Non-linear dynamics and control of chaos for a rotational machine with a hexagonal centrifugal governor with a spring

Ge, Zheng–Ming; Lee, Ching-I

doi:10.1016/s0022-460x(03)00092-0

Cited by 34 publications

(6 citation statements)

References 2 publications

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“…ϑ 12 = −r 12 sign ϑ 12 −θ 11 (13) where the bound filtering error |ϑ 12 −ẋ d | ≤ l ϑ 2 holds. Then, the virtual control input is selected to be…”

Section: B Controller Designmentioning

confidence: 99%

“…12 Aiming to the effect of external disturbance, nonlinear dynamics and chaos control of a rotational machine with a hexagonal centrifugal governor and a spring are addressed. 13 Chaos, its control and synchronization for a fractional-order rotational machine system with a centrifugal governor is investigated. 5 Moreover, the OGY method, 14 linear and nonlinear feedback control, 15,16 adaptive method 17 and time-delay feedback control 18 are considered as the efficient tools for controlling chaotic oscillation.…”

Section: Introductionmentioning

confidence: 99%

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Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

2016

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This paper addresses chaos suppression of the mechanical centrifugal flywheel governor system with output constraint and fully unknown parameters via adaptive dynamic surface control. To have a certain understanding of chaotic nature of the mechanical centrifugal flywheel governor system and subsequently design its controller, the useful tools like the phase diagrams and corresponding time histories are employed. By using tangent barrier Lyapunov function, a dynamic surface control scheme with neural network and tracking differentiator is developed to transform chaos oscillation into regular motion and the output constraint rule is not broken in whole process. Plugging second-order tracking differentiator into chaos controller tackles the “explosion of complexity” of backstepping and improves the accuracy in contrast with the first-order filter. Meanwhile, Chebyshev neural network with adaptive law whose input only depends on a subset of Chebyshev polynomials is derived to learn the behavior of unknown dynamics. The boundedness of all signals of the closed-loop system is verified in stability analysis. Finally, the results of numerical simulations illustrate effectiveness and exhibit the superior performance of the proposed scheme by comparing with the existing ADSC method.

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“…ϑ 12 = −r 12 sign ϑ 12 −θ 11 (13) where the bound filtering error |ϑ 12 −ẋ d | ≤ l ϑ 2 holds. Then, the virtual control input is selected to be…”

Section: B Controller Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

2016

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“…The authors validated their results with the already available data in the literature. Ge and Lee (7) studied the static and dynamic characteristics of the mechanisms like governors. The authors studied all the mechanisms working with the help of external forces upon rotation.…”

Section: Introductionmentioning

confidence: 99%

Study of Watt Governor Mechanism

Hasan¹

2021

IJST

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Objective:The basic aim of the study is to determine the minimum, maximum speeds and sensitivity of the governor of a universal Watt governor setup available in machine dynamics laboratory in the mechanical engineering department at Jamia Millia Islamia New Delhi. Methodology: We used a tachometer to measure the spindle speed in revolution per minute. After assembling the governor setup, the author note down the initial reading of pointer on the vertical scale. After switching on the rotary switch, we slowly increase the governor speed till the sleeve is lifted from its initial position and it should be stabilized. Now, again, we increase the governor speeds in steps to get different position of sleeve lift at different rpm and noted all the observations. Findings: The actual minimum and maximum governor speeds are 211 rpm and 276 rpm respectively. The actual sensitivity of the available governor setup is 26.7 %. With the change of governor speed, the radius of rotation also changes. Novelty: This Study may be sued as simple guide lines for undergraduate / postgraduate / research scholars as well as scientist to select the suitable governor to perform the required task as per specific necessity in their research work.

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“…Ge and Jhuang (2007) have investigated chaos and its control and synchronization for a fractional order rotational mechanical system with a centrifugal governor. Nonlinear dynamics and the control of chaos for a rotational machine with a hexagonal centrifugal governor and a spring considering the effects of external disturbances have been reported by Ge and Lee (2003).Anti-control and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor have been addressed by Ge and Lee (2005a). Moreover, Ge and Lee (2005b) have studied the chaotic behavior of an autonomous rotational machine system with a centrifugal governor and spring.…”

Section: Introductionmentioning

confidence: 99%

Finite-time stabilization of non-autonomous uncertain chaotic centrifugal flywheel governor systems with input nonlinearities

Aghababa

2012

Journal of Vibration and Control

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The centrifugal flywheel governor is a mechanical device that automatically controls the speed of an engine and avoids the damage caused by an abrupt change of load torque. Recent research has discovered that this system exhibits very rich and complex dynamics such as chaos. In this paper, the problem of finite-time stabilization of non-autonomous chaotic centrifugal flywheel governor systems in the presence of model uncertainties, external disturbances, fully unknown parameters and input nonlinearities is studied. Appropriate adaptation laws are designed to undertake the system’s unknown parameters. Using the adaptation laws and finite-time control theory, a robust adaptive controller is derived to stabilize the non-autonomous uncertain centrifugal flywheel governor system with nonlinear control inputs in a given finite time. The finite-time stability and convergence of the closed-loop system are analytically proved. A numerical simulation is given to show the robustness and effectiveness of the proposed finite-time controller and to verify the theoretical results of the paper.

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Non-linear dynamics and control of chaos for a rotational machine with a hexagonal centrifugal governor with a spring

Cited by 34 publications

References 2 publications

Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

Study of Watt Governor Mechanism

Finite-time stabilization of non-autonomous uncertain chaotic centrifugal flywheel governor systems with input nonlinearities

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