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.

Vibration control of an axially moving accelerated/decelerated belt system with input saturation

This article describes an investigation of a boundary control for vibration suppression of an axially moving accelerated or decelerated belt system with input saturation. Firstly, after considering the effects of the high acceleration or deceleration and unknown distributed disturbance, an infinite-dimensional model of the belt system is described by a nonhomogeneous partial differential equation and a set of ordinary differential equations. Secondly, by synthesizing boundary control techniques and Lyapunov’s direct method, a boundary control is developed to suppress the belt’s vibration and to stabilize the belt system at its equilibrium position globally; an auxiliary system is proposed to compensate for the nonlinear input saturation characteristic; a disturbance adaptation law is employed to mitigate the effects of unknown boundary disturbance; and the S-curve acceleration/deceleration method is adopted to plan the belt’s axial speed. Thirdly, with the proposed boundary control, the wellposedness of the closed-loop belt system is mathematically demonstrated and uniformly bounded stability of the closed-loop system is achieved without any discretization of the system dynamic model. Finally, simulation results are presented to verify the validity and effectiveness of the proposed control scheme.