Nonlinear partial differential equation modeling and adaptive fault‐tolerant vibration control of flexible rotatable manipulator in three‐dimensional space

Wang, Jiacheng; Cao, Fangfei; Liu, Jinkun

doi:10.1002/acs.3319

Cited by 5 publications

(2 citation statements)

References 38 publications

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“…Finally, in order to reduce the intensity and amplitude of the command control signal by calculating the predictive tracking error and its rate according to equation ( 14), the fltered quantity of f d (k − 1) is calculated according to equation (15).…”

Section: Trajectory Planning For the Moving Support Based On Dynamic ...mentioning

confidence: 99%

“…Vibrations generated in a continuous system contain multiple frequencies where the experiments show that the smallest frequency has the greatest impact on the overall system vibration. Terefore, with the problem of the presence of actuator bandwidth limitation, the maximum vibrational frequency that can be eliminated according to the mentioned actuation restrictions should be examined [12,15]. Finally, it can be concluded that the recent research studies in the feld of designing nonlinear feedback control systems mainly focus on solving the problem of designing Lyapunov stable control systems in the presence of hard constraints such as system switching, the output constraint, the small gain theorem, unmodeled dynamics, the dead zone of the actuator, the restrictions imposed due to the communication between the sensors, and the presence of time delay in measuring the quantities or in commanding the actuators [11,13,14,16].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Tracking Control Algorithm for Dynamical Output Systems Manipulated by the Hardly Constrained Oscillatory Actuator

Homaeinezhad

Mostaghim

2023

Structural Control and Health Monitoring

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In this article, a nonlinear control algorithm has been presented, in order to reduce vibrational movements of a flexible beam cantilevered in a cart supported by nonlinear stiffness, actuated by a hardly constrained second-order dynamic system. In the presented control algorithm, the interactive model of the solid body and a flexible beam has been extracted and utilized to design an algorithm, based on which the nonlinear vibrations of the tip point of the beam whose function is smooth and nonoscillatory tracking of the predefined desired trajectory are diminished. To design a nonlinear vibration control system of the beam, it has been assumed that the feedback system includes three modules: a vibrational beam cantilevered on a base, a base affected by nonlinear stiffness and actuator’s control force, and a force imposing system with constraints of bandwidth frequency limitation and actuation saturation boundary. In order to design this control system, the generalized tracking error function has been defined to nonlinearly amplify the vibrationally induced error and its rate, which by properly adjusting them, a new quantity can be extracted that satisfies the control system design constraints. To design a tracking control system for a nonlinear vibrating beam for the aforementioned three-modulus system, first, the generalized tracking error for the three modules is separately defined and parametrized, and then, by simultaneously adjusting all the defined parameters systematically, the predominant system presence in Lyapunov stability conditions is guaranteed. To illustrate the multimodule imitative (MMI) controller design algorithm, a moving support connected to a nonlinear spring and damper is considered, which carries a flexible cantilevered beam. The applied actuation system has second-order linear dynamics with the presence of command control saturation boundaries. For each of the abovementioned modules, a generalized tracking error is defined, and then, it is explained to how simultaneously adjust the parameters based on the stability and actuation constraints. The MMI controller is applied to the mentioned mechanical system modeled in the ANSYS® Mechanical APDL environment, and then, the necessary conclusions are discussed about the performance of the control system in eliminating the vibrations of the flexible arm, considering the actuation constraints while possessing the dominant Lyapunov stability.

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Section: Trajectory Planning For the Moving Support Based On Dynamic ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Tracking Control Algorithm for Dynamical Output Systems Manipulated by the Hardly Constrained Oscillatory Actuator

Homaeinezhad

Mostaghim

2023

Structural Control and Health Monitoring

View full text Add to dashboard Cite

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Exploring the Effect of Base Compliance on Physical Human-Robot Collaboration

Wang,

Carmichael

2024

2024 IEEE International Conference on Robotics and Automation (ICRA)

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Discrete variational method for partial differential equations of functionally gradient beam vibration

2024

JCM

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The field of engineering is becoming increasingly complex. In order to adapt to the numerical simulation of solving the partial differential equation of functionally graded beam vibration, a higher order stable numerical algorithm has been constructed. Differential quadrature method is used in discrete space domain. The discrete variational method is constructed in the time domain. The index differential Algebraic equation are obtained by combining the two methods. The discrete variational scheme is constructed for simulation. The results indicate that under long-term simulation, both the velocity and displacement constraints of the Runge Kutta method have defaulted. Displacement constraint values differ by 5 × 10 - 10. The velocity, displacement and acceleration constraints of the discrete variational method are stable. Compared with the Runge Kutta method, the constraint magnitude is reduced. The speed constraint is maintained at within 2.5 × 10 - 15. The displacement constraint level is maintained at within 1 × 10 - 16. This indicates that the discrete variational method has high accuracy and good stability when solving problems such as the vibration equation of functionally graded beams. When the step sizes are h= 0.1 m and h= 0.01 m, the accuracy of the discrete variational method is close. The larger the step size h, the higher the computational efficiency of the discrete variational method. The discrete variational method can maintain structural and energy conservation, making it suitable for long-term simulations. This has a good effect on solving complex problems in the field of partial differential equations.

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Nonlinear partial differential equation modeling and adaptive fault‐tolerant vibration control of flexible rotatable manipulator in three‐dimensional space

Cited by 5 publications

References 38 publications

Nonlinear Tracking Control Algorithm for Dynamical Output Systems Manipulated by the Hardly Constrained Oscillatory Actuator

Nonlinear Tracking Control Algorithm for Dynamical Output Systems Manipulated by the Hardly Constrained Oscillatory Actuator

Exploring the Effect of Base Compliance on Physical Human-Robot Collaboration

Discrete variational method for partial differential equations of functionally gradient beam vibration

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