Controller design for delay-independent stability of linear time-invariant vibration systems with multiple delays

One of the critical parameters that can deteriorate the effectiveness of active vibration control (AVC) is the delay in sensors. Especially, in remote sensing where delays are large, and in high-speed applications with even small delays, instability can be inevitable. This paper presents algebraic approaches to design controllers in order to achieve stability regardless of the amount of delays for AVC applications modeled by linear time-invariant systems with “multiple” constant delays. The approaches are based on a nonconservative framework, and can identify the regions in the controller gain space where delay-independent stability (DIS) is achievable. With these controllers, we demonstrate via simulations that vibration suppression, within certain excitation frequency bands, can be improved or be as effective as those in AVC applications without delays.