Representation of robotic fractional dynamics in the pseudo phase plane

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.

Short Term Stability Using Phase Plane

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.

Yaw controller design of stratospheric airship based on phase plane method

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.

Phase plane design based fast altitude tracking control for hypersonic flight vehicle with angle of attack constraint

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.

Phase-plane analysis of conserved higher-order traffic flow model

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.

ALTERNATIVE DESCRIPTION OF THE SHEAR PLANE OF THE R-PHASE

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.

Optical simulation of in-plane-switching blue phase liquid crystal display using the finite-difference time-domain method

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.

Phase and direction dependence of photorefraction in a low-frequency strong circular-polarized plane wave

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.

嫦娥六号环月飞行双环容错姿态控制

嫦娥六号着陆器和上升器组合体(着上组合体)环月飞行阶段,利用安装于上升器的10 N发动机(可形成力偶控制方式)和安装于着陆器的150 N发动机进行姿态控制。根据发动机安装布局,当力偶控制方式下某10 N发动机常关故障、其配对使用的10 N发动机正常工作时,推进系统将产生与期望相反的控制力矩,导致姿态发散。为了保证在10 N发动机故障情况下着上组合体姿态稳定,给出了双环容错姿态控制策略,包括10 N发动机内环控制和150 N发动机外环控制。数学仿真结果表明,着上组合体环月飞行阶段双环容错姿态控制下,10 N发动机故障后,着上组合体姿态可以稳定在给定范围内。针对配置力偶姿控发动机和冗余发动机的探测器,采用双环容错姿态控制策略,可以有效应对力偶姿控发动机故障影响,保证探测器姿态稳定。

分布式驱动车辆直接横摆力矩与转向控制

为了进一步提高车辆在转向行驶过程中的横向稳定性,针对分布式驱动电动汽车,提出了一种在分层集成架构下利用相平面法确定稳定区域控制车辆运动状态稳定的控制策略。由二自由度模型得到的理想侧向速度、理想横摆角速度与实际差值作为上层控制器输入值,上层控制器采用双滑膜控制器结构分别对理想侧向速度和理想横摆角速度进行追踪,分别得到控制量附加转角和附加横摆力矩;下层控制器主要依据相平面法得到的边界值协调控制转向控制和横摆力矩控制的输入输出值,通过最优分配算法将轮胎力和转向角分配到四轮,最终实现对车辆稳定性控制。对控制算法进行仿真验证,证明了所提控制策略的有效性和可行性。

考虑车辆稳定的避障路径自适应模型预测跟踪

为了提高车辆在稳定行驶前提下的避障路径跟踪控制精度,设计了自适应模型预测路径跟踪控制器和稳定控制器。根据车辆运动特性,建立了车辆在横向和横摆向共三个自由度的车辆动力学方程;基于路径跟踪控制需要,建立了预瞄跟踪控制模型。在避障路径跟踪方面,提出了预测时域随车速和路径曲率自适应变化方法;以提高避障路径跟踪精度和控制量增量最小为优化目标,将路径跟踪控制问题转化为二次型问题,实现了自适应优化求解和时域滚动控制。在车辆行驶稳定方面,从车辆状态的稳定性预判、稳定力矩的计算和分配等方面设计了稳定控制器。经仿真验证,这里的方法能够将车辆状态控制在相平面的双线法稳定区域内,实现了车辆行驶的稳定性和安全性;在避障路径跟踪方面,这里的方法的最大跟踪误差和绝对误差均值远小于传统模型预测控制、文献[14]模糊滑模控制,充分证明了这里的方法在避障路径跟踪控制中的高精度和有效性。

