Optimized decentralized filtered-x least mean square algorithm for over-determined systems with periodic disturbances
Although decentralized control has great potential to facilitate multi-channel active noise/vibration control (ANC/AVC) systems, the practical implementations are greatly restricted by its inherent risk of system instability. In this paper, an optimized decentralized filtered-x least mean square alg...
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| Published in | Journal of sound and vibration Vol. 491; p. 115763 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Ltd
20.01.2021
Elsevier Science Ltd |
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| Online Access | Get full text |
| ISSN | 0022-460X 1095-8568 |
| DOI | 10.1016/j.jsv.2020.115763 |
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| Abstract | Although decentralized control has great potential to facilitate multi-channel active noise/vibration control (ANC/AVC) systems, the practical implementations are greatly restricted by its inherent risk of system instability. In this paper, an optimized decentralized filtered-x least mean square algorithm is proposed for over-determined ANC/AVC systems subject to periodic disturbances. A diagonal parametric matrix is added into the update equations and a set of nonlinear equations is established with respect to the diagonal elements of this parametric matrix. An assumption is made and is verified through simulations that the nonlinear equations are solvable and have multiple solutions. With these solutions, all the eigenvalues of the characteristic matrix corresponding to system stability can be forced close to the point (1,0) in the complex domain. Convergence behaviors of the proposed algorithm are analysed in both frequency-domain and time-domain, through which the existence and characteristics of the convergence ripples are revealed. A criterion function is further established for the diagonal parametric matrix so that the convergence ripples can be restricted in an average sense. Simulations and experiments based on a multi-channel ANC system are carried out to validate the proposed algorithm. Corresponding results demonstrate that, compared with the original decentralized control, the proposed algorithm has advantages of guaranteed stability and accelerated convergence rates over the whole control frequency band without performance degradation as well as extra computational cost. |
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| AbstractList | Although decentralized control has great potential to facilitate multi-channel active noise/vibration control (ANC/AVC) systems, the practical implementations are greatly restricted by its inherent risk of system instability. In this paper, an optimized decentralized filtered-x least mean square algorithm is proposed for over-determined ANC/AVC systems subject to periodic disturbances. A diagonal parametric matrix is added into the update equations and a set of nonlinear equations is established with respect to the diagonal elements of this parametric matrix. An assumption is made and is verified through simulations that the nonlinear equations are solvable and have multiple solutions. With these solutions, all the eigenvalues of the characteristic matrix corresponding to system stability can be forced close to the point (1,0) in the complex domain. Convergence behaviors of the proposed algorithm are analysed in both frequency-domain and time-domain, through which the existence and characteristics of the convergence ripples are revealed. A criterion function is further established for the diagonal parametric matrix so that the convergence ripples can be restricted in an average sense. Simulations and experiments based on a multi-channel ANC system are carried out to validate the proposed algorithm. Corresponding results demonstrate that, compared with the original decentralized control, the proposed algorithm has advantages of guaranteed stability and accelerated convergence rates over the whole control frequency band without performance degradation as well as extra computational cost. |
| ArticleNumber | 115763 |
| Author | An, Fengyan Cao, Yin Liu, Bilong |
| Author_xml | – sequence: 1 givenname: Fengyan surname: An fullname: An, Fengyan email: anfy@qut.edu.cn organization: School of Mechanical and Automotive Engineering, Qingdao University of Technology, No. 777 Jialingjiang Road, Qingdao 266520, China – sequence: 2 givenname: Yin orcidid: 0000-0001-9086-7027 surname: Cao fullname: Cao, Yin email: caoyfive@gmail.com organization: Centre for Vision, Speech and Signal Processing, University of Surrey, Guildford GU2 7XH, United Kingdom – sequence: 3 givenname: Bilong orcidid: 0000-0002-5791-3340 surname: Liu fullname: Liu, Bilong email: Liubilong@qut.edu.cn organization: School of Mechanical and Automotive Engineering, Qingdao University of Technology, No. 777 Jialingjiang Road, Qingdao 266520, China |
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| Cites_doi | 10.1109/TASLP.2018.2869686 10.1016/j.sigpro.2014.07.026 10.1016/j.jsv.2015.12.019 10.1109/89.326611 10.1121/1.2139624 10.1016/j.jsv.2017.06.005 10.1006/jsvi.1999.2338 10.1109/TASL.2013.2263143 10.1016/j.ymssp.2017.04.044 10.1121/10.0001401 10.1109/TASL.2010.2073705 10.1121/1.1427358 10.1109/TASL.2010.2101598 10.1016/j.jsv.2019.04.031 10.1016/j.jsv.2011.06.008 10.1109/TIM.2012.2205492 10.1121/1.5063341 10.1109/87.896748 10.1109/TSP.2017.2742987 |
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| Keywords | Active vibration control Periodic disturbances Decentralized control Active noise control |
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| SubjectTerms | Active noise control Active vibration control Algorithms Control stability Control systems Convergence Decentralized control Disturbances Eigenvalues Frequencies Mean square errors Nonlinear equations Performance degradation Periodic disturbances Ripples Systems stability Vibration analysis Vibration control |
| Title | Optimized decentralized filtered-x least mean square algorithm for over-determined systems with periodic disturbances |
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