Sliding Mode Boundary Control of an Euler–Bernoulli Beam Subject to Disturbances

Karagiannis, Dimitrios; Radisavljević-Gajić, Verica

doi:10.1109/tac.2018.2793940

Cited by 24 publications

(16 citation statements)

References 30 publications

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“…Then, to prove the reaching condition, considering the Lyapunov function be V s (s) = 1 2 S 2 (t), taking the derivative of the Lyapunov function V s (t) and substituting (28) into the derivative of Vs (t) together with…”

Section: Sliding Mode Boundary Controller Designmentioning

confidence: 99%

“…Especially, the sliding mode boundary control for exponential stabilization of the distributed parameter system modeled by the PDEs with boundary external disturbance has also become an attractive research area. 27,28 The sliding mode boundary control for exponential stabilization of cascaded system combining distributed parameter systems and lumped parameter systems with Neumann/mixed boundary conditions and external boundary disturbance has been analyzed by means of sliding mode control method and backstepping techniques. 29,30 The sliding mode control achieve the sliding mode on the sliding manifold within a finite time.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Sliding mode boundary control for exponential stabilization of linear parabolic distributed parameter systems subject to external disturbance

Bao

Cui²,

Lou³

et al. 2023

Intl J Robust & Nonlinear

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In this article, we are concerned with the exponential stabilization of parabolic distributed parameter systems with Neumann/mixed boundary conditions and external disturbance. To deal with the bounded disturbance, a sliding mode boundary control scheme is adopted based on the backstepping method. Firstly, the exponential stability of the considered system is proven along the selected sliding surface. Secondly, a sliding mode boundary controller is designed to regulate the closed‐loop system trajectory to a suitable sliding surface within a prescribed time and then maintain the sliding motion on the surface. Thirdly, on the chosen sliding surface, the closed‐loop system with the sliding mode boundary controller is exponentially stable. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results.

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Section: Sliding Mode Boundary Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sliding mode boundary control for exponential stabilization of linear parabolic distributed parameter systems subject to external disturbance

Bao

Cui²,

Lou³

et al. 2023

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…where µ is the mass per unit length and i 2 and i 3 are the second moments of inertia of the beam's cross-section. For such uncoupled cases, the classical linear Euler-Bernoulli beam description [24] is recovered by setting both the axial and shear stiffness EA, GA 3 → ∞ and removing all quadratic terms in (1)- (2). The much-studied Timoshenko model [25], is analogously obtained, but with GA 3 finite.…”

Section: Intrinsic Beam Equations and Standard Formulationsmentioning

confidence: 99%

Modal-Based Nonlinear Model Predictive Control for 3-D Very Flexible Structures

Artola

Wynn

Palacios

2022

IEEE Trans. Automat. Contr.

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In this paper a novel NMPC scheme is derived, which is tailored to the underlying structure of the intrinsic description of geometrically exact nonlinear beams (in which velocities and strains are primary variables). This is an important class of PDE models whose behaviour is fundamental to the performance of flexible structural systems (e.g., wind turbines, High-Altitude Long-Endurance aircraft). Furthermore, this class contains the much-studied Euler-Bernoulli and Timoshenko beam models, but has significant additional complexity (to capture 3D effects and arbitrarily large displacements) and requires explicit computation of rotations in the PDE dynamics to account for orientation-dependent forces such as gravity. A challenge presented by this formulation is that uncontrollable modes necessarily appear in any finite dimensional approximation to the PDE dynamics. We show, however, that an NMPC scheme can be constructed in which the error introduced by the uncontrollable modes can be explicitly controlled. Furthermore, in challenging numerical examples exhibiting considerable deformation and nonlinear effects, it is demonstrated that the asymptotic error can be made insignificant (from a practical perspective) using our NMPC scheme and excellent performance is obtained even when applied to a highly resolved numerical simulation of the PDEs. We also present a generalisation of Kelvin-Voigt damping to the intrinsic description of geometrically-exact beams. Finally, special emphasis is placed on constructing a framework suitable for real-time NMPC control, where the particular structure of the underlying PDEs is exploited to obtain both efficient finitedimensional models and numerical schemes.

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“…The problems of controlling the coefficient function in the beam equation have been investigated in [2][3][4][5]. The boundary control problems for the beam system have been studied in [6][7][8][9][10][11]. When the control function is the source term, there have been some control problems [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

On optimal control of the initial velocity of an Euler-Bernoulli beam system

2022

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In this study, we consider an optimal control problem for an Euler-Bernoulli beam equation. The initial velocity of the system is given by the control function. We give sufficient conditions for the existence of a unique solution of the hyperbolic system and prove that the optimal solution for the considered optimal control problem is exists and unique. After obtaining the Frechet derivative of the cost functional via an adjoint problem, we also give an iteration algorithm for the numerical solution of the problem by using the Gradient method. Finally, we furnish some numerical examples to demonstrate the effectiveness of the result obtained.

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Sliding Mode Boundary Control of an Euler–Bernoulli Beam Subject to Disturbances

Cited by 24 publications

References 30 publications

Sliding mode boundary control for exponential stabilization of linear parabolic distributed parameter systems subject to external disturbance

Sliding mode boundary control for exponential stabilization of linear parabolic distributed parameter systems subject to external disturbance

Modal-Based Nonlinear Model Predictive Control for 3-D Very Flexible Structures

On optimal control of the initial velocity of an Euler-Bernoulli beam system

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