基于等效同步功率的孤岛并联构网变流器系统暂态稳定性分析

随着构网变流器在微电网中应用的增长,其对微电网暂态稳定的影响受到了广泛关注。不同于单机无穷大系统,孤岛并联构网变流器系统的频率和功角差相互耦合,暂态响应特性更为复杂。为精准分析孤岛并联构网变流器系统的暂态响应,文中基于功角耦合运动方程建立双机频率和功角差的三阶暂态同步模型,并且分析了双机出力差异和下垂系数对于暂态稳定的影响特征。为揭示出力和下垂系数对于暂态稳定的耦合机理,对双机系统进行等效同步功率分析,并且提出一种基于构网变流器出力的自适应下垂系数优化策略,可以根据出力差异自适应提升双机系统的等效同步功率,进而提升系统暂态稳定性。最后,采用实时仿真验证了三阶暂态模型的正确性和所提控制策略的有效性。

基于预警边界的线控转向主动安全控制研究

为提高传统线控转向车辆转向稳定性,提出一种基于相平面预警边界的主动安全控制策略。首先,建立质心侧偏角与质心侧偏角速度β-β相平面图;其次,针对传统相平面稳定区域划分所用双线法在低路面附着系数时存在不足,提出“平行四边形”边界法改善相平面稳定区域的划分,并以稳定域边界建立预警边界模型。然后基于预警边界设计线控转向主动安全控制器,设计预警度PID控制器和横摆角速度滑模控制器联合决策横摆力矩,以保持车辆稳定行驶,避免失稳状态从而起到主动安全作用;最后,结合Simulink和CarSim联合仿真结果表明,控制器能够有效避免线控转向车辆失稳,提高了主动安全性。

基于可拓相平面稳定域划分的Tube-MPC车辆稳定性控制

针对分布式四轮驱动电动车辆在极限工况下稳定性控制难题,考虑了横摆角速度、横纵向加速度等传感器噪声以及质心侧偏角估计误差的影响,提出了基于可拓理论的相平面稳定域划分方法以及自适应管道模型预测控制(ATMPC)算法,以快速量化车辆稳定性程度,并在满足跟踪精度的前提下保证车辆行驶的稳定性。所设计的车辆横摆稳定性控制系统采用分层设计架构,其中上层基于可拓理论,将车辆质心侧偏角-橫摆角速度相平面与可拓控制域相关联,并根据车辆实际状态判断可拓控制域并计算关联函数,实现了下层的管道模型预测控制(TubeMPC)控制目标权重与控制模式的决策;下层基于Tube-MPC对期望横摆角速度和质心侧偏角进行跟踪,实现附加横摆力矩的精准决策,之后采用轮胎负荷率优化方法进行横摆力矩的分配。通过CarSim与Simulink软件联合仿真,对所设计的控制策略进行仿真验证。结果表明,相较于常规MPC算法,所提出的控制架构与ATMPC控制策略能够有效提升车辆在极限工况下的行驶稳定性以及噪声干扰环境下的鲁棒性。

基于相平面的滑模/模糊协调控制方法研究

针对结构化道路下车辆高速、紧急、突发障碍物等工况下所带来的无人车路径规划中的失稳问题,提出了一种模糊控制与滑模变结构控制协调控制的策略。首先,采用了基于五次多项式的路径规划方法。采用一种基于MPC模型预测控制的车辆轨迹跟踪控制策略,通过控制前轮转角主动转向来控制车辆换道。提出了一种滑模控制器与模糊控制器协调控制的控制策略,通过相平面法确定稳定边界方程,然后将边界方程介入控制器,并通过差动制动将横摆力矩合理分配到各车轮。通过Matlab与Carsim联合仿真,设计了不同的仿真工况。结果表明,车辆在高速、紧急的行驶工况下,这里所设计的协调控制方法,能够有效的提高车辆的轨迹跟踪性能与车辆路径规划中的稳定性和安全性。

侧风干扰下汽车稳定性控制研究

文章针对高速行驶的汽车在侧风干扰下易发生横摆失稳与驶离预定路径的问题,建立了考虑侧风作用的整车八自由度动力学模型,并利用相平面法,识别侧风环境中汽车所处的状态,设计了主动前轮转向(AFS)与直接横摆力矩(DYC)协调控制器,对侧风环境中汽车行驶进行稳定性控制。在侧风干扰工况下,对控制算法进行仿真验证,结果表明:具有AFS与DYC协调控制器车辆的侧向位移小于无控制及单一控制器的车辆,横摆角速度、质心侧偏角和侧向加速度均得到明显改善,提高了车辆在侧风环境中行驶的安全性和稳定性。

