Browsing by Author "Ge, ZM"

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A Melnikov method for strongly odd nonlinear oscillators
(1998-03-01)
Ge, ZM
;
Ku, FN
;
機械工程學系
;
Department of Mechanical Engineering
In this paper. explicit calculations that extend the applicability of the Melnikov method to include strongly odd nonlinear and large forcing amplitude oscillating systems, are presented. We consider the response of the strongly nonlinear oscillating system governed by an equation of motion containing a parameter epsilon which need not be small. Phenomena considered are steady state response of strongly nonlinear oscillators subject to harmonic excitation. Two examples are given, they are the strongly nonlinear Duffing's equation and a pendulum suspended on a rotating arm. Finally, a adjustable factor is used to fit the simulation data. The theoretical chaotic behavior regions thus defined and plotted in the forcing amplitude versus parameter plane give the lower bounds for the true chaotic motion zones.
A modified interpolated cell mapping method
(1997-01-16)
Ge, ZM
;
Lee, SC
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
A modified interpolated cell mapping (MICM) method is developed for global analysis of deterministic dynamical systems with smooth basin boundaries. By improving the algorithm of the interpolated cell mapping (ICM) and including the idea of sampling mappings of cells from the generalized cell mapping (GCM), MICM gives a more complete and precise global analysis of systems than ICM. In addition, based on analysis using MICM, a method using exact mappings is proposed to remedy the inaccuracy and incompleteness of global analysis due to interpolated mappings and the assumption of the sink cell. For the three systems studied in this paper, this method locates identical attractors and basins of attraction as the integration of a grid of points (IGP) method, with a 100-fold improvement in computational efficiency. (C) 1997 Academic Press Limited.
An interval method for computing the stability margin of real uncertainty problems
(2000-07-01)
Ge, ZM
;
Chu, LW
;
機械工程學系
;
Department of Mechanical Engineering
Frequently, in practical control system design, some designing parameters are uncertain. These uncertain parameters may vary with temperature, humidity or other environmental variable, and these variations will have an impact on the stability of the system. In this paper, we use a global optimal method-interval method, by which stability margins of these uncertain parameters can be computed. Copyright (C) 2000 John Wiley & Sons, Ltd.
An interval method for computing the structured singular value of a transfer matrix with real uncertainty
(1998-12-01)
Ge, ZM
;
Chu, LW
;
機械工程學系
;
Department of Mechanical Engineering
Singular value robustness tests can be used to analyze real parameter variations, but it is difficult to calculate the structured singular value (mu-norm) of a transfer matrix with real uncertainty. Thus far, the MATLAB (Matrix Laboratory) with mu-tools toolbox software package is the most widely used method for numerical computation of structured singular values. However, it can only obtain the lower and upper bounds of the mu-norm. We present a method developed from interval analysis which can compute the true value of the mu-norm in numerical computation.
Analysis of random dynamical systems by interpolated cell mapping
(1996-07-25)
Ge, ZM
;
Lee, SC
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
A method of interpolated cell mapping (ICM) is developed for global analysis of random dynamical systems. In this method, one first analyzes a random system by constructing a uniform number of sample interpolated trajectories for each cell. More sample interpolated trajectories are then constructed for critical cells sensitive to random effects to characterize the global behaviour of the system. When applied to the global analysis of non-linear systems with uncertain external loadings or system parameters, the proposed method yields more precise results than the generalized cell mapping (GCM) method. These results agree well with those obtained by Monte Carlo simulation. Additionally, the proposed method allows global analyses of random systems to be improved easily when the original regions of study are too large to give precise analyses. (C) 1996 Academic Press Limited
Analysis of random dynamical systems by interpolated cell mapping
(1996-07-25)
Ge, ZM
;
Lee, SC
;
機械工程學系
;
Department of Mechanical Engineering
A method of interpolated cell mapping (ICM) is developed for global analysis of random dynamical systems. In this method, one first analyzes a random system by constructing a uniform number of sample interpolated trajectories for each cell. More sample interpolated trajectories are then constructed for critical cells sensitive to random effects to characterize the global behaviour of the system. When applied to the global analysis of non-linear systems with uncertain external loadings or system parameters, the proposed method yields more precise results than the generalized cell mapping (GCM) method. These results agree well with those obtained by Monte Carlo simulation. Additionally, the proposed method allows global analyses of random systems to be improved easily when the original regions of study are too large to give precise analyses. (C) 1996 Academic Press Limited
Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems
(2006-03-01)
Ge, ZM
;
Chang, CM
;
Chen, YS
;
機械工程學系
;
Department of Mechanical Engineering
Anti-control of chaos of single time scale brushless dc motors (BLDCM) and chaos synchronization of different order systems are studied in this paper. By addition of an external nonlinear term, we can obtain anti-control of chaos. Then, by addition of the coupling terms, by the use of Lyapunov stability theorem and by the linearization of the error dynamics, chaos synchronization between a third-order BLDCM and a second-order Duffing system are presented. (c) 2005 Elsevier Ltd. All rights reserved.
