Non-Linear Vibration Isolators with Unknown Excitation and Unmodelled Dynamics: Sliding Mode Active Control

Hu Hu,Liu Liu,Ouyang Ouyang,Zhang Zhang

doi:10.3390/app9173567

Hu Hu, Liu Liu + Show 2 more

Open Access

https://doi.org/10.3390/app9173567

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Abstract

For a class of single-degree-of-freedom non-linear passive vibration isolators with unknown excitation and unmodelled dynamics, two sliding mode control methods—a conventional one and the other using a super-twisting algorithm—were proposed to complement and improve the performances and the robustness of the passive isolators. The proposed control methods only require the estimation of the loading and measured velocities of the isolators. Numerical simulations for a non-linear isolator with quasi-zero stiffness demonstrated that both methods were effective and easy to implement, and the one using a super-twisting algorithm was more promising from the perspective of practical application.

Highlights

Non-linear passive vibration isolators have been proven to be advantageous to overcome the inherent drawback of linear isolators in different applications [1]
It should be noted that isolators with quasi-zero stiffness (QZS) are very sensitive facilities and if something occurs to cause deviation of its characteristic parameters and/or change in the non-linearity properties of its forces, the isolation performance will change dramatically [19,20,21,22]
In order to make the non-linear vibration isolator more robust and improve its dynamics behavior, we proposed two slidingmode modecontrol control (SMC) to supplement the isolation performance

Summary

Introduction

Non-linear passive vibration isolators have been proven to be advantageous to overcome the inherent drawback of linear isolators in different applications [1]. A simple linear time-delayed displacement feedback control strategy was introduced to improve the robustness and transmissibility performance of an isolator with QZS under both force and base excitation in Reference [23]. It turned out that a better isolation performance in the high-frequency band where isolation is required can be achieved, but the 1/3 subharmonic resonance can occur for a smaller excitation amplitude and increasing the feedback gain cannot eliminate the 1/3 subharmonic resonance In these studies, a single-degree-of-freedom (SDOF) oscillator with cubic non-linearity was analyzed by using some approximate analytical methods, e.g., the multiple scales method and the harmonic balance method, and the amplitude–frequency responses were obtained.

Force Controller Design

Description of a Quasi-Zero-Stiffness Isolator

Simulation Results and Analyses

Conclusions