Recently, stratospheric airships prefer to employ a vectored tail rotor or differential main propellers for the yaw control, rather than the control surfaces like common low-altitude airship. The load capacity of vect...Recently, stratospheric airships prefer to employ a vectored tail rotor or differential main propellers for the yaw control, rather than the control surfaces like common low-altitude airship. The load capacity of vectored mechanism and propellers are always limited by the weight and strength, which bring challenges for the attitude controller. In this paper, the yaw channel of airship dynamics is firstly rewritten as a simplified two-order dynamics equation and the dynamic charac- teristics is analyzed with a phase plane method. Analysis shows that when ignoring damping, the yaw control channel is available to the minimum principle of Pontryagin for optimal control, which can obtain a Bang-Bang controller. But under this controller, the control output could he bouncing around the theoretical switch curve due to the presence of disturbance and damping, which makes adverse effects for the servo structure. Considering the structure requirements of actuators, a phase plane method controller is employed, with a dead zone surrounded by several phase switch curve. Thus, the controller outputs are limited to finite values. Finally, through the numerical simulation and actual flight experiment, the method is proved to be effective.展开更多
This paper analyses robotic signals in the perspective of fractional dynamics and the pseudo phase plane （PPP）.It is shown that the spectra of several experimental signals can be approximated by trend lines whose sl...This paper analyses robotic signals in the perspective of fractional dynamics and the pseudo phase plane （PPP）.It is shown that the spectra of several experimental signals can be approximated by trend lines whose slope characterizes their fractional behavior.For the PPP reconstruction of each signal,the time lags are calculated through the fractal dimension.Moreover,to obtain a smooth PPP,the noisy signals are filtered through wavelets.The behavior of the spectra reveals a relationship with the fractal dimension of the PPP and the corresponding time delay.展开更多
In this paper, fast setpoint altitude tracking control for Hypersonic Flight Vehicle(HFV)satisfying Angle of Attack(AOA) constraint is studied with a two-loop structure controller, in the presence of parameter uncerta...In this paper, fast setpoint altitude tracking control for Hypersonic Flight Vehicle(HFV)satisfying Angle of Attack(AOA) constraint is studied with a two-loop structure controller, in the presence of parameter uncertainties and disturbances. For the outer loop, phase plane design is adopted for the simplified model under Bang-Bang controller to generate AOA command guaranteeing fast tracking performance. Modifications based on Feedback-Linearization(FL) technique are adopted to transform the phase trajectory into a sliding curve. Moreover, to resist mismatch between design model and actual model, Fast Exponential Reaching Law(FERL) is augmented with the baseline controller to maintain state on the sliding curve. The inner-loop controller is based on backstepping technique to track the AOA command generated by outer-loop controller. Barrier Lyapunov Function(BLF) design is employed to satisfy AOA requirement. Moreover, a novel auxiliary state is introduced to remove the restriction of BLF design on initial tracking errors. Dynamic Surface Control(DSC) is utilized to ease the computation burden. Rigorous stability proof is then given, and AOA is guaranteed to stay in predefined region theoretically. Simulations are conducted to verify the efficiency and superior performance of the proposed method.展开更多
One of the most important problems in the study of transient stability of power systems is the determination of perturbation’s maximum time of permanence without losing the synchronism of the generators that feed the...One of the most important problems in the study of transient stability of power systems is the determination of perturbation’s maximum time of permanence without losing the synchronism of the generators that feed the network. The problem is generally solved by either the application of the equal-area criterion or through numerical integration methods. In the present work, the phase-plane is proposed as an alternative tool to solve the above-mentioned problem with greater efficiency.展开更多
