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几何非线性 2

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解耦控制 2

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MPPT）；差分功率处理（Differential power processing 1

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Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

null

《机械工程前沿（英文）》 2014年 第9卷 第2期   页码 177-190 doi: 10.1007/s11465-014-0288-8

摘要：

In the present paper, three complicated nonlinear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method (AGM). Investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by numerical method (Runge-Kutte 4th). Based on the comparisons which have been made between the gained solutions by AGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. The results reveal that this method is not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear problems.

关键词： Algebraic Method (AGM)     Angular Frequency     Vanderpol     Rayleigh     Duffing    

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Velocity gradient elasticity for nonlinear vibration of carbon nanotube resonators

Hamid M. SEDIGHI, Hassen M. OUAKAD

《结构与土木工程前沿（英文）》 2020年 第14卷 第6期   页码 1520-1530 doi: 10.1007/s11709-020-0672-x

摘要： In this study, for the first time, we investigate the nonlocality superimposed to the size effects on the nonlinear dynamics of an electrically actuated single-walled carbon-nanotube-based resonator. We undertake two models to capture the nanostructure nonlocal size effects: the strain and the velocity gradient theories. We use a reduced-order model based on the differential quadrature method (DQM) to discretize the governing nonlinear equation of motion and acquire a discretized-parameter nonlinear model of the system. The structural nonlinear behavior of the system assuming both strain and velocity gradient theories is investigated using the discretized model. The results suggest that nonlocal and size effects should not be neglected because they improve the prediction of corresponding dynamic amplitudes and, most importantly, the critical resonant frequencies of such nanoresonators. Neglecting these effects may impose a considerable source of error, which can be amended using more accurate modeling techniques.

关键词： velocity gradient elasticity theory     nanotube resonators     differential-quadrature method     nonlinear vibration    

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Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes

M.R. AKBARI,D.D. GANJI,A.R. AHMADI,Sayyid H. Hashemi KACHAPI

《机械工程前沿（英文）》 2014年 第9卷 第1期   页码 58-70 doi: 10.1007/s11465-014-0289-7

摘要：

In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

关键词： Algebraic Method (AGM)     tower crane     oscillating system     angular frequency    

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Scrutiny of non-linear differential equations Euler-Bernoulli beam with large rotational deviation by

M. R. AKBARI,M. NIMAFAR,D. D. GANJI,M. M. AKBARZADE

《机械工程前沿（英文）》 2014年 第9卷 第4期   页码 402-408 doi: 10.1007/s11465-014-0316-8

摘要：

The kinematic assumptions upon which the Euler-Bernoulli beam theory is founded allow it to be extended to more advanced analysis. Simple superposition allows for three-dimensional transverse loading. Using alternative constitutive equations can allow for viscoelastic or plastic beam deformation. Euler-Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams and geometrically nonlinear beam deflection. In this study, solving the nonlinear differential equation governing the calculation of the large rotation deviation of the beam (or column) has been discussed. Previously to calculate the rotational deviation of the beam, the assumption is made that the angular deviation of the beam is small. By considering the small slope in the linearization of the governing differential equation, the solving is easy. The result of this simplification in some cases will lead to an excessive error. In this paper nonlinear differential equations governing on this system are solved analytically by Akbari-Ganji’s method (AGM). Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration solving. The solution of the problem can be obtained very simply and easily. Furthermore, to enhance the accuracy of the results, the Taylor expansion is not needed in most cases via AGM manner. Also, comparisons are made between AGM and numerical method (Runge-Kutta 4th). The results reveal that this method is very effective and simple, and can be applied for other nonlinear problems.

