Journal of Northeastern University Natural Science ›› 2019, Vol. 40 ›› Issue (9): 1217-1222.DOI: 10.12068/j.issn.1005-3026.2019.09.001

• Information & Control •     Next Articles

Impact of Complex Eigenvalues on Their Robust H Control Performance in Second-Order Systems

WANG Zhan-shan1, WANG Ji-dong1,2, LIU Xiu-chong1, SUN Jian1   

  1. 1. School of Information Science & Engineering, Northeastern University, Shenyang 110819, China; 2. School of Electrical Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450045, China.
  • Received:2018-08-21 Revised:2018-08-21 Online:2019-09-15 Published:2019-09-17
  • Contact: WANG Zhan-shan
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Abstract: Robust H performance is studied for a class of second-order linear systems with complex eigenvalues, especially the impact of imaginary part of complex eigenvalues on the H performance is studied. It is found that when the real part of the complex eigenvalues is fixed, the impact of the imaginary part of the complex eigenvalues on the H performance becomes little when the value of the imaginary part exceeds a threshold. Based on this observation, a fixed proportional relation between the imaginary part and the real part of the complex eigenvalues is found for a given system matrix under the framework of H performance. Referring to the classical control theory of second-order systems in frequency domain, the relationship between the selection ranges of damping ratio and the complex eigenvalue is further discussed in the framework of H performance, in which a reasonable explanation on the selection ranges of damping ratio is presented. This analysis procedure forms the time-frequency domain interaction synthesis method, which provides a theoretical guidance for the selection and determination of the desired closed-loop poles in the control theory based on the pole placement method.

Key words: H norm, H performance, H control, disturbance, damping ratio, time-frequency domain interaction synthesis method

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