Delayed dynamic-feedback controller design for multi-frequency vibration suppression

TL;DR

This paper introduces a novel methodology for designing delayed dynamic output feedback controllers aimed at suppressing vibrations across multiple frequencies, utilizing delay-differential algebraic equations and non-convex optimization techniques.

Contribution

It develops a systematic approach to synthesize delay-based controllers for multi-frequency vibration suppression, transforming the problem into a solvable unconstrained optimization.

Findings

Effective vibration suppression demonstrated across multiple frequencies.

The delay-based controller design is adaptable using existing static feedback tools.

Optimization successfully minimizes spectral abscissa under polynomial constraints.

Abstract

We present a methodology for designing a dynamic controller with delayed output feedback for achieving non-collocated vibration suppression with a focus on the multi-frequency case. To synthesize the delay-based controller, we first remodel the system of equations as a delay-differential algebraic equation (DDAE) in such a way that existing tools for design of a static output feedback controller can be easily adapted. The problem of achieving non-collocated vibration suppression with sufficient damping is formulated as a constrained optimization problem of minimizing the spectral abscissa in the presence of zero-location constraints, with the constraints exhibiting polynomial dependence on its parameters. We transform the problem into an unconstrained one using elimination, following which we solve the resulting non-convex, non-smooth optimization problem.