Combining passivity and classical frequency-domain methods: An insight into decentralised control

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.