The Non-Singular Fast Terminal Sliding Mode Control of Interior Permanent Magnet Synchronous Motor Based on Deep Flux Weakening Switching Point Tracking

This paper presents a novel non-singular fast terminal sliding mode control(NFTSMC)based on the deep flux weakening switching point tracking method in order to improve the control performance of permanent interior magnet synchronous motor(IPMSM)drive systems.The mathematical model of flux weakening(FW)control is established,and the deep flux weakening switching point is calculated accurately by analyzing the relationship between the torque curve and voltage decline curve.Next,a second-order NFTSMC is designed for the speed loop controller to ensure that the system converges to the equilibrium state in finite time.Then,an extended sliding mode disturbance observer(ESMDO)is designed to estimate the uncertainty of the system.Finally,compared with both the PI control and sliding mode control(SMC)by simulations and experiments with different working conditions,the method proposed has the merits of accelerating convergence,improving steady-state accuracy,and minimizing the current and torque pulsation.

On non-singular GRADELA crack fields

A brief account is provided on crack-tip solutions that have recently been published in the literature by employing the so-called GRADELA model and its variants. The GRADELA model is a simple gradient elasticity theory involving one internal length in addition to the two Lame＇ constants, in an effort to eliminate elastic singularities and discontinuities and to interpret elastic size effects. The non-singular strains and non-singular （but sometimes singular or even hypersingular） stresses derived this way under different boundary conditions differ from each other and their physical meaning in not clear. This is discussed which focus on the form and physical meaning of non-singular solutions for crack-tip stresses and strains that are possible to obtain within the GRADELA model and its extensions.

Inconsistence of Non-Singular Spherically Symmetric Solution and a Satisfactory Energy-Momentum Complex

Two spherically symmetric non-singular black hole solutions in Moiler tetrad theory of gravitation have been obtained. Although the two solutions have the same form of metric （spherically symmetric nonsingular black hole）, their energy contents are different. We use another method given by Gibbons and Hawking to calculate the energy content of these solutions. We also obtained different value of energy. Study the requirements of a satisfactory energymomentum complex given by Moiler we find that the second solution, which behaves as 1/√r, is not transformed as a four-vector under Lorentz transformation.

Non-Singular Trees, Unicyclic Graphs and Bicyclic Graphs

We called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, as we all know, each connected bicyclic graph must contain ∞(a,s,b) or?θ(p,l,q) as the induced subgraph. In this paper, by using three graph transformations which do not change the singularity of the graph, the non-singular trees, unicyclic graphs and bicyclic graphs are obtained.

Creation of a Non-Expanding, Non-Singular Universe

A theory of gravitation in flat space-time is applied to homogeneous, isotropic cosmological models. There are non-singular cosmological models. A natural interpretation is a non-expanding universe. The redshift is an intrinsic effect and not a Doppler effect. The universe contains only energy in the beginning, i.e. no matter exists. In the course of time matter and radiation are created from energy where the whole energy is conserved. Matter increases with time but a certain time after the beginning of the universe the creation of matter is finished and the universe appears like a static one. A modified Hubble law is considered which may explain the high redshifts of objects in the universe without the assumption of dark energy.

A Proof of the Non-Singularity of the <i>D</i>Matrix Used in Deriving the Two—Step Butcher’s Hybrid Scheme for the Solution of Initial Value Problems

In this paper, we state and prove the conditions for the non-singularity of the D matrix used in deriving the continuous form of the Two-step Butcher’s hybrid scheme and from it the discrete forms are deduced. We also show that the discrete scheme gives outstanding results for the solution of stiff and non-stiff initial value problems than the 5th order Butcher’s algorithm in predictor-corrector form.