Anti-control of chaos of two-degrees-of-freedom loudspeaker system and chaos synchronization of different order systems
(2004-05-01)
Ge, ZM
;
Leu, WY
;
機械工程學系
;
Department of Mechanical Engineering
The chaos anti-control and synchronization of a two-degrees-of-freedom loudspeaker system are studied in this paper. Anti-control term is added to change state from regular to chaos. The anti-control methods such as addition of a constant force, of a periodic square wave, of a periodic saw tooth wave, of a periodic triangle wave, of a periodic rectified sinusoidal wave and of the xx term are used. The results are illustrated by numerical results, i.e. bifurcation diagram and Lyapunov exponents. Next, chaos synchronization of different order system is studied. Two methods are presented to achieve the synchronization: the addition of the coupling terms, the linearization of the error dynamics. The results are illustrated by phase diagram and time response. (C) 2003 Elsevier Ltd. All rights reserved.
Anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor
(2005-04-22)
Ge, ZM
;
Lee, CI
;
機械工程學系
;
Department of Mechanical Engineering
Anticontrol and synchronization of chaos for an autonomous rotational machine system with a hexagonal centrifugal governor are studied in the paper. Two different procedures for the design of the controller are proposed to anticontrol the governor system effectively. Finally, five methods are studied for chaos synchronization. (c) 2004 Elsevier Ltd. All rights reserved.
Bifurcations and chaos in a rate gyro with harmonic excitation
(1996-07-04)
Ge, ZM
;
Chen, HH
;
機械工程學系
;
Department of Mechanical Engineering
Bifurcations and chaos in a rate gyro with harmonic excitation
(1996-07-04)
Ge, ZM
;
Chen, HH
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
Bifurcations and chaos of a two-degree-of-freedom dissipative gyroscope
(2005-04-01)
Chen, HK
;
Ge, ZM
;
機械工程學系
;
Department of Mechanical Engineering
The dynamic behaviors of a dissipative gyroscope mounted on a vibrating base are investigated qualitatively and numerically. It is shown that the nonlinear system can exhibit regular and chaotic motions. The qualitative behaviors of the system are studied by the center manifold theorem and the normal form theorem. The co-dimension one bifurcation analysis for the Hopf bifurcation is carried out. The pitchfork, Hopf, and saddle connection bifurcations for co-dimension two bifurcation are also found in this study. Regular and chaotic motions are shown to be possible in the parameter space. Numerical methods are used to obtain the time histories, the Poincare maps, the Liapunov exponents, and the Liapunov dimensions. The effect of the spin speed of the gyroscope on its dynamic behavior is also studied by numerical simulation in conjunction with the Liapunov exponents, and it has been found that the higher spin speed of the gyroscope can quench the chaotic motion. (C) 2004 Elsevier Ltd. All rights reserved.
Bifurcations and chaotic motions in a rate gyro with a sinusoidal velocity about the spin axis
(1997-02-20)
Ge, ZM
;
Chen, HH
;
機械工程學系
;
Department of Mechanical Engineering
An analysis is presented for a single-axis rate gyro mounted on a space vehicle undergoing sinusoidal motion and steady rotation about its spin and output axes. By varying the amplitude of sinusoidal motion, the periodic and chaotic responses of this parametrically excited non-linear system are investigated using the incremental harmonic balance (IHB) method and numerical integration. The multi-variable Floquet theory is applied to analyze the stability of periodic attractors and the behavior of bifurcations. Additionally, phase portraits, Poincare maps, average power spectra, bifurcation diagrams, parametric diagrams and Lyapunov exponents are presented to observe Hopf bifurcation, symmetry-breaking bifurcations, period-doubling bifurcations and chaotic motions. The cell mapping technique (MICM) is also used to study the basins of attraction of periodic attractors. (C) 1997 Academic Press Limited
Bifurcations and chaotic motions in a rate gyro with a sinusoidal velocity about the spin axis
(1997-02-20)
Ge, ZM
;
Chen, HH
;
交大名義發表
;
機械工程學系
;
National Chiao Tung University
An analysis is presented for a single-axis rate gyro mounted on a space vehicle undergoing sinusoidal motion and steady rotation about its spin and output axes. By varying the amplitude of sinusoidal motion, the periodic and chaotic responses of this parametrically excited non-linear system are investigated using the incremental harmonic balance (IHB) method and numerical integration. The multi-variable Floquet theory is applied to analyze the stability of periodic attractors and the behavior of bifurcations. Additionally, phase portraits, Poincare maps, average power spectra, bifurcation diagrams, parametric diagrams and Lyapunov exponents are presented to observe Hopf bifurcation, symmetry-breaking bifurcations, period-doubling bifurcations and chaotic motions. The cell mapping technique (MICM) is also used to study the basins of attraction of periodic attractors. (C) 1997 Academic Press Limited
Chaos anticontrol and synchronization of three time scales brushless DC motor system
(2004-12-01)
Ge, ZM
;
Cheng, JW
;
Chen, YS
;
機械工程學系
;
Department of Mechanical Engineering
Chaos anticontrol of three time scale brushless dc motors and chaos synchronization of different order systems are studied. Nondimensional dynamic equations of three time scale brushless DC motor system are presented. Using numerical results, such as phase diagram, bifurcation diagram, and Lyapunov exponent, periodic and chaotic motions can be observed. By adding constant term, periodic square wave, the periodic triangle wave, the periodic sawtooth wave, and kxx term, to achieve anticontrol of chaotic or periodic systems, it is found that more chaotic phenomena of the system can be observed. Then, by coupled terms and linearization of error dynamics, we obtain the partial synchronization of two different order systems, i.e. brushless DC motor system and rate gyroscope system. (C) 2004 Elsevier Ltd. All rights reserved.