关键词： AGM     critical load of columns     large deformations of beam     nonlinear differential equation    

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非线性系统高阶微分反馈控制

齐国元,陈增强,袁著祉

《中国工程科学》 2003年 第5卷 第8期   页码 35-44

摘要：

提出了不依赖系统模型的高阶微分反馈控制思想，控制目标是系统输出及其微分和高阶微分逼近设定输入及其微分和高阶微分，极大地提高了对控制品质要求。基于这种思想设计了能高品质地提取量测信号的微分和高阶微分的高阶微分器（HOD, high order differentiator），该HOD参数少，容易调节，并给出其稳定性、收敛性和滤波特性的证明；另外，对带有未知扰动、模型未知的非线性SISO和MIMO系统分别设计了基于HOD的高阶微分反馈自适应控制器（HODFC, high order differentials feedback adaptive controller），给出了闭环系统稳定性和鲁棒性分析，并且实现了线性化解耦控制。

关键词： 高阶微分器     高阶微分反馈控制器     稳定性     鲁棒性     解耦控制    

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Stability and coupling dynamic behavior of nonlinear journal active electromagnetic bearing rotor system

LU Yanjun, HEI Di, WANG Yuan, DAI Rong, LU Yanjun, LIU Heng, YU Lie

《机械工程前沿（英文）》 2008年 第3卷 第2期   页码 193-199 doi: 10.1007/s11465-008-0023-4

摘要： The stability and coupling dynamic behavior of a journal active electromagnetic bearing rotor system are analyzed. The gyroscopic effect is considered in the rotor model. The system equations are formulated by combining equations for rotor motion and decentralized proportional integral differential (PID) controllers. A method combining the predictor-corrector mechanism and the Netwon-Raphson method is presented to calculate the critical speed at the corresponding Hopf bifurcation point of the system. For periodic motions, a continuation method combining the predictor-corrector mechanism and shooting method is presented. Nonlinear unbalanced periodic motions and their stability margins are obtained using the shooting method and established continuation method for periodic motions. With the change of control parameters, the system local stability and bifurcation behaviors are obtained using the Floquet theory. The numerical examples show that the schemes not only significantly save computing cost, but also have high precision.

关键词： proportional integral     bifurcation     corresponding     integral differential     predictor-corrector mechanism    

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Analytical method of capsizing probability in the time domain for ships in the random beam seas

LIU Liqin, TANG Yougang, LI Hongxia

《结构与土木工程前沿（英文）》 2007年 第1卷 第3期   页码 361-366 doi: 10.1007/s11709-007-0048-5

摘要： The methods for constructing safe basins of ships and predicting their survival probability in random waves were studied. The nonlinear differential equation of the rolling motion of ships in random beam seas was established considering nonlinear damping, nonlinear restoring moment, and random waves. The random rolling differential equation was solved in the time domain by applying the harmonic acceleration method and by synthetically considering the instantaneous state of ships and the narrowband wave energy spectrum. The numerical simulation of random capsizing course was brought forward, the safe basins were constructed for safe navigation, and the survival probabilities of ships were calculated. As an example, the safe basins on the rolling initial value plane were constructed for a 30.27-meter-long fishing vessel according to different initial conditions and random wave parameters. The survival probabilities of the fishing vessel under different significant wave heights were predicted. Thus, the survival probabilities of ships in random seas can be predicted quantitatively by the proposed method.

关键词： different     survival probability     different significant     nonlinear differential     narrowband    

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Classical state feedback controller for nonlinear systems using mean value theorem: closed loop-FOC of

Abrar ALLAG,Abdelhamid BENAKCHA,Meriem ALLAG,Ismail ZEIN,Mohamed Yacine AYAD

《能源前沿（英文）》 2015年 第9卷 第4期   页码 413-425 doi: 10.1007/s11708-015-0379-1

摘要： The problem of state feedback controllers for a class of Takagi-Sugeno (T-S) Lipschitz nonlinear systems is investigated. A simple systematic and useful synthesis method is proposed based on the use of the differential mean value theorem (DMVT) and convex theory. The proposed design approach is based on the mean value theorem (MVT) to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients as linear parameter varying (LPV) systems. Using the Lyapunov theory, stability conditions are obtained and expressed in terms of linear matrix inequalities (LMIs). The controller gains are then obtained by solving linear matrix inequalities. The effectiveness of the proposed approach for closed loop-field oriented control (CL-FOC) of permanent magnet synchronous machine (PMSM) drives is demonstrated through an illustrative simulation for the proof of these approaches. Furthermore, an extension for controller design with parameter uncertainties and perturbation performance is discussed.

