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

2016 ◽  
Vol 40 (2) ◽  
pp. 685-697 ◽  
Author(s):  
Yu Liu ◽  
Zhijia Zhao ◽  
Fang Guo ◽  
Yun Fu
Keyword(s):  
Boundary Control ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Direct Method ◽  
Input Saturation ◽  
Unknown Boundary ◽  
Disturbance Adaptation ◽  
Axially Moving ◽  
Adaptation Law ◽  
Belt System

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.

Adaptive boundary control and vibration suppression of a flexible satellite system with input saturation

2018 ◽  
Vol 41 (9) ◽  
pp. 2666-2677
Author(s):  
Yun Fu ◽  
Yu Liu ◽  
Daoping Huang
Keyword(s):  
Boundary Control ◽  
Closed Loop ◽  
Vibration Suppression ◽  
Input Saturation ◽  
Satellite System ◽  
Closed Loop System ◽  
Adaptive Law ◽  
Control Scheme ◽  
Boundary Disturbance ◽  
Adaptive Boundary Control

In this paper, the vibration suppression problem of a flexible satellite system is addressed. The dynamic model of the flexible satellite system is expressed by a set of non-homogeneous partial differential equations (PDEs). By using the theory of systems with uniform ultimate bounded (UUB) solutions and adaptive techniques, adaptive boundary control is presented to suppress the vibration of the flexible satellite with parametric uncertainties. A disturbance adaptive law is constructed to compensate for the effect of the boundary disturbance, and an auxiliary system is considered to mitigate the effect of input saturation. The well-posedness of the closed-loop system is discussed, and UUB stability can be ensured through a rigorous Lyapunov-like analysis. Numerical simulation results show the effectiveness of the proposed control scheme.

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

2017 ◽  
Vol 40 (12) ◽  
pp. 3525-3533 ◽  
Author(s):  
Zhijia Zhao ◽  
Yu Liu ◽  
Fei Luo
Keyword(s):  
Boundary Control ◽  
Disturbance Observer ◽  
Direct Method ◽  
Input Saturation ◽  
Infinite Dimensional ◽  
Uniform System ◽  
Unknown Disturbances ◽  
Saturation Constraint ◽  
Axially Moving ◽  
Boundary Disturbance

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.

scholarly journals Modeling and Control for a Multi-Rope Parallel Suspension Lifting System under Spatial Distributed Tensions and Multiple Constraints

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 412 ◽  
Author(s):  
Naige Wang ◽  
Guohua Cao ◽  
Lu Yan ◽  
Lei Wang
Keyword(s):  
Differential Equations ◽  
Direct Method ◽  
Input Saturation ◽  
System Stability ◽  
Unknown Boundary ◽  
Multiple Constraints ◽  
Modeling And Control ◽  
Position Regulation ◽  
Lifting System ◽  
And Control

The modeling and control of the multi-rope parallel suspension lifting system (MPSLS) are investigated in the presence of different and spatial distributed tensions; unknown boundary disturbances; and multiple constraints, including time varying geometric constraint, input saturation, and output constraint. To describe the system dynamics more accurately, the MPSLS is modelled by a set of partial differential equations and ordinary differential equations (PDEs-ODEs) with multiple constraints, which is a nonhomogeneous and coupled PDEs-ODEs, and makes its control more difficult. Adaptive boundary control is a recommended method for position regulation and vibration degradation of the MPSLS, where adaptation laws and a boundary disturbance observer are formulated to handle system uncertainties. The system stability is rigorously proved by using Lyapunov’s direct method, and the position and vibration eventually diminish to a bounded neighborhood of origin. The original PDEs-ODEs are solved by finite difference method, and the multiple constraints problem is processed simultaneously. Finally, the performance of the proposed control is demonstrated by both the results of ADAMS simulation and numerical calculation.

scholarly journals BOUNDARY CONTROL AND STABILIZATION OF AN AXIALLY MOVING VISCOELASTIC STRING UNDER A BOUNDARY DISTURBANCE

2017 ◽  
Vol 22 (6) ◽  
pp. 763-784 ◽  
Author(s):  
Abdelkarim Kelleche
Keyword(s):  
Boundary Control ◽  
Multiplier Method ◽  
Control Law ◽  
System Modelling ◽  
Unknown Boundary ◽  
Transverse Vibrations ◽  
Axially Moving ◽  
Boundary Disturbance ◽  
The Right

In this paper, we consider a system modelling an axially moving viscoelastic string subject to an unknown boundary disturbance. It is controlled by a hydraulic touch-roll actuator at the right boundary which is capable of suppressing the transverse vibrations that occur during the movement of the string. The multiplier method is employed to design a robust boundary control law to ensure the reduction of the transvesre vibrations of the string.

Output feedback boundary control of a flexible marine riser system

2017 ◽  
Vol 24 (16) ◽  
pp. 3617-3630 ◽  
Author(s):  
Yu Liu ◽  
Fang Guo
Keyword(s):  
Boundary Control ◽  
Closed Loop ◽  
Vibration Suppression ◽  
High Gain ◽  
Loop System ◽  
System State ◽  
Marine Riser ◽  
Closed Loop System ◽  
Observer Error ◽  
System States

This paper is concerned with the design of boundary control for globally stabilizing a flexible marine riser system. The dynamics of the riser system are represented in the form of hybrid partial–ordinary differential equations. Firstly, when the system state available for feedback is unmeasurable, an observer backstepping method is employed to reconstruct the system state and then design the boundary control for vibration suppression of the riser system. Subsequently, for the case that the system states in the designed control law cannot be accurately obtained, the high-gain observers are utilized to estimate those unmeasurable system states. With the proposed control, the uniformly ultimately bounded stability of the closed-loop system is demonstrated by the use of Lyapunov’s synthetic method and the state observer error is converged exponentially to zero as time approaches to infinity. In addition, the disturbance observer is introduced to track external environmental disturbance. Finally, the control performance of the closed-loop system is validated by carrying out numerical simulation.

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