基于幅相复平面的空管雷达测高方法研究

针对两坐标体制的空管一次雷达对目标高度测量需求,提出了一种基于幅相复平面的空管一次雷达测高方法.利用高低双波束幅相差构建复平面,在复平面-仰角形成的复空间内形成拟合曲线,通过待测样本的高低波束幅相差值在三维拟合曲线进行插值,从而得到目标仰角,进而结合目标距离获得目标高度.实录数据统计分析表明,相比传统的比相测角方法,该方法在对低仰角和低信噪比目标的仰角测量精度上具有明显优势.

基于相空间重构的中性点非有效接地系统铁磁谐振故障辨识研究

准确辨识铁磁谐振故障是启动微机消谐装置的前提,而现有时频分析方法提取铁磁谐振过电压信号特征时存在容易误判和相邻频率模态相互混叠的缺点。针对上述问题,从铁磁谐振过电压时间序列的混沌特征出发,提出了基于相空间重构的中性点非有效接地系统铁磁谐振故障辨识方法。首先利用C-C法计算相空间重构的特征参数(嵌入维数、延迟时间),然后通过相空间重构技术将过电压时间序列引入到高维空间,分析重构吸引子相平面轨迹的属性特征(关联维数、点分布因数)和几何特征(矢径偏移、中心距),并揭示了不同铁磁谐振类型重构相平面轨迹特征。最后,引入K值作为4种特征量变化规律的特征参数,结合特征量变化规律给出不同类型铁磁谐振的参考K值,以此作为谐振判据进而辨识谐振类型。通过仿真分析和云南某10 kV配电系统发生的铁磁谐振实例验证了所提方法的可行性。

极限工况下AFS与DYC可拓协调控制

主动前轮转向系统(AFS)和直接横摆力矩控制(DYC)集成控制可提高商用货车的操纵稳定性。由于主动前轮转向在轮胎非线性区作用效果有限,与直接横摆力矩控制简单叠加的控制效果不一定能达到预期,为此这里设计了可拓协调控制系统。该系统分为上、中、下三层,上层为AFS与DYC协调切换控制层。采用试验法得到前轮临界转角,根据线性二自由度车辆模型反推临界转角下的稳态质心侧偏角,结合车辆实际质心侧偏角及其速度的相平面稳定域将相平面图分区,设计了3种不同协调控制策略;中层是基于指数趋近律设计的AFS与DYC滑模控制器,可得到前轮附加转角和附加横摆力矩;附加横摆力矩由下层控制器根据车辆实时状态进行制动力分配。采用TruckSim、Matlab/Simulink建立联合仿真平台,在极限工况下进行仿真验证可拓协调控制系统。仿真结果得到最优可拓协调策略,该协调控制弥补了AFS/DYC单一控制的缺陷,可保证车辆的操纵稳定性和行驶安全性。

基于混合相位的多平面全息显示

在计算全息术中,基于层析法实现多平面全息显示是最常用的方法之一。针对层析法中多个平面之间存在串扰的问题,本文结合随机相位和二次相位的优点,提出了一种基于混合相位的多平面全息显示方法。首先,选择合适的权重因子生成混合相位代替随机相位作为初始相位。利用迭代傅里叶变换算法进行迭代后,将获得的每个子全息图与具有不同重建距离的菲涅尔波带片叠加,接着将每个全息图以复振幅叠加,获取相位后得到纯相位全息图,从而将分层图像重构于指定的平面上。利用硅基液晶空间光调制器搭建多平面全息显示系统开展了相关的光学实验。实验结果表明,与基于随机相位的方法相比,本文方法提高了结构相似性参数(最高可达4.6%),减弱了多个全息重构平面之间的串扰,提高了多平面全息显示的再现质量。