We investigate phase-plane analysis of general relativistic orbits in a gravitational field of the Reissner–Nordstr?m-type regular black hole spacetime.We employ phase-plane analysis to obtain different phase-plane d...We investigate phase-plane analysis of general relativistic orbits in a gravitational field of the Reissner–Nordstr?m-type regular black hole spacetime.We employ phase-plane analysis to obtain different phase-plane diagrams of the test particle orbits by varying charge q and dimensionless parameterβ,whereβcontains angular momentum of the test particle.We compute numerical values of radii for the innermost stable orbits and corresponding values of energy required to place the test particle in orbits.Later on,we employ similar analysis on an Ayón–Beato–García(ABG)regular black hole and a comparison regarding key results is also included.展开更多
The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of t...The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.展开更多
A high density of {110} shear planes has been observed in the R-phase (Al5CuLi3)following phase transformation from the AlCuLi icosahedral Phase. The Present paper shows that the atomic arrangement in the vicinity of ...A high density of {110} shear planes has been observed in the R-phase (Al5CuLi3)following phase transformation from the AlCuLi icosahedral Phase. The Present paper shows that the atomic arrangement in the vicinity of the shear planes can be described as a two-dimensional periodic array of atom clusters with 5-fold symmetry. This result is obtained by projecting along the [1. 618...01] direction of the atomic positions from four adjacent lattice planes that cross the shear plane. The projection reveals that the shear plane consists of pentagonal arrangements of double triacontahedra,each pentagon incorporating 606 atoms. The calculated diffraction pattern from the pentagon has approximate 10-fold symmetry characteristic of a quasicrystal.展开更多
The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the ...The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.展开更多
Contrary to the superposition principle, it is well known that photorefraction exists in the vacuum with the presence of a strong static field, a laser field, or a rotational magnetic field. Different from the classic...Contrary to the superposition principle, it is well known that photorefraction exists in the vacuum with the presence of a strong static field, a laser field, or a rotational magnetic field. Different from the classical optical crystals, the refractive index also depends on the phase of the strong electromagnetic field. We obtain the phase and direction dependence of the refractive index of a probe wave incident in the strong field of a circular-polarized plane wave by solving the Maxwell equations corrected by the effective Lagrangian. It may provide a valuable theoretical basis to calculate the polarization evolution of waves in the strong electromagnetic circumstances of pulsar or neutron stars.展开更多
基金sponsored by the National Defense Science and Technology Innovation Fund Projects of Chinese Academy of Science(No.CXJJ-14-M06)
文摘Recently, stratospheric airships prefer to employ a vectored tail rotor or differential main propellers for the yaw control, rather than the control surfaces like common low-altitude airship. The load capacity of vectored mechanism and propellers are always limited by the weight and strength, which bring challenges for the attitude controller. In this paper, the yaw channel of airship dynamics is firstly rewritten as a simplified two-order dynamics equation and the dynamic charac- teristics is analyzed with a phase plane method. Analysis shows that when ignoring damping, the yaw control channel is available to the minimum principle of Pontryagin for optimal control, which can obtain a Bang-Bang controller. But under this controller, the control output could he bouncing around the theoretical switch curve due to the presence of disturbance and damping, which makes adverse effects for the servo structure. Considering the structure requirements of actuators, a phase plane method controller is employed, with a dead zone surrounded by several phase switch curve. Thus, the controller outputs are limited to finite values. Finally, through the numerical simulation and actual flight experiment, the method is proved to be effective.
文摘This paper analyses robotic signals in the perspective of fractional dynamics and the pseudo phase plane （PPP）.It is shown that the spectra of several experimental signals can be approximated by trend lines whose slope characterizes their fractional behavior.For the PPP reconstruction of each signal,the time lags are calculated through the fractal dimension.Moreover,to obtain a smooth PPP,the noisy signals are filtered through wavelets.The behavior of the spectra reveals a relationship with the fractal dimension of the PPP and the corresponding time delay.
