Reconstruction of pitchfork bifurcation with exogenous disturbances based on equivalent-input-disturbance approach

Reconstructing a pitchfork bifurcation that is destroyed by an exogenous disturbance is important to control it. This paper extends the equivalent-input-disturbance (EID) approach to solve the problem of reconstructing a pitchfork bifurcation when there is an exogenous disturbance for the first time...

Full description

Saved in:
Bibliographic Details
Published inNonlinear dynamics Vol. 102; no. 4; pp. 2699 - 2709
Main Authors She, Jinhua, Yin, Xiang, Wu, Min, Sato, Daiki, Ohnishi, Kouhei
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2020
Springer Nature B.V
Subjects
Automotive Engineering
Bifurcations
Classical Mechanics
Control
Control systems
Dynamical Systems
Engineering
Equivalence
Exact solutions
Mechanical Engineering
Noise control
Noise measurement
Nonlinearity
Original Paper
Reconstruction
Robustness (mathematics)
Vibration
Equivalent input disturbance
Disturbance rejection
Bifurcation analysis
Bifurcation control
Online AccessGet full text

Cover

More Information
Summary:Reconstructing a pitchfork bifurcation that is destroyed by an exogenous disturbance is important to control it. This paper extends the equivalent-input-disturbance (EID) approach to solve the problem of reconstructing a pitchfork bifurcation when there is an exogenous disturbance for the first time. A nonlinear term and a bifurcation parameter are designed in the system to reconstruct the pitchfork bifurcation. The bifurcation characteristics of the equilibriums of the system are analyzed by exploring the features of the EID-based system. This provides us analytic solutions for a system with a degree higher than four for the first time. Unlike other pitchfork-bifurcation control systems, the EID-based control system only rejects the disturbance and retains the nonlinearity. Numerical examples demonstrate the effectiveness of the presented method and show its superiority over others. The robustness of the reconstruction with respect to measurement noise and control of a pitchfork bifurcation are also shown by the examples.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-020-06066-8