Combining Passivity and Classical Frequency-Domain Methods: An Insight into Decentralised Control Articles uri icon



publication date

  • February 2010

start page

  • 4426

end page

  • 4438


  • 12


  • 215

International Standard Serial Number (ISSN)

  • 0096-3003

Electronic International Standard Serial Number (EISSN)

  • 1873-5649


  • A novel approach to tackle passivity-related issues in the frequency domain for linear multiple-input multiple-output (MIMO) cross-coupled systems is given. The aim is to design passivity-based stabilising
    diagonal controllers within the framework of Individual Channel Analysis
    and Design (ICAD). Two main results are presented. First, the ICAD is
    reinterpreted in terms of the passivity-related properties of either the
    channels or the closed-loop system. The notion of practical passivity
    is introduced. Second, for linear MIMO systems, a novel
    frequency-domain passification procedure is proposed. This procedure is
    used in the design process of the diagonal controllers. Furthermore, an
    indicator of how far the system is from being passive is defined. This
    indicator is stated in terms of gain and phase margins, with the
    consequent statement of robustness. Such a passivity indicator has not
    been established so far, and for practical applications can be more
    useful than setting the passivity of the system. Classical
    frequency-domain control techniques based on Bode and Nyquist plots are
    used. The results are applied to a 2-input-2-output system modelling an
    induction motor.