关键词： Takagi-Sugeno (T-S) fuzzy systems     sector nonlinearity     nonlinear controller     linear matrix inequality (LMI) approach     differential mean value theorem (DMVT)     field oriented control (FOC)     linear parameter varying (LPV)    

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Robust nonlinear control via feedback linearization and Lyapunov theory for permanent magnet synchronous

Ridha CHEIKH, Arezki MENACER, L. CHRIFI-ALAOUI, Said DRID

《能源前沿（英文）》 2020年 第14卷 第1期   页码 180-191 doi: 10.1007/s11708-018-0537-3

摘要： In this paper, the method for the nonlinear control design of a permanent magnet synchronous generator based-wind energy conversion system (WECS) is proposed in order to obtain robustness against disturbances and harvest a maximum power from a typical stochastic wind environment. The technique overcomes both the problem of nonlinearity and the uncertainty of the parameter compared to such classical control designs based on traditional control techniques. The method is based on the differential geometric feedback linearization technique (DGT) and the Lyapunov theory. The results obtained show the effectiveness and performance of the proposed approach.

关键词： permanent magnet synchronous generator     wind energy conversion system     stochastic     differential geometric     feedback linearization     maximum power point tracking     Lyapunov     robust control    

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基于大气阻力的立方星编队飞行非线性规划控制算法 Article

Sheng-chao DENG, Tao MENG, Zhong-he JIN

《信息与电子工程前沿（英文）》 2017年 第18卷 第7期   页码 867-881 doi: 10.1631/FITEE.1500493

摘要： 立方星由于体积和功率限制，难以配置传统的推进系统以实现编队飞行。而大气阻力是低轨卫星可以用于轨道调整的空间环境动力之一。本文提出一种通过大气阻力实现轨道面内沿迹跟飞编队的综合策略，并将用于浙江大学下一颗皮纳卫星（该卫星是国际QB50项目成员之一）。QB50项目主要任务是90–300 km高度近地大气层探测。在这一轨道高度，大气阻力对卫星姿态和轨道的影响均不能忽略。本文通过空气动力学分析，同时考虑大气阻力对轨道半长轴和偏心率的影响，设计了一种多维非线性约束规划策略，以计算实现编队所需的卫星之间不同的目标面质比和相应的轨道调整保持时间。此外，通过俯仰姿态机动调整目标面质比。该算法策略无需卫星配置任何展开机构。基于ZJUCubeSat的数值仿真验证了这一设计的可行性和优势。

关键词： QB50；ZJUCubeSat；大气阻力；编队飞行    

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Tuned reactive power dispatch through modified differential evolution technique

S. BISWAS (RAHA), N. CHAKRABORTY

《能源前沿（英文）》 2012年 第6卷 第2期   页码 138-147 doi: 10.1007/s11708-012-0188-8

摘要： This paper explores the capability of modified differential evolution (MDE) technique for solving the reactive power dispatch (RPD) problem. The proposed method is based on the basic differential evolution (DE) technique with a few modifications made into it. DE is one of the strongest optimization techniques though it suffers from the problem of slow convergence while global minima appear. The proposed modifications are tried to resolve the problem. The RPD problem mainly defines loss minimization with stable voltage profile. To solve the RPD problem, the generator bus voltage, transformer tap setting and shunt capacitor placements are controlled by the MDE approach. In this paper, IEEE 14-bus and IEEE 30-bus systems are chosen for MDE implementation. The applied modification show much improved result in comparison to normal DE technique. Comparative study with other soft-computing technique including DE validates the effectiveness of the proposed method.

