Robust Boundary Vibration Control of Uncertain Flexible Robot Manipulator with Spatiotemporally-varying Disturbance and Boundary Disturbance

Eshag, Mohamed Ahmed; Ma, Lei; Sun, Yongkui; Zhang, Kai

doi:10.1007/s12555-020-0070-0

Cited by 18 publications

(5 citation statements)

References 37 publications

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“…θ] t . Eventually, using the obtained Equations ( 47) and ( 48), the dynamic equation of the system (44) can be converted to the form of relation (4). Then, the following equations are obtained after substituting the values in Table 1.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…This is further exacerbated when disturbances are added to the system. To date, various approaches have been developed and implemented to control and/or stabilize nonlinear disturbed systems [1][2][3][4][5]. Because system states are affected by disturbances and nonlinearities, errors emerge in dynamical systems, and disregarding their impact, may lead to extreme deterioration in system performance and even instability [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

Chatavi

Mobayen

et al. 2022

Mathematics

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In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

Chatavi

Mobayen

et al. 2022

Mathematics

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show abstract

“…The flexible cantilever beam is a distributed parameter system with an infinite number of vibration modes. Its dynamics are characterized by partial differential equations (PDEs) 5 – 8 . When a flexible beam is fixed on a translating base, the base’s dynamics (as a lumped parameter system) are described by ordinary differential equations (ODEs) to be considered simultaneously with the beam’s dynamics.…”

Section: Introductionmentioning

confidence: 99%

Vibration control of a nonlinear cantilever beam operating in the 3D space

Pham

Nguyen

Yoon³

et al. 2022

Sci Rep

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This paper addresses a control problem of a nonlinear cantilever beam with translating base in the three-dimensional space, wherein the coupled nonlinear dynamics of the transverse, lateral, and longitudinal vibrations of the beam and the base’s motions are considered. The control scheme employs two control inputs applied to the beam’s base to control the base’s position while simultaneously suppressing the beam’s transverse, lateral, and longitudinal vibrations. According to the Hamilton principle, a hybrid model describing the nonlinear coupling dynamics of the beam and the base is established: This model consists of three partial differential equations representing the beam’s dynamics and two ordinary differential equations representing the base’s dynamics. Subsequently, the control laws are designed to move the base to the desired position and attenuate the beam’s vibrations in all three directions. The asymptotic stability of the closed-loop system is proven via the Lyapunov method. Finally, the effectiveness of the designed control scheme is illustrated via the simulation results.

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“…In literature [9], the FE method is used to establish an accurate dynamic model of the manipulator with a flexible load. In literature [10][11][12], the flexible load's deformation is described by the AMM. The FE method is more suitable for the flexible load with irregular shapes.…”

Section: Introductionmentioning

confidence: 99%

Vibration Suppression Method for Dual-flexible Manipulator Considering Bearing Friction Based on Adaptive PI Control Strategy with Nonlinear Disturbance Observer

Shang

Yin

et al. 2022

Preprint

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A manipulator that contains both flexible joints and flexible loads is called a dual-flexible manipulator. The vibration of dual-flexible manipulators is affected by the bearing friction torque and the double flexibilities. This vibration phenomenon will reduce the motion accuracy in dual-flexible manipulators. In this study, an adaptive PI control strategy using a nonlinear disturbance observer (DOB) is proposed to reduce speed fluctuations of the servo system, thereby suppressing the vibration. Firstly, the mechanical model of the dual-flexible manipulator considering bearing frictions is established. Then, the adaptive law of the PI controller is proposed by the Lyapunov stability theorem. The optimal values of controller parameters are obtained by the adaptive law. Finally, the numerical simulation and control experiments of the dual-flexible manipulator prove that the control strategy can powerfully reduce the vibration. The experimental results show that the control strategy can reduce the acceleration in the vibration sensitive direction of the flexible manipulator by 41.78% compared with the PI control strategy.

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Robust Boundary Vibration Control of Uncertain Flexible Robot Manipulator with Spatiotemporally-varying Disturbance and Boundary Disturbance

Cited by 18 publications

References 37 publications

H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

H∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

Vibration control of a nonlinear cantilever beam operating in the 3D space

Vibration Suppression Method for Dual-flexible Manipulator Considering Bearing Friction Based on Adaptive PI Control Strategy with Nonlinear Disturbance Observer

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