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
Partial agglomeration is a major problem in fluidized beds. A chaotic analytical method based on the phase-plane invariant of the pressure fluctuations in the fluidized beds has been used to warn of agglomeration at a...Partial agglomeration is a major problem in fluidized beds. A chaotic analytical method based on the phase-plane invariant of the pressure fluctuations in the fluidized beds has been used to warn of agglomeration at an early stage. Cold tests （no combustion） and hot tests （combustion） in fluidized beds show that the phase-plane invariant of the pressure fluctuations can distinguish the dynamic behavior of fluidized beds with different flow rates in cold tests. With combustion, when the flow rate was kept constant, agglomeration was detected very early by looking at the phase-plane invariant. The phase-plane invariant can be used to distinguish changes in fluidized beds due to changes in the flow rate, agglomeration, or various other factors. Therefore, this reliable agglomeration early warning system can be used for better control of circulating fluidized beds.展开更多
在无人矿用卡车的轨迹跟踪任务中,露天矿的地形信息繁杂且路面类型多样,导致跟踪精度与横向稳定性之间的矛盾突出;此外,无人矿卡轮地交互的动力学特性复杂,矿卡的轨迹跟踪面临建模难度大的挑战。针对以上问题,提出了一种基于稳定性评价...在无人矿用卡车的轨迹跟踪任务中,露天矿的地形信息繁杂且路面类型多样,导致跟踪精度与横向稳定性之间的矛盾突出;此外,无人矿卡轮地交互的动力学特性复杂,矿卡的轨迹跟踪面临建模难度大的挑战。针对以上问题,提出了一种基于稳定性评价的无模型自适应控制(Stability-based Model Free Adaptive Control,SMFAC)方法,以数据驱动的方式实现对行驶稳定性和跟踪精确性的协调控制。在Pacejka轮胎公式的基础上引入路面附着系数对矿卡的影响,结合简化的动力学方程构建矿卡的质心侧偏角-质心侧偏角速度相平面,并对不同环境工况的稳定域边界实现动态辨识,实时求解矿卡的稳定系数。基于径向基网络构建Actor-Critic无模型轨迹跟踪控制器,Actor网络依据系统状态计算控制量,Critic网络评估实时控制量的价值并对价值函数进行拟合;结合稳定系数设计学习过程中的网络误差,以最小化误差函数为目标求解隐藏层权值的更新律,通过矿卡与环境的交互迭代出轨迹跟踪的最优策略。基于CarSim与MATLAB/Simulink搭建轨迹跟踪联合仿真系统,以验证所提出的SMFAC方法的有效性。结果表明:相比于无模型的PID算法与有模型的MPC与LQR算法,所提方法在低速与高速的情况下均可兼顾角度跟踪精度与横向跟踪精度,在双移线、单移线、曲线工况中均取得最优轨迹跟踪性能。此外,SMFAC方法可抑制输出动作的波动,生成较为平滑的行驶轨迹,保障了无人矿卡的操纵稳定性。展开更多
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.
基金the Ishikawajima-Harima Heavy Industries Co., Ltd., Japan
文摘Partial agglomeration is a major problem in fluidized beds. A chaotic analytical method based on the phase-plane invariant of the pressure fluctuations in the fluidized beds has been used to warn of agglomeration at an early stage. Cold tests （no combustion） and hot tests （combustion） in fluidized beds show that the phase-plane invariant of the pressure fluctuations can distinguish the dynamic behavior of fluidized beds with different flow rates in cold tests. With combustion, when the flow rate was kept constant, agglomeration was detected very early by looking at the phase-plane invariant. The phase-plane invariant can be used to distinguish changes in fluidized beds due to changes in the flow rate, agglomeration, or various other factors. Therefore, this reliable agglomeration early warning system can be used for better control of circulating fluidized beds.
文摘在无人矿用卡车的轨迹跟踪任务中,露天矿的地形信息繁杂且路面类型多样,导致跟踪精度与横向稳定性之间的矛盾突出;此外,无人矿卡轮地交互的动力学特性复杂,矿卡的轨迹跟踪面临建模难度大的挑战。针对以上问题,提出了一种基于稳定性评价的无模型自适应控制(Stability-based Model Free Adaptive Control,SMFAC)方法,以数据驱动的方式实现对行驶稳定性和跟踪精确性的协调控制。在Pacejka轮胎公式的基础上引入路面附着系数对矿卡的影响,结合简化的动力学方程构建矿卡的质心侧偏角-质心侧偏角速度相平面,并对不同环境工况的稳定域边界实现动态辨识,实时求解矿卡的稳定系数。基于径向基网络构建Actor-Critic无模型轨迹跟踪控制器,Actor网络依据系统状态计算控制量,Critic网络评估实时控制量的价值并对价值函数进行拟合;结合稳定系数设计学习过程中的网络误差,以最小化误差函数为目标求解隐藏层权值的更新律,通过矿卡与环境的交互迭代出轨迹跟踪的最优策略。基于CarSim与MATLAB/Simulink搭建轨迹跟踪联合仿真系统,以验证所提出的SMFAC方法的有效性。结果表明:相比于无模型的PID算法与有模型的MPC与LQR算法,所提方法在低速与高速的情况下均可兼顾角度跟踪精度与横向跟踪精度,在双移线、单移线、曲线工况中均取得最优轨迹跟踪性能。此外,SMFAC方法可抑制输出动作的波动,生成较为平滑的行驶轨迹,保障了无人矿卡的操纵稳定性。