基于改进非线性滑模控制的轮式机器人轨迹跟踪

针对轮式机器人的轨迹跟踪控制存在的问题,设计了一种改进非线性快速终端滑模控制器(improved nonlinear fast terminal sliding mode controller,INFTSMC)的控制方案。首先,通过对轮式机器人运动学的分析建立了轨迹跟踪误差模型;其次,在设计滑模控制器阶段,针对非线性快速终端滑模控制器存在奇异点,采用一种新的滑模面幂指数时变策略来设计非奇异终端滑模控制器,解决了非线性快速终端滑模控制器奇异问题,通过构造Lyapunov函数进行稳定性分析证明了该策略的稳定性,并且进行收敛时间分析给出系统从任意初始状态收敛至平衡点所需要的时间;然后,在新的滑模面幂指数时变策略的基础上设计了轮式机器人线速度和角速度控制律,使得轮式机器人轨迹跟踪误差快速收敛至0,实现了移动机器人对期望轨迹的快速跟踪。通过仿真实验与非线性快速终端滑模控制器和传统滑模控制其进行对比,验证了改进非线性快速终端滑模控制器的优越性。

基于奇异摄动分解的带机械臂旋翼无人机飞行稳定性研究

为了降低无人机和机械臂之间的耦合作用,提高带臂四旋翼无人机飞行过程中的稳定性,首先建立系统动力学模型,然后根据实际情况,对模型进行简化。在此基础上进行内、外环分解,外环为四旋翼位置控制和机械臂角度控制,内环为四旋翼俯仰角控制。对于外环的动力学模型,根据速度变化特点,利用奇异摄动理论对外环变量,即四旋翼线速度和机械臂角速度,进行快、慢变子系统分解,再次降低了系统间的耦合性。对于分解后的快、慢变子系统,设计非奇异终端滑模控制并引入干扰观测器,以期提高带臂四旋翼无人机飞行过程中的稳定性。最后,仿真验证了所设计算法的优越性。

A Novel Disturbance Observer Based Fixed-Time Sliding Mode Control for Robotic Manipulators With Global Fast Convergence

This paper proposes a new global fixed-time sliding mode control strategy for the trajectory tracking control of uncertain robotic manipulators.First,a fixed-time disturbance observer(FTDO) is designed to deal with the adverse effects of model uncertainties and external disturbances in the manipulator systems.Then an adaptive scheme is used and the adaptive FTDO(AFTDO) is developed,so that the priori knowledge of the lumped disturbance is not required.Further,a new non-singular fast terminal sliding mode(NFTSM) surface is designed by using an arctan function,which helps to overcome the singularity problem and enhance the robustness of the system.Based on the estimation of the lumped disturbance by the AFTDO,a fixed-time non-singular fast terminal sliding mode controller(FTNFTSMC)is developed to guarantee the trajectory tracking errors converge to zero within a fixed time.The settling time is independent of the initial state of the system.In addition,the stability of the AFTDO and FTNFTSMC is strictly proved by using Lyapunov method.Finally,the fixed-time NFESM(FTNFTSM) algorithm is validated on a 2-link manipulator and comparisons with other existing sliding mode controllers(SMCs) are performed.The comparative results confirm that the FTNFTSMC has superior control performance.

Evolutionary Safe Padé Approximation Scheme for Dynamical Study of Nonlinear Cervical Human Papilloma Virus Infection Model

This study proposes a structure-preserving evolutionary framework to find a semi-analytical approximate solution for a nonlinear cervical cancer epidemic(CCE)model.The underlying CCE model lacks a closed-form exact solution.Numerical solutions obtained through traditional finite difference schemes do not ensure the preservation of the model’s necessary properties,such as positivity,boundedness,and feasibility.Therefore,the development of structure-preserving semi-analytical approaches is always necessary.This research introduces an intelligently supervised computational paradigm to solve the underlying CCE model’s physical properties by formulating an equivalent unconstrained optimization problem.Singularity-free safe Padérational functions approximate the mathematical shape of state variables,while the model’s physical requirements are treated as problem constraints.The primary model of the governing differential equations is imposed to minimize the error between approximate solutions.An evolutionary algorithm,the Genetic Algorithm with Multi-Parent Crossover(GA-MPC),executes the optimization task.The resulting method is the Evolutionary Safe PadéApproximation(ESPA)scheme.The proof of unconditional convergence of the ESPA scheme on the CCE model is supported by numerical simulations.The performance of the ESPA scheme on the CCE model is thoroughly investigated by considering various orders of non-singular Padéapproximants.

