On the achievable stability margin for resonant systems with negative imaginary controllers: MEMS force sensor example

Abstract

This paper presents a root locus analysis to determine the maximum achievable stability margin for three types of standard single input single output negative imaginary controllers when applied to a single mode undamped resonant plant. The controllers under consideration are integral resonant controllers, positive position controllers and phase lead controllers. It is found that both the integral resonant controllers and the positive position controllers can achieve only a finite stability margin, with the positive position controllers achieving a higher stability margin than the integral resonant controllers. It is also found that at least in theory, phase lead controllers could achieve an arbitrarily large stability margin. The results are also validated experimentally on an experimental platform involving a lightly damped SISO MEMS force sensor. Show more