Acceleration Control in Nonlinear Vibrating Systems based on Damped Least Squares

TL;DR

This paper presents a discrete-time control algorithm using damped least squares for managing acceleration and energy exchange in nonlinear vibrating systems, demonstrating its effectiveness on coupled Duffing oscillators.

Contribution

It introduces a novel control algorithm that links damping constant and sampling time, improving control in nonlinear vibratory systems.

Findings

Damping constant and sampling time must be inversely related.

The algorithm effectively suppresses nonlinear beat phenomena.

Varying dissipation ratios influences energy exchange control.

Abstract

A discrete time control algorithm using the damped least squares is introduced for acceleration and energy exchange controls in nonlinear vibrating systems. It is shown that the damping constant of least squares and sampling time step of the controller must be inversely related to insure that vanishing the time step has little effect on the results. The algorithm is illustrated on two linearly coupled Duffing oscillators near the 1:1 internal resonance. In particular, it is shown that varying the dissipation ratio of one of the two oscillators can significantly suppress the nonlinear beat phenomenon.