永磁同步电机非线性增益非奇异快速终端滑模控制

为了研究传统滑模控制中系统误差在有限时间内无法收敛至0以及传统滑模控制中系统抖振与收敛速度互不兼容的问题,提出一种非奇异快速终端滑模控制与扰动观测器结合的速度控制器。通过将参数可变的非线性函数作为增益代替固定增益加入滑模控制策略中从而改善系统响应速度同时减小系统的抖振。针对转矩扰动对系统的影响,加入负载转矩扰动观测器并补偿到q轴电流中以进一步提高控制器抗负载扰动能力。根据李雅普诺夫稳定性理论对提出的新型滑模控制器进行稳定性证明,经过仿真和实验证明,电机在启动时响应快、无超调且抖振较小,在突加转矩时转速波动小且恢复时间迅速,证明了改进后的变增益非奇异终端滑模控制与传统非奇异快速终端滑模控制策略相比可以提高动态性能的同时抑制系统抖振、增强系统的鲁棒性。

一种新型永磁同步电机高阶滑模控制算法

针对永磁同步电机控制系统易因外部扰动等不确定性影响而导致控制性能下降的问题,提出了一种基于改进自适应非奇异终端滑模控制器和滑模扰动观测器补偿技术的复合控制算法。选择新型自适应指数趋近律设计非奇异终端滑模转速环控制器,新型趋近律可以在保证减少抖振的同时保证控制系统能够快速收敛,可动态适应被控系统的变化;利用扩展滑模扰动观测器实时估计系统中不确定性参数,并对控制器进行前馈补偿,且通过Lyapunov函数证明了其稳定性。仿真和试验结果表明,与PI控制、传统滑模控制方法相比,所提方法有效改善了抖振问题,提高了控制系统对电机的控制精度,提升了系统的鲁棒性和抗干扰性能。

基于自回归小波神经网络的机械臂自适应滑模控制

针对机械臂存在模型不确定和未知扰动的问题,提出一种动力学模型参数分块逼近的神经网络非奇异终端滑模(nonsingular terminal sliding mode, NTSM)控制方法.为加快系统跟踪误差的收敛速度,避免传统终端滑模存在的奇异性问题,采用一种非奇异终端滑模面.利用多组自回归小波神经网络(self-recurrent wavelet neural network, SRWNN)分块逼近系统未知的动力学模型参数,并采用自适应更新律调整权重.通过积分控制项补偿SRWNN的逼近误差,并使用Lyapunov稳定性理论证明了系统稳定性.使用MATLAB进行仿真分析,分块SRWNN滑模控制与滑模控制、整体SRWNN滑模控制相比,关节角度跟踪误差的平均稳态误差分别降低了31.9%、76.5%,表明此方法是一种可靠、有效的轨迹跟踪控制方法.

NFTSM控制的光伏并网系统低压穿越控制策略

针对现有PI与ISMC控制下光伏并网系统LVRT过程响应速度慢、不对称故障时控制效果较差或抖振效果明显等问题,提出一种NFTSM控制的LVRT控制策略。考虑光伏并网系统外部条件多变的特性,采用双指数滑模超平面与控制率,选取指数趋近律加速趋近速率,构造出具有调节有功、无功输出的非奇异快速滑模控制器,并验证其稳定与收敛性,简单且有效地实现了光伏并网LVRT。Matlab/Simulink仿真结果表明,NFTSM控制的光伏并网LVRT具有收敛速度快、谐波含量低、抗外界干扰与抖振抑制能力强等优点。

基于混沌的H桥逆变器的非奇异终端滑膜控制

针对逆变器的分岔和混沌现象,建立逆变器的离散模型,通过分岔图、Lyapunov指数和折叠图分析非线性行为,并计算出系统的稳定运行范围及混沌运行范围。文中提出一种非奇异终端滑膜控制策略,设计切换面函数,推导逆变器的反馈控制律。最后进行仿真,仿真结果表明:非奇异滑膜控制能够有效抑制系统的混沌行为,从而拓宽了系统稳定工作范围,相比于比例积分控制(proportional integral derivative,PI),稳定范围扩大了80%。由此可以使得逆变器实现稳定工作,有很强的实际应用价值。

