scholarly journals Robust orbital stabilization: A Floquet theory–based approach

2021 ◽  
Author(s):  
Christian Fredrik Sætre ◽  
Anton S. Shiriaev ◽  
Leonid B. Freidovich ◽  
Sergei V. Gusev ◽  
Leonid M. Fridman
Keyword(s):  
Floquet Theory ◽  
Orbital Stabilization

Floquet Theory in Magnetic Resonance: Formalism and Applications

2021 ◽  
Author(s):  
Konstantin L. Ivanov ◽  
Kaustubh R. Mote ◽  
Matthias Ernst ◽  
Asif Equbal ◽  
Perunthiruthy K. Madhu
Keyword(s):  
Magnetic Resonance ◽  
Floquet Theory

scholarly journals Period-doubling bifurcation analysis and chaos control for load torque using FLC

2021 ◽  
Author(s):  
Eman Moustafa ◽  
Abdel-Azem Sobaih ◽  
Belal Abozalam ◽  
Amged Sayed A. Mahmoud
Keyword(s):  
Floquet Theory ◽  
Chaos Control ◽  
Fuzzy Logic Controller ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Parameter Variation ◽  
Period Doubling Bifurcation ◽  
Load Torque ◽  
Nonlinear Behaviors ◽  
Scientific Fields

AbstractChaotic phenomena are observed in several practical and scientific fields; however, the chaos is harmful to systems as they can lead them to be unstable. Consequently, the purpose of this study is to analyze the bifurcation of permanent magnet direct current (PMDC) motor and develop a controller that can suppress chaotic behavior resulted from parameter variation such as the loading effect. The nonlinear behaviors of PMDC motors were investigated by time-domain waveform, phase portrait, and Floquet theory. By varying the load torque, a period-doubling bifurcation appeared which in turn led to chaotic behavior in the system. So, a fuzzy logic controller and developing the Floquet theory techniques are applied to eliminate the bifurcation and the chaos effects. The controller is used to enhance the performance of the system by getting a faster response without overshoot or oscillation, moreover, tends to reduce the steady-state error while maintaining its stability. The simulation results emphasize that fuzzy control provides better performance than that obtained from the other controller.

scholarly journals On excessive Transverse Coordinates for Orbital Stabilization of Periodic Motions

2020 ◽  
Vol 53 (2) ◽  
pp. 9250-9255
Author(s):  
Christian Fredrik Sætre ◽  
Anton Shiriaev
Keyword(s):  
Periodic Motions ◽  
Orbital Stabilization

scholarly journals The Rabi problem with elliptical polarization

2020 ◽  
Vol 75 (11) ◽  
pp. 937-962
Author(s):  
Heinz-Jürgen Schmidt
Keyword(s):  
Floquet Theory ◽  
Equation Of Motion ◽  
Quantum Spin ◽  
Heun Equation ◽  
Elliptical Polarization ◽  
Third Order ◽  
Polynomial Coefficients ◽  
Resonance Frequencies ◽  
Classical Quantum ◽  
Elliptically Polarized

AbstractWe consider the solution of the equation of motion of a classical/quantum spin subject to a monochromatical, elliptically polarized external field. The classical Rabi problem can be reduced to third-order differential equations with polynomial coefficients and hence solved in terms of power series in close analogy to the confluent Heun equation occurring for linear polarization. Application of Floquet theory yields physically interesting quantities like the quasienergy as a function of the problem’s parameters and expressions for the Bloch–Siegert shift of resonance frequencies. Various limit cases are thoroughly investigated.

scholarly journals Geometry of the Rabi Problem and Duality of Loops

2020 ◽  
Vol 75 (5) ◽  
pp. 381-391 ◽  
Author(s):  
Heinz-Jürgen Schmidt
Keyword(s):  
Magnetic Field ◽  
Differential Geometry ◽  
Floquet Theory ◽  
Bloch Sphere ◽  
Classical Spin ◽  
Periodic Magnetic Field

AbstractWe investigate the motion of a classical spin processing around a periodic magnetic field using Floquet theory, as well as elementary differential geometry and considering a couple of examples. Under certain conditions, the role of spin and magnetic field can be interchanged, leading to the notion of “duality of loops” on the Bloch sphere.

Floquet theory for a Volterra integro-dynamic system

2014 ◽  
Vol 93 (9) ◽  
pp. 2002-2013 ◽  
Author(s):  
R.P. Agarwal ◽  
V. Lupulescu ◽  
D. O’Regan ◽  
A. Younus
Keyword(s):  
Dynamic System ◽  
Floquet Theory

An Application of the Poincare´ Map to the Stability of Nonlinear Normal Modes

1980 ◽  
Vol 47 (3) ◽  
pp. 645-651 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Floquet Theory ◽  
Poincaré Map ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Theory Approach ◽  
Poincare Map ◽  
Linearized Stability ◽  
Nonlinear Normal ◽  
The Stability ◽  
Two Degree Of Freedom

The stability of periodic motions (nonlinear normal modes) in a nonlinear two-degree-of-freedom Hamiltonian system is studied by deriving an approximation for the Poincare´ map via the Birkhoff-Gustavson canonical transofrmation. This method is presented as an alternative to the usual linearized stability analysis based on Floquet theory. An example is given for which the Floquet theory approach fails to predict stability but for which the Poincare´ map approach succeeds.

Sign in / Sign up

Export Citation Format

Share Document