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
The conventional phase plane method estimates the stability of vehicle systems using fixed inputs.This approach exhibits a clear inclination towards conservatism,potentially leading to unnecessary interference with th...The conventional phase plane method estimates the stability of vehicle systems using fixed inputs.This approach exhibits a clear inclination towards conservatism,potentially leading to unnecessary interference with the driver or failures in collision avoidance due to stringent limitations during emergency scenarios.To address the aforementioned issues,this study introduces a regression region constraint by extending the phase plane method.Subsequently,an emergency collision avoidance system(ECAS)is developed based on this regression region.According to the emergency degree of the scenario,ECAS system is divided into 2 modes:the immediate takeover mode and the risk monitoring mode.In the mode of immediate takeover,the system promptly substitutes the driver upon encountering obstacles and employs the collision avoidance algorithm based on optimal control and model predictive control to avoid collisions.When the vehicle states exceed the constraint of the regression region,the regression stability algorithm is triggered to make the vehicle regress to stability.In the risk monitoring mode,the driver avoids collision by himself,and the system monitors the vehicle states.The regression stability algorithm replaces the driver once the regression region constraint is reached.The performance of two intervention modes was validated based on the dSPACE HIL platform and G29 driving simulator correspondingly.The results suggest that the immediate takeover mode can be qualified for collision avoidance conditions with the longitudinal distance of 33.0 m at the speed of 30 m/s,while the shortest distance the existing studies can deal with is 37.5 m,and the risk monitoring mode can also successfully avoid unnecessary interference when the driver is competent.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
Taking Al-2%mole-Cu binary alloy as an example, the influence of grain orientation on competitive growth of dendrites under different competitive modes was investigated by using the three-dimensional(3-D) phasefield m...Taking Al-2%mole-Cu binary alloy as an example, the influence of grain orientation on competitive growth of dendrites under different competitive modes was investigated by using the three-dimensional(3-D) phasefield method. The result of phase-field simulation was verified by applying cold spray and directional remelting. In the simulation process, two competitive modes were designed: in Scheme 1, the monolayer columnar grains in multilayer columnar crystals had different orientations; while in Scheme 2, they had the same orientation. The simulation result showed that in Scheme 1, the growth of the dendrites, whose orientation had a certain included angle with the direction of temperature gradient, was restrained by the growth of other dendrites whose direction was parallel to the direction of temperature gradient. Moreover, the larger the included angle between the grain orientation and temperature gradient, the earlier the cessation of dendrite growth. The secondary dendrites of dendrites whose grain orientation was parallel to the temperature gradient flourished with increasing included angles between the grain orientation and temperature gradient. In Scheme 2, the greater the included angle between grain orientation and temperature gradient, the easier the dendrites whose orientation showed a certain included angle with temperature gradient inserted between those grew parallel to the temperature gradient, and the better the growth condition thereafter. Some growing dendrites after intercalation were deflected to the temperature gradient, and the greater the included angle, the lower the deflection. The morphologies of the competitive growth dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the two modes of competitive growth of dendrites characterized in the simulation do exist and frequently appear in practical solidification processes.展开更多
The hydrostatic-pressure-induced transition phase of BaS from the NaCl-type structure （B1） to the CsCl-type structure （B2） is investigated by ab initio plane-wave pseudopotential den-sity functional theory method....The hydrostatic-pressure-induced transition phase of BaS from the NaCl-type structure （B1） to the CsCl-type structure （B2） is investigated by ab initio plane-wave pseudopotential den-sity functional theory method. It is found that the transition pres-sure from B1 to B2 phases is 8.2 GPa according to the usual con-dition of equal enthalpy. Through the quasi-harmonic Debye model,the dependences of the relative volume V/V0 on the pres-sure P,the thermal expansion parameter ratio on pressure P,and the Debye temperature Θ and heat capacity CV on pressure P and temperature T are estimated.展开更多
This paper studies the viscid and inviscid fluid resonance in gaps of bottom mounted caissons onthe basis of the plane wave hypothesis and full wave model, The theoretical analysis and the numerical results demonstrat...This paper studies the viscid and inviscid fluid resonance in gaps of bottom mounted caissons onthe basis of the plane wave hypothesis and full wave model, The theoretical analysis and the numerical results demonstrate that the condition for the appearance of fluid resonance in narrow gaps is kh=（2n＋1）π （n=0, 1, 2, 3 ）, rather than kh=nn （n=0, 1, 2, 3, ...）; the transmission peaks in viscid fluid are related to the resonance peaks in the gaps. k and h stand for the wave number and the gap length. The combination of the plane wave hypothesis or the full wave model with the local viscosity model can accurately determine the heights and the locations of the resonance peaks. The upper bound for the appearance of fluid resonance in gaps is 2b/L〈l （2b, grating constant; L, wave length） and the lower bound is h/b〈~ l. The main reason for the phase shift of the resonance peaks is the inductive factors. The number of resonance peaks in the spectrum curve is dependent on the ratio of the gap length to the grating constant. The heights and the positions of the resonance peaks predicted by the present models agree well with the experimental data.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supported jointly by the National Natural Science Foundation of China(51875184,52202466,52262054)the Natural Science Foundation of Fujian Province(2023J01245).
