Zhijia Zhao

Modelling and control for a class of axially moving nonuniform system

ABSTRACT In this paper, we deal with the active control problem for a class of axially moving system. The system is nonuniform due to the spatial-varying mass and spatiotemporally varying tension. The infinite dimensional model of the nonuniform system represented by the hybrid partial-ordinary differential equations is derived with consideration of the spatiotemporally varying distributed disturbance. To suppress the vibration of the nonuniform system, full state feedback boundary control is developed. For the case that the system states cannot be measured, output feedback boundary control is proposed by using the high-order observers for the estimation of the unmeasurable states. The disturbance observer is introduced to mitigate the effects of the boundary disturbance. With the proposed boundary control, the stability of the closed-loop nonuniform system is achieved through rigorous analysis and the uniform boundedness of the all closed-loop signals is guaranteed. Numerical simulations are performed to validate the performance of the control scheme proposed.

Output feedback boundary control of an axially moving system with input saturation constraint

This paper is concerned with boundary control for an axially moving belt system with high acceleration/deceleration subject to the input saturation constraint. The dynamics of belt system is expressed by a nonhomogeneous hyperbolic partial differential equation coupled with an ordinary differential equation. First, state feedback boundary control is designed for the case that the boundary states of the belt system can be measured. Subsequently, output feedback boundary control is developed when some of the system states can not be accurately obtained. The well-posedness and the uniformly bounded stability of the closed-loop system are achieved through rigorous mathematical analysis. In addition, high-gain observers are utilized to estimate those unmeasurable states, the auxiliary system is introduced to eliminate the constraint effects of the input saturation, and the disturbance observer is adopted to cope with unknown boundary disturbance. Finally, the control performance of the belt system is illustrated by carrying out numerical simulations.

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.

Infinite-dimensional disturbance-observer-based control for an axially moving non-uniform system with input constraint:

In this paper, the vibration control and input saturation constraint problem of an axially moving non-uniform system subject to unknown disturbances is investigated. The key control objectives are to control the vibration of the system and eliminate the effects of the input saturation constraint. To that end, a boundary control with an auxiliary system is designed by utilizing Lyapunov’s direct method. Additionally, a boundary disturbance observer is proposed to deal with the boundary disturbance, and an infinite-dimensional disturbance observer is introduced to mitigate the effects of the distributed disturbance. With the designed boundary control, uniformly bounded stability of the controlled system is achieved through rigorous Lyapunov analysis without any model reduction. Finally, simulation results are given to show the effectiveness of the designed control scheme.

Robust output feedback stabilization for a flexible marine riser system

The aim of this paper is to develop a boundary control for the vibration reduction of a flexible marine riser system in the presence of parametric uncertainties and system states obtained inaccurately. To this end, an adaptive output feedback boundary control is proposed to suppress the risers vibration fusing with observer-based backstepping, high-gain observers and robust adaptive control theory. In addition, the parameter adaptive laws are designed to compensate for the system parametric uncertainties, and the disturbance observer is introduced to mitigate the effects of external environmental disturbance. The uniformly bounded stability of the closed-loop system is achieved through rigorous Lyapunov analysis without any discretisation or simplification of the dynamics in the time and space, and the state observer error is ensured to exponentially converge to zero as time grows to infinity. In the end, the simulation and comparison studies are carried out to illustrate the performance of the proposed control under the proper choice of the design parameters.

Adaptive control of a flexible riser system

An adaptive boundary controller is developed in this article for minimizing the vibration displacement of a flexible riser. The dynamics of riser system is represented by partial-ordinary differential equations. Through combining boundary control, adaptive technique with backstepping technique, an adaptive boundary controller is given for realizing vibration restraint for the riser system, where an adaptive law is developed for coping with parametric uncertainties and a signum function is introduced for mitigating the boundary disturbance. With the designed adaptive boundary controller, the spillover instability can be successfully avoided. Finally, simulations are displayed to explain that the given controller is valid to realize vibration restraint of a flexible riser.

Vibration suppression of a flexible marine riser by output feedback boundary control

In this paper, output feedback boundary control of a flexible marine riser coupled with the internal fluid dynamics is investigated. By merging Lyapunovs direct method, boundary control technique and high-gain observers, an output feedback boundary control with disturbance observer is proposed to suppress the risers vibration and deal with the effects of the external environment disturbance. The stability of the closed-looped system is achieved without any discretisation or simplification of the dynamics in the time and space, thus the control spillover will not arise. Simulation results are provided to verify the effectiveness of the proposed output feedback boundary control.