Analysis of a high-order finite difference detector for discontinuities

Oliveira, Maria; Pires, Vitor Alves

doi:10.1080/00207160.2015.1124100

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…where β indicates the angle between the y-axis and the taut cable. As shown in Figure 4, the flexural beam is transversely discretized along the x-axis, and the finite difference method [17][18][19] is applied to obtain a more accurate control model compared to the assumed modes method. First, the flexible beam is partitioned into N elements along the x-axis and each element length is Δx = l/N; the total number of nodes of the beam is N + 1, the location of the ith element is determined by the coordinate x i = (i − 1) * Δx, and its mass is m i = ρAΔx, i = 0 , 1 , 2 ⋯ , N; the bending deflection in the continuous system is expressed as the elastic displacement w x i ; t ð Þ ¼ w i ; i ¼ 0; 1; 2⋯; N .…”

Section: Discretization Of the Continuous Dynamic Modelmentioning

confidence: 99%

Active vibration control of large space flexible slewing truss using cable actuator with input saturation

Jin

Huang

2017

Intl J Robust & Nonlinear

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Summary This paper proposes a composite approach to implementing attitude tracking and active vibration control of a large space flexible truss system. The system dynamic model is based on Hamilton's principle and discretized using the finite difference method. A nonlinear attitude controller for position tracking is developed based on the input‐output linearization of the discretized system, which can effectively improve system performance compared with a traditional proportional‐differential feedback controller. A taut cable actuator scheme is presented to suppress tip vibration because the mechanical model is a large large‐span spatial structure; furthermore, because the cable has the feature of unilateral input saturation constraint, which can provide only a pulling force, a nonlinear quadratic regulator controller is developed by introducing a piecewise nonquadratic cost function to suppress the vibration of the flexible structure. To investigate the factors that influence the damping effects of the cable, the parametrically excited instability of a cable under 2 supports is analyzed. Simulation results illustrate that the proposed attitude controller can implement the task of position tracking, and the vibration suppression control law is shown to be optimal for functional performance with input saturation.

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Section: Discretization Of the Continuous Dynamic Modelmentioning

confidence: 99%

Active vibration control of large space flexible slewing truss using cable actuator with input saturation

Jin

Huang

2017

Intl J Robust & Nonlinear

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“…we can time-evolve the Navier-Stokes equations. * This is not the shock-detector version used in 28 , but the same results apply to this one.…”

Section: Shock Detectormentioning

confidence: 99%

“…In this chapter I will only describe one of them, leaving the other to chapter 4. In 2016, Bambozzi and Pires 28 introduced a shock-detector capable of detecting discontinuities not only in the function, but in any of it's derivatives. The shock detector works by comparing the approximation obtained using all the grid points with the approximation obtained using, say, only the odd grid points.…”

Section: Shock Detectormentioning

confidence: 99%

Immersed-interface methods in the presence of shock waves

Aurichio¹

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Fluid motion has always been of great importance for humanity since much of our progress has been related to our understanding of fluid dynamics and to our control over the fluids surrounding us. In particular, the experimental techniques and the methods for numerical simulation developed during the last century allowed for great progresses both in creating new technologies and in improving old ones. Despite the great importance of experimental techniques, measuring all properties of a fluid throughout the whole domain, without intefering with the flow to be studied, is impossible. Also, building models even in scale is usually expansive. Both of these reasons have driven the development of numerical methods to the point they became an invaluable tool for fluid dynamic studies and the main tool for developing engineering solutions. If numerical methods are to be of any use, though, they have to correctly describe the problem geometry as well as capture the rich dynamics in a variety of flow situations, such as turbulence, boundary-layers and shock-waves. This thesis addresses two of these problems. In particular, I show modified versions of two immersed-interface methods to describe the geometry, simplifying their implementations with no impact to their applicability. I also introduce two methods for handling shock-waves: first aiming to minimize computational costs, then improving shock-wave resolution without increasing the number of grid points.

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