Chaos synchronization and chaos anticontrol of a rotationally supported simple pendulum
(2004-03-01)
Ge, ZM
;
Yu, CY
;
Chen, YS
;
機械工程學系
;
Department of Mechanical Engineering
Chaos synchronization and anticontrol of a rotationally supported simple pendulum was studied in this paper. Different kinds of coupling terms are used to synchronize the two identical chaotic systems with different initial conditions. An observed-based scheme is also used to achieve synchronization. The results are demonstrated by phase portrait, Lyapunov exponent, Poincare maps and synchronization time. Next, in order to analyze the transient behavior of the synchronized systems, Euclidean distance is used to plot a figure with coupling strength versus the distance. The chaotic signals are used to mask the message function in the secure communication system. Finally, anticontrol of chaos is achieved by adding constant term, periodic term, impulse term, time-delay term and adaptive control.
Chaos synchronization and chaos anticontrol of a suspended track with moving loads
(2004-03-05)
Ge, ZM
;
Wu, HW
;
機械工程學系
;
Department of Mechanical Engineering
In this paper, we first study the chaotic synchronization phenomenon of the suspended track with moving load system and then the transient response of chaos synchronization. The Lyapunov exponent is utilized to prove the chaos synchronization, but under certain conditions it is more complicated. Next, we study the synchronization of autonomous and non-autonomous systems. We find that slave systems cannot be synchronized with master system for certain time excitations no matter how large A is. Next, the phase synchronization between them will be studied. An application of chaos synchronization and secure communication is presented. Finally, in order to increase the chaos phenomena, we use anticontrol. Constant torque, periodic torque, periodic impulse signal, time delay function, and adaptive control are used successfully to control the state from order to chaos. (C) 2003 Elsevier Science Ltd. All rights reserved.
Chaos synchronization and parameter identification for gyroscope system
(2005-04-15)
Ge, ZM
;
Lee, JK
;
機械工程學系
;
Department of Mechanical Engineering
Synchronization of chaos for a two-degree-of-freedom heavy symmetric gyroscope system are studied in this paper. Because of the nonlinear terms of the system, the system exhibits both regular and chaotic motions. By Lyapunov stability theory with control terms, by adaptive control and by random optimization method, the synchronization of two identical systems and tracking of the parameter of the systems are Studied. (c) 2004 Elsevier Inc. All rights reserved.
Chaos synchronization and parameter identification for loudspeaker systems
(2004-09-01)
Ge, ZM
;
Leu, WY
;
機械工程學系
;
Department of Mechanical Engineering
The identical two-degrees-of-freedom loudspeaker systems are discussed for synchronization of chaos in this paper. Two methods are used to synchronize two identical chaotic systems with different initial condition: the adaptive control and the Gerschgorin's theorem. Finally we research the parameter identification for two identical two-degrees-of-freedom loudspeaker systems by adaptive control and random optimization method. (C) 2004 Elsevier Ltd. All rights reserved.
Chaos synchronization and parameter identification of three time scales brushless DC motor system
(2005-04-01)
Ge, ZM
;
Cheng, JW
;
機械工程學系
;
Department of Mechanical Engineering
Chaotic anticontrol and chaos synchronization of brushless DC motor system are studied in this paper. Nondimensional dynamic equations of three time scale brushless DC motor system are presented. Using numerical results, such as phase diagram, bifurcation diagram, and Lyapunov exponent, periodic and chaotic motions can be observed. Then, chaos synchronization of two identical systems via additional inputs and Lyapunov stability theory are studied. And further, the parameter of the system is traced via adaptive control and random optimization method. (C) 2004 Elsevier Ltd. All rights reserved.