Discrete mass and stiffness modifications for the inverse eigenstructure assignment in vibrating systems: Theory and experimental validation

Ouyang, Huajiang; Richiedei, Dario; Trevisani, Alberto; Zanardo, Gabriele

doi:10.1016/j.ijmecsci.2012.06.015

Cited by 24 publications

(14 citation statements)

References 19 publications

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“…P. Liu & Patton, 1998;Y. Liu, Tan, Wang, & Wang, 2013;Moore, 1976;Ouyang, Richiedei, Trevisani, & Zanardo, 2012;Piou & Sobel, 1994, 1995Pomfret & Clarke, 2009;Shi & Patton, 2012;Wahrburg & Adamy, 2013;White, 1995;White, Bruyere, & Tsourdos, 2007). EA facilitates control system design by synthesizing a feedback gain matrix that exactly places the closed loop eigenvalues whilst matching the closed loop eigenvectors as closely as possible to a desired set.…”

mentioning

confidence: 99%

Increasing eigenstructure assignment design degree of freedom using lifting

Chen

Pomfret

Clarke

2016

International Journal of Control

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This paper presents the exposition of an output-lifting eigenstructure assignment (EA) design framework, wherein the available EA design degrees of freedom (DoF) is significantly increased, and the desired eigenstructure of a single-rate full state feedback solution can be achieved within an output feedback system. A structural mapping is introduced to release the output-lifting causality constraint. Additionally, the available design DoF can be further enlarged via involving the input-lifting into the output-lifting EA framework. The newly induced design DoF can be utilised to calculate a structurally-constrained, causal gain matrix which will maintain the same assignment capability. In this paper, the robustification of the output-lifting EA is also proposed, which allows a trade-off between performance and robustness in the presence of structured model uncertainties to be established. A lateral flight control benchmark in the EA literature and a numerical example are used to demonstrate the effectiveness of the design framework.Keywords: lifting; eigenstructure assignment; causality constraint IntroductionEigenstructure assignment (EA) is a mature technique for the design of control systems, especially for flight control system (Alireza & Batool, 2012;B. Chen & Nagarajaiah, 2007;Clake, Ensor, & Griffin, 2003;Farineau, 1989;Kshatriya, Annakkage, Hughes, & Gole, 2007;G. P. Liu & Patton, 1998;Y. Liu, Tan, Wang, & Wang, 2013;Moore, 1976;Ouyang, Richiedei, Trevisani, & Zanardo, 2012;Piou & Sobel, 1994, 1995Pomfret & Clarke, 2009;Shi & Patton, 2012;Wahrburg & Adamy, 2013;White, 1995;White, Bruyere, & Tsourdos, 2007). EA facilitates control system design by synthesizing a feedback gain matrix that exactly places the closed loop eigenvalues whilst matching the closed loop eigenvectors as closely as possible to a desired set. Some useful properties EA imbues on a system are: stability of response, appropriateness of transient response, decoupling of state or output response and disturbance rejection. Compared with many other competitive approaches exist to manipulate the eigenvalues of the closed-loop system and do not takes into account the role of the eigenvector, EA clearly exploits how system inputs affect mode dynamics and how these mode dynamics will be assigned to system states. Through defining a set of ideal closed-loop eigenstructure (e.g. eigenstructure which represents the realistic handling qualities of the flight control system), the realistic control effect will be guaranteed. In addition, the algorithm itself and the expression of the available design DoF can be highly visible. However, due to the lack of design DoF, e.g. the Kimura condition is not satisfied (Kimura, 1975), output feedback EA usually cannot fully assign the desired eigenstructure. This is an open problem which has been widely discussed in the literature (Andry, Shapiro, & Chung, 1983;L. Chen & Clarke, 2009;Clarke & Griffin, 2004;Pomfret, Clarke, & Ensor, 2005;Roppenecker & O'Reilly, 1989;Srinathkumar, 1978;Zhao & Lam, 2016a, 2016b.Mul...

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mentioning

confidence: 99%

Increasing eigenstructure assignment design degree of freedom using lifting

Chen

Pomfret

Clarke

2016

International Journal of Control

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“…In this case, a tray closely matching the desired stiffness and mass has been found. In the case the practical implementation of the modifications would impose a rough discrete approximation of the theoretical modifications computed through the proposed method, the design problem can be easily extended in the frame of the mixed-integer nonlinear convex programming for preserving optimality, as discussed in [15].…”

Section: Experimental Design Of the Feedermentioning

confidence: 99%

“…Therefore, in the last decades, an increasing interest towards the study of IDSM has arisen, and several solutions have been developed and proposed in literature (see, e.g. [7][8][9][10][11][12][13][14][15]). The main issue to be coped in developing these approaches for complex multi-dimensional mechanical systems is defining a suitable problem formulation.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, by taking advantage of the theory developed in ( [13][14][15]), the optimal design of a vibratory feeder is formulated as a constrained inverse eigenvalue problem within the frame of convex quadratic optimization. This kind of formulation overcomes the main limitation of most of the nonlinear optimization problems, whose numerical solutions usually converge to one of the many local optima depending on the chosen initial guess.…”

Section: Introductionmentioning

confidence: 99%

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Designing vibratory linear feeders through an inverse dynamic structural modification approach

Caracciolo

Richiedei

Trevisani

et al. 2015

Int J Adv Manuf Technol

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The design of vibratory feeders ensuring effective product feeding is particularly demanding since the flexibility of the device components severely affects the dynamic response. Traditional design approaches are based on expensive and time-consuming trial and error iterations, which include building and testing tentative devices. In order to overcome these limitations, this paper proposes a novel systematic approach for designing linear vibratory feeders, based on an inverse dynamic structural modification approach. After synthesising a reduced-order model, the design is cast as an inverse eigenvalue problem and solved numerically through the minimization of a convex quadratic function. Constraints on the design variables, i.e. inertial and elastic parameters, are represented through a convex domain and included in the optimization problem. The numerical and experimental results obtained prove the effectiveness of the method and its ease of application, that make is suitable for both the design of new feeders and the optimization of existing one

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“…Moreover, the critical angular speed Ω cr [42][43][44][45] of the current disc without any thermal stress is defined by Ω cr ¼ Ω 0,0 min(ω m,n /n). As a result, the lowest critical speed is about 22,121 rpm, which corresponds to disc mode (0, 2), and it is much higher than the maximum disc speed Ω M ¼8000 rpm in the current analysis of this paper.…”

Section: Solution Procedures For Rotating Flexible Discmentioning

confidence: 99%