Static output feedback for partial eigenstructure assignment of undamped vibration systems

Zhang, Jiafan; Ye, Jianping; Ouyang, Huajiang

doi:10.1016/j.ymssp.2015.07.012

Cited by 23 publications

(9 citation statements)

References 21 publications

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“…But due to the recent progress of the smart materials with distributed arrays of transducers the application of dense matrices B and C can be made feasible. 19 (iii) If B and C are determined a prior for some other considerations, ϕ1, ϕ2 (or ϕ) can be figured out from the linear matrix equations (14a), (14b) (or (12a)). There may be a trial of some adjustment of B and C for satisfying the solvability condition of the matrix equations.…”

Section: Applications Of the Formulamentioning

confidence: 99%

“…Many aspects of the inverse problem of structural and mechanical dynamics have been involved in the research, such as the structural inverse modification, [1][2][3] model updating [4][5][6] and active vibration control. [7][8][9][10][11][12] These cited here are a small part of the literatures published in recent years. In the above research content, the proposed methods have a nice feature, that is, all the unassigned eigenvalues (or unmodified natural frequencies) with the corresponding eigenvectors remain unchanged while a small number of eigenvalues of a structure are assigned to the targeted values.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An explicit formula of perturbating stiffness matrix for partial natural frequency assignment using static output feedback

Zhang

Ouyang

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

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The partial eigenvalue (or natural frequency) assignment or placement, only by the stiffness matrix perturbation, of an undamped vibrating system is addressed in this paper. A novel and explicit formula of determining the perturbating stiffness matrix is deduced from the eigenvalues perturbation theorem for a low-rank perturbed matrix. This formula is then utilized to solve the partial eigenvalue (or natural frequency) assignment via the static output feedback. The control matrix, output matrix and feedback gain matrix can be explicitly expressed and easily constructed.

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Section: Applications Of the Formulamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An explicit formula of perturbating stiffness matrix for partial natural frequency assignment using static output feedback

Zhang

Ouyang

et al. 2018

Journal of Low Frequency Noise, Vibration and Active Control

Self Cite

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“…The remaining unchanged eigenvalues and corresponding eigenvectors satisfy the no spill-over property which ensures that there exist no spurious modes in the frequency range of interests in an engineering practice [20]. In recent years, partial eigenstructure assignment problems have attached a great deal of attention by using several feedback control laws, including velocity-displacement feedback [5,8,18,21,22], acceleration-velocity feedback [7,23], and accelerationdisplacement feedback [19,24]. Some researches on partial eigenstructure assignment problems for vibration systems have been generalized to high-order systems [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Partial eigenstructure assignment problem for vibration system via feedback control

2020

Asian Journal of Control

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The partial eigenstructure assignment problem is to replace a small number of eigenvalues and eigenvectors of system while the remaining eigenvalues and corresponding eigenvectors are kept unchanged. The paper studies partial eigenstructure assignment problem for vibration system via accelerationvelocity feedback control. Two new orthogonality relations are established to construct a feedback control law which can solve the proposed partial eigenstructure assignment problem. The solvability condition and parametric expressions of feedback gains are derived for solving this problem. The minimum norm partial eigenstructure assignment problem is further considered by using gradient-based optimization method. An optimization algorithm is proposed for solving the minimum norm partial eigenstructure assignment problem. Numerical examples are provided to show the effectiveness of the algorithm.

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“…are altered as required and the resting eigenpairs remain unchanged -i.e. possessing the no spill-over property [20][21][22][23][24]. This leads to the partial eigenvalue assignment problem of undamped gyroscopic control systems (GPEAP).…”

Section: Introductionmentioning

confidence: 99%

Partial Eigenvalue Assignment for Undamped Gyroscopic Systems in Control

Líu¹

2019

EAJAM

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The solvability of a partial eigenvalue assignment problem for undamped gyroscopic control systems is proved and its explicit solutions are found. In addition, the problem of replacing certain eigenvalues by required ones while keeping the remaining eigenpairs unchanged, is solved by a multi-step method. The method is easily implementable and does not involve receptance matrices and Sylvester equation solutions. Numerical examples show the efficiency of the method.

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Static output feedback for partial eigenstructure assignment of undamped vibration systems

Cited by 23 publications

References 21 publications

An explicit formula of perturbating stiffness matrix for partial natural frequency assignment using static output feedback

An explicit formula of perturbating stiffness matrix for partial natural frequency assignment using static output feedback

Partial eigenstructure assignment problem for vibration system via feedback control

Partial Eigenvalue Assignment for Undamped Gyroscopic Systems in Control

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