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

• Published in: Journal of low frequency noise, vibration, and active control Vol. 37; no. 2; pp. 253 - 268
• Main Authors: Araújo, José M, Dórea, Carlos ET, Gonçalves, Luiz MG, Carvalho, João BP, Datta, Biswa N
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.06.2018; Sage Publications Ltd; SAGE Publishing
• Subjects: Active control; Algorithms; Comparative studies; Control systems design; Eigenvalues; Eigenvectors; Explicit knowledge; Feedback; Operations research; Optimization; Robustness; Transient response; Vibration control; robustness; spectrum sensitivity; active vibration control; Partial eigenvalue assignment
• ISSN: 1461-3484; 2048-4046
• DOI: 10.1177/1461348418755614

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.