Boundary stabilization for axially moving Kirchhoff string under fractional PI control

Cheng, Yi; Guo, Bao‐Zhu; Wu, Yuhu

doi:10.1002/zamm.202100524

Cited by 4 publications

(6 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…s(L, t)]w(L), ∀w ∈  2 , and t ∈ [0, T] a.e. (42) and by passing to the limit as n → ∞ to (12). Set w ∈  2 0 ∶= {w ∈  2 ∶ w(L) = 0}.…”

Section: Well-posedness Of the Closed-loop Systemmentioning

confidence: 99%

“…In addition, for the investigation of the vibration control of some axial moving systems, we refer the interested reader to earlier research. [40][41][42] Introduce nondimensional variables…”

Section: Introductionmentioning

confidence: 99%

“…In Hassan and Tatar, 39 high‐gain adaptive regulators are designed to establish an exponential stability result for the Timoshenko beam equation subject to two control inputs at the right end by means of the multiplier method. In addition, for the investigation of the vibration control of some axial moving systems, we refer the interested reader to earlier research 40–42 …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High‐gain stabilization for an axially moving beam under boundary feedback control

Cheng

O’Regan

2022

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

This paper establishes the global existence and high-gain stabilization of a nonlinear axially moving beam with control input at the free boundary. A high-gain controller based on the transverse velocity feedbacks of the moving beam at the free end is designed. The existence and uniqueness of the solution depending on the initial values continuously for the resulting closed-loop system are established by invoking the Faedo-Galerkin approximation approach. Then constructing a novel energy-like function, the explicit exponential decay rate of the closed-loop system is obtained via a generalized Gronwall-type integral inequality.

show abstract

“…s(L, t)]w(L), ∀w ∈  2 , and t ∈ [0, T] a.e. (42) and by passing to the limit as n → ∞ to (12). Set w ∈  2 0 ∶= {w ∈  2 ∶ w(L) = 0}.…”

Section: Well-posedness Of the Closed-loop Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

High‐gain stabilization for an axially moving beam under boundary feedback control

Cheng

O’Regan

2022

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…The designed boundary controller can achieve the convergence of the controlled system and ensure the stability of the controlled system. The boundary controllers are also used to control the vibrations of the axially moving strings [14][15][16]. Cheng et al [14] introduced the fractional PI boundary damping to construct a closed-loop system.…”

Section: Introductionmentioning

confidence: 99%

“…The boundary controllers are also used to control the vibrations of the axially moving strings [14][15][16]. Cheng et al [14] introduced the fractional PI boundary damping to construct a closed-loop system. The fractional PI boundary controller suppressed the axial translational string vibrations.…”

Section: Introductionmentioning

confidence: 99%

A time-varying string length method for a suppression string vibration

Wang

Liu

2023

2022 Workshop on Electronics Communication Engineering

View full text Add to dashboard Cite

Strings are often used to increase the strength of the structures, such as stay cables in bridges. The string vibrations can affect the stability of the structure. In this paper, a method of a suppressing multi-order string resonance by controlling the length of the string to be continuously time-varying is proposed. The model of the time-varying length string is given. The vibration responses of the timevarying length string are solved by the finite difference method. The suppression effect of the time-varying string length method on the free vibrations and forced vibrations is analyzed. The results show that the controlling of the time-varying length of the string can effectively weaken the free vibration peaks and the forced vibration peaks of the string. It can suppress the multi-order resonance.

show abstract

Adaptive neural network control of multiple‐sectioned flexible riser with time‐varying output constraint and input nonlinearity

Liu,

Yao,

Liu

2023

Asian Journal of Control

View full text Add to dashboard Cite

In this paper, an adaptive neural network controller is proposed for vibration suppression of a multisectional riser system with unknown boundary disturbance, time‐varying asymmetric output constraint, and input nonlinearity. The considered riser system is composed of a continuous connection of several different pipes, and its dynamic models are represented by a set of multiple continuously connected partial differential equations (PDEs) and an ordinary differential equation (ODE) at the top boundary. Considering input nonlinearity, external disturbance, and system uncertainty, radial basis function (RBF) neural networks are adopted to eliminate the effect of these uncertain terms. Besides, a barrier Lyapunov function is employed to guarantee the restrictions. With the proposed boundary control, the stability of the closed‐loop system is proved and simulations are given to illustrate the well performance of the proposed control strategy.

show abstract

Boundary stabilization for axially moving Kirchhoff string under fractional PI control

Cited by 4 publications

References 57 publications

High‐gain stabilization for an axially moving beam under boundary feedback control

High‐gain stabilization for an axially moving beam under boundary feedback control

A time-varying string length method for a suppression string vibration

Adaptive neural network control of multiple‐sectioned flexible riser with time‐varying output constraint and input nonlinearity

Contact Info

Product

Resources

About