文摘The conventional phase plane method estimates the stability of vehicle systems using fixed inputs.This approach exhibits a clear inclination towards conservatism,potentially leading to unnecessary interference with the driver or failures in collision avoidance due to stringent limitations during emergency scenarios.To address the aforementioned issues,this study introduces a regression region constraint by extending the phase plane method.Subsequently,an emergency collision avoidance system(ECAS)is developed based on this regression region.According to the emergency degree of the scenario,ECAS system is divided into 2 modes:the immediate takeover mode and the risk monitoring mode.In the mode of immediate takeover,the system promptly substitutes the driver upon encountering obstacles and employs the collision avoidance algorithm based on optimal control and model predictive control to avoid collisions.When the vehicle states exceed the constraint of the regression region,the regression stability algorithm is triggered to make the vehicle regress to stability.In the risk monitoring mode,the driver avoids collision by himself,and the system monitors the vehicle states.The regression stability algorithm replaces the driver once the regression region constraint is reached.The performance of two intervention modes was validated based on the dSPACE HIL platform and G29 driving simulator correspondingly.The results suggest that the immediate takeover mode can be qualified for collision avoidance conditions with the longitudinal distance of 33.0 m at the speed of 30 m/s,while the shortest distance the existing studies can deal with is 37.5 m,and the risk monitoring mode can also successfully avoid unnecessary interference when the driver is competent.
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.
基金funded by the National Natural Science Foundation of China(Grant Nos.:11504149,11364024,51661020)
文摘Taking Al-2%mole-Cu binary alloy as an example, the influence of grain orientation on competitive growth of dendrites under different competitive modes was investigated by using the three-dimensional(3-D) phasefield method. The result of phase-field simulation was verified by applying cold spray and directional remelting. In the simulation process, two competitive modes were designed: in Scheme 1, the monolayer columnar grains in multilayer columnar crystals had different orientations; while in Scheme 2, they had the same orientation. The simulation result showed that in Scheme 1, the growth of the dendrites, whose orientation had a certain included angle with the direction of temperature gradient, was restrained by the growth of other dendrites whose direction was parallel to the direction of temperature gradient. Moreover, the larger the included angle between the grain orientation and temperature gradient, the earlier the cessation of dendrite growth. The secondary dendrites of dendrites whose grain orientation was parallel to the temperature gradient flourished with increasing included angles between the grain orientation and temperature gradient. In Scheme 2, the greater the included angle between grain orientation and temperature gradient, the easier the dendrites whose orientation showed a certain included angle with temperature gradient inserted between those grew parallel to the temperature gradient, and the better the growth condition thereafter. Some growing dendrites after intercalation were deflected to the temperature gradient, and the greater the included angle, the lower the deflection. The morphologies of the competitive growth dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the two modes of competitive growth of dendrites characterized in the simulation do exist and frequently appear in practical solidification processes.
基金Supported by the Natural Science Foundation of the Education Department of Henan Province of China (2009B590001)the Research Project of Henan Science and Technology Agency of China (092102210314)
文摘The hydrostatic-pressure-induced transition phase of BaS from the NaCl-type structure （B1） to the CsCl-type structure （B2） is investigated by ab initio plane-wave pseudopotential den-sity functional theory method. It is found that the transition pres-sure from B1 to B2 phases is 8.2 GPa according to the usual con-dition of equal enthalpy. Through the quasi-harmonic Debye model,the dependences of the relative volume V/V0 on the pres-sure P,the thermal expansion parameter ratio on pressure P,and the Debye temperature Θ and heat capacity CV on pressure P and temperature T are estimated.
基金financially supported by the National Key R&D Program of China(Grant No.2017YFC0405402)
文摘This paper studies the viscid and inviscid fluid resonance in gaps of bottom mounted caissons onthe basis of the plane wave hypothesis and full wave model, The theoretical analysis and the numerical results demonstrate that the condition for the appearance of fluid resonance in narrow gaps is kh=（2n＋1）π （n=0, 1, 2, 3 ）, rather than kh=nn （n=0, 1, 2, 3, ...）; the transmission peaks in viscid fluid are related to the resonance peaks in the gaps. k and h stand for the wave number and the gap length. The combination of the plane wave hypothesis or the full wave model with the local viscosity model can accurately determine the heights and the locations of the resonance peaks. The upper bound for the appearance of fluid resonance in gaps is 2b/L〈l （2b, grating constant; L, wave length） and the lower bound is h/b〈~ l. The main reason for the phase shift of the resonance peaks is the inductive factors. The number of resonance peaks in the spectrum curve is dependent on the ratio of the gap length to the grating constant. The heights and the positions of the resonance peaks predicted by the present models agree well with the experimental data.
