Stability analysis and vibration control of a class of negative imaginary systems

This paper presents stability analysis and vibration control of a class of negative imaginary systems. A flexible manipulator that moves in a horizontal plane is considered and is modelled using the finite element method. The system with two poles at the origin is shown to possess negative imaginary properties. Subsequently, an integral resonant controller (IRC) which is a strictly negative imaginary controller is designed for the position and vibration control of the system. Using the IRC, the closed-loop system is observed to be internally stable and simuation results show that satisfactory hub angle response is achieved. Furthermore, vibration magnitudes at the resonance modes are suppressed by 48 dB

Spectral Conditions for Symmetric Positive Real and Negative Imaginary Systems

Abstract — Non-Hamiltonian spectral conditions for the class of symmetric multivariable strictly positive real and strictly negative imaginary systems are derived. They represent generalizations of known ones for strict positive realness to the cases with singular feedthrough matrix, and are novel in the context of strict negative imaginariness. Moreover, we propose a concept of strong negative imaginariness and establish its links to strict positive realness of symmetric systems. The proposed spectral conditions are useful in the corresponding assessment and enforcement procedures, as well as in quadratic stability analysis of uncertain and switched systems. I