IEEE Transactions on Industrial Electronics.

[4]  Keum-Shik Hong,et al.  Robust Adaptive Control of a Cantilevered Flexible Structure with Spatiotemporally Varying Coefficients and Bounded Disturbance , 2004 .

[5]  M. Krstić,et al.  Boundary Control of PDEs , 2008 .

[6]  Xuefang Li,et al.  D-type anticipatory iterative learning control for a class of inhomogeneous heat equations , 2013, Autom..

[7]  Zhijia Zhao,et al.  Adaptive boundary control of an axially moving belt system with high acceleration/deceleration , 2016 .

[8]  Christopher D. Rahn,et al.  Mechatronic control of distributed noise and vibration , 2001 .

[9]  Shuzhi Sam Ge,et al.  Cooperative control of a nonuniform gantry crane with constrained tension , 2016, Autom..

[10]  Shihua Li,et al.  Continuous finite-time anti-disturbance control for a class of uncertain nonlinear systems , 2014 .

[11]  Shuang Zhang,et al.  Control Design for Nonlinear Flexible Wings of a Robotic Aircraft , 2017, IEEE Transactions on Control Systems Technology.

[12]  Ömer Morgül,et al.  Boundary control of a rotating shear beam with observer feedback , 2012 .

[13]  Yu Liu,et al.  Boundary control of an axially moving accelerated/decelerated belt system , 2016 .

[14]  M. Balas.  Active control of flexible systems , 1978 .

[15]  K. D. Do,et al.  Boundary control of two-dimensional marine risers with bending couplings , 2013 .

[16]  Khac Duc Do,et al.  Global Stabilization of Marine Risers with Varying Tension and Rotational Inertia , 2014 .

[17]  Yu Liu,et al.  Modelling and control for a class of axially moving nonuniform system , 2017, Int. J. Syst. Sci..

[18]  Shuzhi Sam Ge,et al.  Vibration Control of Flexible Marine Riser Systems With Input Saturation , 2016, IEEE/ASME Transactions on Mechatronics.

[19]  S. Ge,et al.  Modeling and Vibration Control for a Nonlinear Moving String With Output Constraint , 2015, IEEE/ASME Transactions on Mechatronics.

[20]  Zhijia Zhao,et al.  Adaptive Lyapunov-based backstepping control for an axially moving system with input saturation , 2016 .

[21]  G. Smith,et al.  Numerical Solution of Partial Differential Equations: Finite Difference Methods , 1978 .

[22]  Han-Xiong Li,et al.  Fuzzy Boundary Control Design for a Class of Nonlinear Parabolic Distributed Parameter Systems , 2014, IEEE Transactions on Fuzzy Systems.

[23]  Shuzhi Sam Ge,et al.  Adaptive Control of a Flexible Crane System With the Boundary Output Constraint , 2014, IEEE Transactions on Industrial Electronics.

[24]  Shuzhi Sam Ge,et al.  Boundary Control of a Coupled Nonlinear Flexible Marine Riser , 2010, IEEE Transactions on Control Systems Technology.

[25]  K. D. Do,et al.  Boundary control of transverse motion of marine risers with actuator dynamics , 2008 .

[26]  Fumitoshi Matsuno,et al.  Energy-based control of axially translating beams: varying tension, varying speed, and disturbance adaptation , 2005, IEEE Transactions on Control Systems Technology.

[27]  Jun Yang,et al.  Disturbance Observer-Based Control: Methods and Applications , 2014 .

[28]  Khac Duc Do,et al.  Boundary control of three-dimensional inextensible marine risers , 2009 .

[29]  Sakdirat Kaewunruen,et al.  Nonlinear free vibrations of marine risers/pipes transporting fluid , 2005 .

[30]  Shuzhi Sam Ge,et al.  Vibration Control of a Nonuniform Wind Turbine Tower via Disturbance Observer , 2015, IEEE/ASME Transactions on Mechatronics.

[31]  Bao-Zhu Guo,et al.  Parameter estimation and stabilization for a wave equation with boundary output harmonic disturbance and non-collocated control , 2011 .

[32]  Andrey Smyshlyaev,et al.  Adaptive Control of Parabolic PDEs , 2010 .

[33]  Shuzhi Sam Ge,et al.  Boundary control of a flexible marine riser with vessel dynamics , 2010, Proceedings of the 2010 American Control Conference.

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

[35]  Xinghuo Yu,et al.  Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances , 2013, Autom..

[36]  Miroslav Krstic.  Systematization of approaches to adaptive boundary stabilization of PDEs , 2006 .

[37]  Bao-Zhu Guo,et al.  Output Feedback Stabilization for One-Dimensional Wave Equation Subject to Boundary Disturbance , 2015, IEEE Transactions on Automatic Control.

[38]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[39]  Shuzhi Sam Ge,et al.  Active control of flexible marine risers , 2009 .

[40]  Jinkun Liu,et al.  Observer design for a flexible-link manipulator with PDE model , 2015 .

[41]  Zhijia Zhao,et al.  Vibration control of an axially moving accelerated/decelerated belt system with input saturation , 2018, Trans. Inst. Meas. Control.

[42]  Zhijia Zhao,et al.  Stabilization of an axially moving accelerated/decelerated system via an adaptive boundary control. , 2016, ISA transactions.