Tuning Mechanism and Parameter Optimization of a Dynamic Vibration Absorber with Inerter and Negative Stiffness Under Delayed FOPID

Junlin Li, Yunxia Sun, Xueling Liu () and Yufeng Zhang ()
Additional contact information
Junlin Li: School of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, China
Yunxia Sun: School of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, China
Xueling Liu: Department of Electronic and Information Engineering, Bozhou University, Bozhou 236800, China
Yufeng Zhang: School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China

Mathematics, 2025, vol. 13, issue 13, 1-18

Abstract: The dynamic vibration absorber (DVA) based on delayed fractional PID (DFOPID) can achieve a more superior vibration suppression effect. However, the strong nonlinear characteristics of the system and the computational burden resulting from its high dimensionality make solving and optimizing more challenging. This paper presents a coupled model of DFOPID and DVA, exploring its parameter tuning mechanism and optimization problem. First, using the averaging method and Lyapunov stability theory, the amplitude-frequency equation and the stability condition of the steady-state solution of the primary system are derived. Numerical simulations validate the accuracy of the analytical result. Next, based on the mechanics of vibration, the approximate expressions of the controller under different differential conditions are calculated, and their equivalent action mechanisms are analyzed. Finally, by minimizing the maximum amplitude of the primary system as the objective function, the Particle Swarm Optimization (PSO) algorithm is applied to optimize the parameters of the passive DVA and the DVA models controlled by PID, FOPID, and DFOPID, successfully addressing the parameter optimization challenges posed by traditional fixed-point theory. The vibration reduction performance is compared across different loading environments. The results demonstrate that the model presented in this paper performs the best, exhibiting excellent vibration suppression and robustness.

Keywords: dynamic vibration absorber; delayed fractional PID; averaging method; Particle Swarm Optimization algorithm; vibration control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/13/2124/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/13/2124/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:13:p:2124-:d:1690288

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().