Stabilization and positioning control of a rolling disk by using the Bogdanov-Takens bifurcation

DOI10.1016/j.physd.2012.05.007zbMath1415.70031OpenAlexW1984860621MaRDI QIDQ453146

Javier Gil Chica, Manuel F. Pérez Polo, Manuel Pérez Molina

Publication date: 18 September 2012

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2012.05.007

zbMATH Keywords

nonholonomic constraintsrolling diskBogdanov-Takens bifurcationnonlinear control law

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Control of mechanical systems (70Q05) Bifurcations of singular points in dynamical systems (37G10) Dynamical systems in control (37N35) Nonholonomic systems related to the dynamics of a system of particles (70F25) Nonholonomic dynamical systems (37J60) Bifurcation control of ordinary differential equations (34H20)

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Steady-state, self-oscillating and chaotic behavior of a PID controlled nonlinear servomechanism by using Bogdanov-Takens and Andronov-Poincaré-Hopf bifurcations

Cites Work

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• A generalized mathematical model to analyze the nonlinear behavior of a controlled gyroscope in gimbals
• Integrability of the motion of a rolling disk of finite thickness on a rough plane
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Nonlinear control systems: An introduction
• Closed-loop control of the motion of a disk-rod system
• Dynamics of rolling disk
• Asymptotics of homoclinic bifurcation in a three-dimensional system
• Modelling and control of the motion of a rolling disk: Effect of motor dynamics on the dynamical model
• Stabilization and control of the motion of a rolling disk
• Bifurcation problems with high codimensions.
• Regular self-oscillating and chaotic behaviour of a PID controlled gimbal suspension gyro
• Feasible command strategies for the control of a rolling disk with a rod fixed along its axis
• Stabilization and control of the motion of a rolling disk by using two rotors fixed along its axis
• The Lagrange-d'Alembert-Poincaré equations and integrability for the rolling disk
• Tuning of a PID controlled gyro by using the bifurcation theory
• Hopf bifurcation control: a new approach
• Control and stabilization of nonholonomic dynamic systems
• Elements of applied bifurcation theory
• Nonlinear oscillations in the rolling motion of Euler's disk