弱电网下基于超螺旋滑模的LCL并网逆变器控制研究

针对LCL型滤波器的固有谐振、滤波器参数及弱电网下电网阻抗的波动会严重破坏并网系统稳定性的问题,提出了弱电网下基于超螺旋滑模的LCL并网逆变器控制策略。根据并网系统模型构建超螺旋滑模观测器,对滤波电容电压及逆变器侧输出电流进行估计,消除额外传感器需要,降低成本。采用具有非奇异快速终端滑模面控制(NFTSMC)的超螺旋滑模控制器来快速地跟踪参考给定电流及降低并网系统动稳态误差,且提高并网系统对外界干扰和参数不确定性的全局鲁棒性。仿真结果表明,当滤波参数摄动和电网阻抗变化时,系统表现出较强的鲁棒性,且并网电流的THD值保持在0.5%左右。

永磁直驱风力发电机非奇异终端滑模控制

为提高永磁直驱风力发电系统的抗扰能力和控制精度,提出了一种扰动观测器与非奇异快速终端滑模控制相结合的最大功率跟踪控制策略。利用扰动观测器得到风力发电机的转矩变化,对控制器进行前馈补偿;采用非奇异快速终端滑模面提高控制器的动态性能,实现系统快速收敛,减少因扰动引起的抖振。仿真结果表明,所提策略在随机风速的情况下可以准确估计转矩变化,提高最大功率跟踪过程中的转速跟踪精度和风能利用率。

永磁同步电机改进无模型超螺旋滑模控制

针对永磁同步电机在复杂工况下控制性能下降问题,提出一种改进型无模型超螺旋非奇异快速终端滑模控制(IMFNFTSMC)算法。首先,建立复杂工况下的SPMSM数学模型;其次,提出新型超局部模型,与二阶超螺旋控制律(ST-)和非奇异快速终端滑模面(NFTSM)结合,设计转速环IMFNFTSM控制器,在减小滑模抖振的同时加快系统收敛速度;为加强控制精度,设计超螺旋扩展滑模扰动观测器(STESMDO)对系统扰动进行估计并前馈补偿;最后,通过仿真及RT-LAB实验对所提方法和PI以及传统无模型非奇异终端滑模控制算法(MFNFTSMC)进行对比,证明了所设计算法的有效性和优越性。

多电机速度同步控制性能优化研究

为了提高多电机转速的同步性和系统鲁棒性,提出了一种新颖的控制方法,即基于非奇异快速终端滑模控制(Non-singular Fast Terminal Sliding Mode Control,NFTSMC)与改进型偏差耦合控制结构(Improve Deviation Coupling Control,IDCC)相结合的多电机速度同步控制方法(NFTSMC+IDCC)。为了提高多电机系统的控制精度和整体稳定性,引入非奇异快速终端滑模控制算法,从而提升单个电机转速的鲁棒性。对传统的偏差耦合多电机速度同步结构进行改进,仿真结果表明,NFTSMC+IDCC方法下的速度同步总误差为17.58 r/min,多电机同步性上相较于其他两组方法提高了50.5%和29%。

一种改进趋近律的PMSM非奇异终端滑模控制

为了提高永磁同步电机(PMSM)伺服控制系统的响应速度和鲁棒性,文章提出了一种基于终端滑模的永磁同步电机控制方法。首先对传统滑模面收敛性进行分析,引入了非奇异终端滑模面;其次在传统趋近律的基础上提出了一种新型趋近律,并设计了基于新型的趋近律的电流-转速控制器;最后设计了滑模观测器对电机存在的扰动进行前馈补偿,并进行转速观测。通过软件仿真和实验证明,所提出的新型控制算法较好地抑制了永磁同步电机在接近平衡点时的抖振问题,且具有较低的超调量、良好的抗扰动能力和较快的响应速度,验证了所提方法的可行性和有效性。