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

2017 ◽  
Vol 40 (5) ◽  
pp. 1407-1416 ◽  
Author(s):  
Fang Guo ◽  
Yu Liu ◽  
Zhijia Zhao ◽  
Fei Luo
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Control ◽  
Vibration Suppression ◽  
Original Position ◽  
Backstepping Technique ◽  
Marine Riser ◽  
Partial Differential ◽  
Disturbance Adaptation ◽  
Adaptive Boundary Control

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.

scholarly journals Weighted multiple model adaptive boundary control for a flexible manipulator

2019 ◽  
Vol 103 (1) ◽  
pp. 003685041988646
Author(s):  
Weicun Zhang ◽  
Qing Li ◽  
Yuzhen Zhang ◽  
Ziyi Lu ◽  
Cheng Nian
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Control ◽  
Control Strategy ◽  
Flexible Manipulator ◽  
Multiple Model ◽  
Parameter Uncertainties ◽  
Partial Differential ◽  
Local Boundary ◽  
Adaptive Boundary Control

In this article, a weighted multiple model adaptive boundary control scheme is proposed for a flexible manipulator with unknown large parameter uncertainties. First, the uncertainties are approximatively covered by a finite number of constant models. Second, based on Euler–Bernoulli beam theory and Hamilton principle, the distributed parameter model of the flexible manipulator is constructed in terms of partial differential equation for each local constant model. Correspondingly, local boundary controllers are designed to control the manipulator movement and suppress its vibration for each partial differential equation model, which are based on Lyapunov stability theory. Then, a novel weighted multiple model adaptive control strategy is developed based on an improved weighting algorithm. The stability of the overall closed-loop system is ensured by virtual equivalent system theory. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed control strategy.

Boundary control design based on partial differential equation observer for vibration suppression and attitude control of flexible satellites with multi-section solar panels

2021 ◽  
pp. 107754632199015
Author(s):  
Mohammad Mahdi Ataei ◽  
Hassan Salarieh ◽  
Hossein Nejat Pishkenari ◽  
Hadi Jalili
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Attitude Control ◽  
Vibration Suppression ◽  
Equation System ◽  
Solar Panels ◽  
Attitude Dynamics ◽  
Partial Differential ◽  
Satellite Attitude ◽  
Element Technique

A novel partial differential equation observer is proposed to be used in boundary attitude and vibration control of flexible satellites. Solar panels’ vibrations and attitude dynamics form a coupled partial differential equation–ordinary differential equation system which is controlled directly without discretization. Few feedback signals from boundaries are required which are estimated via a partial differential equation observer. Consequently, just satellite attitude and angular velocity should be measured and still the control system benefits information from continuous part vibrations. The closed-loop system is proved to be asymptotically stable. Simulations with a finite element technique illustrate good performance of this observer-based boundary controller.

Axial Vibration Suppression in a Partial Differential Equation Model of Ascending Mining Cable Elevator

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Ji Wang ◽  
Shumon Koga ◽  
Yangjun Pi ◽  
Miroslav Krstic
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Feedback Control ◽  
Output Feedback ◽  
Vibration Suppression ◽  
Output Feedback Control ◽  
Control Law ◽  
Axial Vibration ◽  
Hydraulic Actuator ◽  
Partial Differential

Lifting up a cage with miners via a mining cable causes axial vibrations of the cable. These vibration dynamics can be described by a coupled wave partial differential equation-ordinary differential equation (PDE-ODE) system with a Neumann interconnection on a time-varying spatial domain. Such a system is actuated not at the moving cage boundary, but at a separate fixed boundary where a hydraulic actuator acts on a floating sheave. In this paper, an observer-based output-feedback control law for the suppression of the axial vibration in the varying-length mining cable is designed by the backstepping method. The control law is obtained through the estimated distributed vibration displacements constructed via available boundary measurements. The exponential stability of the closed-loop system with the output-feedback control law is shown by Lyapunov analysis. The performance of the proposed controller is investigated via numerical simulation, which illustrates the effective vibration suppression with the fast convergence of the observer error.

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