Local feedback stabilization and bifurcation control, II. Stationary bifurcation

Abed, Eyad H.; Fu, Jyun-Horng

doi:10.1016/0167-6911(87)90089-2

Cited by 234 publications

(57 citation statements)

References 4 publications

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“…The direction of a pitchfork bifurcation is its subcriticality or supercriticality. As discussed by Abed and Fu (1987), the supercritical pitchfork bifurcation (figure 1(c)) is preferable in practice since after the nominal solution has lost stability, new stable equilibria arise that provide a nearby operating condition.…”

Section: Introductionmentioning

confidence: 99%

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Stationary Bifurcation Control for Systems with Uncontrollable Linearization

Kim¹,

Abed²

1999

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ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, heterogeneous and dynamic problems of engineering technology and systems for industry and government. ISR is a permanent institute of the University of MarylandAbstract Stationary bifurcation control is studied under the assumption that the critical zero eigenvalue is uncontrollable for the linearized system. The development facilitates explicit construction of feedback control laws that render the bifurcation supercritical. Thus, the bifurcated equilibria in the controlled system are guaranteed stable. Both pitchfork bifurcation and transcritical bifurcation are addressed. The results obtained for pitchfork bifurcations apply to general nonlinear models smooth in the state and the control. For transcritical bifurcations, the results require the system to be affine in the control.

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Section: Introductionmentioning

confidence: 99%

“…The aim of the control design is described as follows Abed and Fu (1987). A nonlinear system is given for which a nominal equilibrium loses stability through a real eigenvalue crossing the imaginary axis at the origin.…”

Section: Introductionmentioning

confidence: 99%

Stationary Bifurcation Control for Systems with Uncontrollable Linearization

Kim¹,

Abed²

1999

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“…Using the controlled laws derived and used in [10], we transform an unstable subcritical bifurcation point into a point to be considered as supercritical stable bifurcationized. These control laws are called "static state feedback" and have the general form of u = u(x).…”

Section: Introductionmentioning

confidence: 99%

“…In the end, we reshape the bifurcation diagram of the system [10]. Using the controlled laws derived and used in [10], we transform an unstable subcritical bifurcation point into a point to be considered as supercritical stable bifurcationized.…”

Section: Introductionmentioning

confidence: 99%

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Control of Instable Chaotic Small Power System

Shariff¹,

Harb²

2015

JPEE

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In this paper, we aim to control an instable chaotic oscillation in power system that is considered to be small system by using a linear state feedback controller. First we will analyze the stability of the mentioned power system by means of modern nonlinear theory (Bifurcation and Chaos). Our model is based on a three bus power system that consists of multi generators containing both dynamic and static loads. They are considered to be in the form of an induction motor in parallel with a capacitor, as well as a combination of constant power along with load impedance, PQ. We consider the load reactive power as the control parameter. At this stage, after changing the control parameter, the study showed that the system is experiencing a subcritical Hopf bifurcation point. This leads to a chaos within the system period doubling path. We then discuss the system controllability and present that the all chaotic oscillations fade away through the linear controller that we impose on the system.

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Generic Families and Generic Bifurcations of Control‐Affine Systems

Rupniewski

Respondek²

2013

Taming Heterogeneity and Complexity of Embedded Control

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Local feedback stabilization and bifurcation control, II. Stationary bifurcation

Cited by 234 publications

References 4 publications

Stationary Bifurcation Control for Systems with Uncontrollable Linearization

Stationary Bifurcation Control for Systems with Uncontrollable Linearization

Control of Instable Chaotic Small Power System

Generic Families and Generic Bifurcations of Control‐Affine Systems

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