A modified optimization method for robust partial quadratic eigenvalue assignment using receptances and system matrices

2021 ◽  
Vol 159 ◽  
pp. 73-92
Author(s):  
Min Lu ◽  
Zheng-Jian Bai
Keyword(s):  
Optimization Method ◽  
Quadratic Eigenvalue ◽  
Eigenvalue Assignment

An Approach to Partial Quadratic Eigenvalue Assignment of Damped Vibration Systems Using Static Output Feedback

2018 ◽  
Vol 18 (01) ◽  
pp. 1850012 ◽  
Author(s):  
Jiafan Zhang ◽  
Yongxin Yuan ◽  
Hao Liu
Keyword(s):  
Output Feedback ◽  
Second Order ◽  
Order System ◽  
Feedback Gain ◽  
Static Output Feedback ◽  
Homogeneous Matrix ◽  
Quadratic Eigenvalue ◽  
Static Output ◽  
Damped Vibration Systems ◽  
Eigenvalue Assignment

This paper addresses the problem of the partial eigenvalue assignment for second-order damped vibration systems by static output feedback. The presented method uses the combined acceleration, velocity and displacement output feedback and works directly on second-order system models without the knowledge of the unassigned eigenpairs. It allows the input and output matrices to be prescribed beforehand in a simple form. The real-valued spectral decomposition of the symmetric quadratic pencil is adopted to derive a homogeneous matrix equation of output feedback gain matrices that assure the no spillover eigenvalue assignment. The method is validated by some illustrative numerical examples.

scholarly journals Robustness of the quadratic partial eigenvalue assignment using spectrum sensitivities for state and derivative feedback designs

2018 ◽  
Vol 37 (2) ◽  
pp. 253-268 ◽  
Author(s):  
José M Araújo ◽  
Carlos ET Dórea ◽  
Luiz MG Gonçalves ◽  
João BP Carvalho ◽  
Biswa N Datta
Keyword(s):  
Closed Loop ◽  
Explicit Knowledge ◽  
Active Vibration Control ◽  
Real Life ◽  
Optimization Approach ◽  
Practical Applications ◽  
Loop Feedback ◽  
Active Vibration ◽  
Quadratic Eigenvalue ◽  
Eigenvalue Assignment

Based on the notions of spectrum sensitivities, proposed by us earlier, we develop a novel optimization approach to deal with robustness in the closed-loop eigenvalues for partial quadratic eigenvalue assignment problem arising in active vibration control. A distinguished feature of this new approach is that the objective function is composed of only the system and the closed-loop feedback matrices. It does not need an explicit knowledge of the eigenvalues and eigenvectors. Furthermore, the approach is applicable to both the state-feedback and derivative feedback designs. These features make the approach viable to design an active vibration controller for practical applications to large real-life structures. A comparative study with existing algorithms and a study on the transient response of a real-life system demonstrate the effectiveness, superiority, and competitiveness of the proposed approach.

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