Bifurcation and control of chaos in Induction motor drives

Krishnendu Chakrabarty; Urmila Kar

Home/Archive/arXiv

arXiv · 1410.6574

Bifurcation and control of chaos in Induction motor drives

Krishnendu Chakrabarty·Urmila Kar

View original source ↗Read source document ↗Export metadata ↓

Abstract

The induction motor controlled by Indirect Field Oriented Control (IFOC) is known to have high performance and better stability. This paper reports the dynamical behavior of an indirect field oriented control (IFOC) induction motor drive in the light of bifurcation theory. The speed of high performance induction motor drive is controlled by IFOC method. The knowledge of qualitative change of the behavior of the motor such as equilibrium points, limit cycles and chaos with the change of motor parameters and load torque are essential for proper control of the motor. This paper provides a numerical approach to understand better the dynamical behavior of an indirect field oriented control of a current-fed induction motor. The focus is on bifurcation analysis of the IFOC motor, with a particular emphasis on the change that affects the dynamics and stability under small variations of Proportional Integral controller (PI) parameters, load torque and k, the ratio of the rotor time constant and its estimate etc. Bifurcation diagrams are computed. This paper also attempts to discuss various types of the transition to chaos in the induction motor. The results of the obtained bifurcation simulations give useful guidelines for adjusting both motor model and PI controller parameters. It is also important to ensure desired operation of the motor when the motor shows chaotic behavior. Infinite numbers of unstable periodic orbits are embedded in a chaotic attractor. Any unstable periodic orbit can be stabilized by proper control algorithm. The delayed feedback control method to control chaos has been implemented in this system.

Explore related subjects

nlin.CD

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Krishnendu Chakrabarty, Urmila Kar. 2014-10-24. Bifurcation and control of chaos in Induction motor drives. https://arxiv.org/abs/1410.6574

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Final state sensitivity and fractal basin boundaries from coupled Chialvo neurons

We investigate and quantify the basin geometry and extreme final state uncertainty of two identical electrically asymmetrically coupled Chialvo neurons. The system's diverse behaviors are presented, along with the mathematical reasoning behind its chaotic and nonchaotic dynamics as determined by the structure of the coupled equations. The system is found to be multistable with two qualitatively different attractors. Although each neuron is individually nonchaotic, the chaotic basin takes up the vast majority of the coupled system's state space, but the nonchaotic basin stretches to infinity due to chance synchronization. The boundary between the basins is found to be fractal, leading to extreme final state sensitivity. This uncertainty and its potential effect on the synchronization of biological neurons may have implications for understanding neuronal biology.

nlin.CD↗

arXiv2026

Jordan-Block Degeneracy and Cubic-Order Bifurcating Periodic Orbits in Minimum-Energy Optimal Control of Hamiltonian Equilibria

Equilibria of the Hamiltonian system associated with Pontryagin's minimum principle exhibit an exact doubling of the natural spectrum and, under a simple pairing condition, a Jordan block at every simple purely imaginary eigenvalue. Consequently, the classical Lyapunov Center Theorem does not apply to the augmented system, and no periodic orbit with nonzero optimal control bifurcates at linear order. We establish this mechanism in general and show that an optimal-control-induced periodic family emerges at cubic order in a Lindstedt--Poincaré expansion. The mechanism is illustrated in closed form for the pendulum and evaluated numerically for the planar $L_2$ equilibrium of Hill's restricted three-body problem, where the third-order approximation is validated against an independently computed family of periodic orbits.

nlin.CD↗

arXiv2026

Hypersensitivity and Turnpikes in Optimal Control of Inverted Pendulum: A Dynamical Systems Perspective

The hypersensitivity and turnpike phenomena in the optimal control of an inverted pendulum are investigated from a dynamical-systems perspective. We show that, for a fixed terminal time and a fixed terminal state optimal control problem, (1) the hypersensitivity originates from the fractal structure of the set of initial adjoint variables in the associated Hamiltonian dynamics, (2) the turnpike arises from slow dynamics in the vicinity of a degenerate center manifold, and (3) the escape channels are formed by normally hyperbolic invariant manifolds (NHIMs). As a consequence, small perturbations in the initial adjoint variables lead to qualitatively distinct extremal trajectories, resulting in severe numerical instability in trajectory optimization. Both the fractal structure and the invariant sets are characterized numerically and analytically.

nlin.CD↗