基金supported by the National Natural Science Foundation of China (Nos. 61833016, 61873295, 61622308and 61933010)。
文摘In this paper, fast setpoint altitude tracking control for Hypersonic Flight Vehicle(HFV)satisfying Angle of Attack(AOA) constraint is studied with a two-loop structure controller, in the presence of parameter uncertainties and disturbances. For the outer loop, phase plane design is adopted for the simplified model under Bang-Bang controller to generate AOA command guaranteeing fast tracking performance. Modifications based on Feedback-Linearization(FL) technique are adopted to transform the phase trajectory into a sliding curve. Moreover, to resist mismatch between design model and actual model, Fast Exponential Reaching Law(FERL) is augmented with the baseline controller to maintain state on the sliding curve. The inner-loop controller is based on backstepping technique to track the AOA command generated by outer-loop controller. Barrier Lyapunov Function(BLF) design is employed to satisfy AOA requirement. Moreover, a novel auxiliary state is introduced to remove the restriction of BLF design on initial tracking errors. Dynamic Surface Control(DSC) is utilized to ease the computation burden. Rigorous stability proof is then given, and AOA is guaranteed to stay in predefined region theoretically. Simulations are conducted to verify the efficiency and superior performance of the proposed method.
文摘One of the most important problems in the study of transient stability of power systems is the determination of perturbation’s maximum time of permanence without losing the synchronism of the generators that feed the network. The problem is generally solved by either the application of the equal-area criterion or through numerical integration methods. In the present work, the phase-plane is proposed as an alternative tool to solve the above-mentioned problem with greater efficiency.
基金the University of KwaZulu-Natalthe National Research Foundation for financial support.
文摘We investigate phase-plane analysis of general relativistic orbits in a gravitational field of the Reissner–Nordstr?m-type regular black hole spacetime.We employ phase-plane analysis to obtain different phase-plane diagrams of the test particle orbits by varying charge q and dimensionless parameterβ,whereβcontains angular momentum of the test particle.We compute numerical values of radii for the innermost stable orbits and corresponding values of energy required to place the test particle in orbits.Later on,we employ similar analysis on an Ayón–Beato–García(ABG)regular black hole and a comparison regarding key results is also included.
基金Project supported by the National Natural Science Foundation of China(No.11072141)the Shanghai Program for Innovative Research Team in Universities,the Graduate Innovation Foundation of Shanghai University(No.SHUCX101078)and the University Research Committee,HKU SPACE Research Fund and Faculty of Engineering Top-up Grant of the University of Hong Kong(No.201007176059)
文摘The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.
文摘A high density of {110} shear planes has been observed in the R-phase (Al5CuLi3)following phase transformation from the AlCuLi icosahedral Phase. The Present paper shows that the atomic arrangement in the vicinity of the shear planes can be described as a two-dimensional periodic array of atom clusters with 5-fold symmetry. This result is obtained by projecting along the [1. 618...01] direction of the atomic positions from four adjacent lattice planes that cross the shear plane. The projection reveals that the shear plane consists of pentagonal arrangements of double triacontahedra,each pentagon incorporating 606 atoms. The calculated diffraction pattern from the pentagon has approximate 10-fold symmetry characteristic of a quasicrystal.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11304074,61475042,and 11274088)the Natural Science Foundation of Hebei Province,China(Grant Nos.A2015202320 and GCC2014048)the Key Subject Construction Project of Hebei Province University,China
文摘The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell＇s equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change.
基金supported by the National Basic Research Program of China(Grant No.2011CB808104)the National Natural Science Foundation of China(Grant No.11105233)
文摘Contrary to the superposition principle, it is well known that photorefraction exists in the vacuum with the presence of a strong static field, a laser field, or a rotational magnetic field. Different from the classical optical crystals, the refractive index also depends on the phase of the strong electromagnetic field. We obtain the phase and direction dependence of the refractive index of a probe wave incident in the strong field of a circular-polarized plane wave by solving the Maxwell equations corrected by the effective Lagrangian. It may provide a valuable theoretical basis to calculate the polarization evolution of waves in the strong electromagnetic circumstances of pulsar or neutron stars.