关键词： reactive power dispatch (RPD)     modified differential evolution (MDE)     differential evolution algorithm with localizations around the best vector (DELB)    

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Review of MEMS differential scanning calorimetry for biomolecular study

Shifeng YU, Shuyu WANG, Ming LU, Lei ZUO

《机械工程前沿（英文）》 2017年 第12卷 第4期   页码 526-538 doi: 10.1007/s11465-017-0451-0

摘要：

Differential scanning calorimetry (DSC) is one of the few techniques that allow direct determination of enthalpy values for binding reactions and conformational transitions in biomolecules. It provides the thermodynamics information of the biomolecules which consists of Gibbs free energy, enthalpy and entropy in a straightforward manner that enables deep understanding of the structure function relationship in biomolecules such as the folding/unfolding of protein and DNA, and ligand bindings. This review provides an up to date overview of the applications of DSC in biomolecular study such as the bovine serum albumin denaturation study, the relationship between the melting point of lysozyme and the scanning rate. We also introduce the recent advances of the development of micro-electro-mechanic-system (MEMS) based DSCs.

关键词： differential scanning calorimetry     biomolecule     MEMS     thermodynamic    

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Precision analysis of a weakly-coupled parallel mechanism with three translational degrees of freedom

MA Lv-zhong, GUO Zong-he, YANG Qi-zhi, YIN Xiao-qin, HAN Ya-li, SHEN Hui-ping

《机械工程前沿（英文）》 2006年 第1卷 第2期   页码 227-232 doi: 10.1007/s11465-006-0005-3

摘要： This paper analyzes the precision of the dissymmetrical parallel mechanism of 3-RRRP(4R) with three translational degrees of freedom (DOF). The parallel mechanism has weakly-coupled, decoupled and real-time characteristics, thus error compensation can be done using control software. Based on topology structure analysis, the inverse and forward solutions are analyzed and the precision is studied using complete differential method. The influencing factors of the manipulator s precision are studied carefully and the means to enhance the precision are also discussed. It is found that the position errors of the moving platform have nonlinear relation with the position of the mechanism. The δθ' error has the biggest influence on the nonlinear errors of the position. Otherwise, the original errors of the mechanism are the main reason leading to more errors. Thus enhancing machining and assembling precision is an important method to enhance the precision of the mechanism.

关键词： manipulator     nonlinear     δθ     influence     differential    

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Solving multi-objective optimal power flow problem considering wind-STATCOM using differential evolution

Belkacem MAHDAD, K. SRAIRI

《能源前沿（英文）》 2013年 第7卷 第1期   页码 75-89 doi: 10.1007/s11708-012-0222-x

摘要： In this paper, a simple strategy based differential evolution was proposed for solving the problem of multi-objective environmental optimal power flow considering a hybrid model (Wind-Shunt-FACTS). The DE algorithm optimized simultaneously a combined vector control based active power of wind sources and reactive power of multi STATCOM exchanged with the electrical power system to minimize fuel cost and emissions. The proposed strategy was examined and applied to the standard IEEE 30-bus with smooth cost function to solve the problem of security environmental economic dispatch considering multi distributed hybrid model based wind and STATCOM controllers. In addition, the proposed approach was validated on a large practical electrical power system 40 generating units considering valve point effect. Simulation results demonstrate that choosing the installation of multi type of FACTS devices in coordination with many distributed wind sources is a vital research area.

关键词： differential evolution     multi-objective function     optimal power flow     economic dispatch     valve point effect     environment     wind source     STATCOM    

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Cluster voltage control method for “Whole County” distributed photovoltaics based on improved differential

《能源前沿（英文）》   页码 782-795 doi: 10.1007/s11708-023-0905-8

摘要： China is vigorously promoting the “whole county promotion” of distributed photovoltaics (DPVs). However, the high penetration rate of DPVs has brought problems such as voltage violation and power quality degradation to the distribution network, seriously affecting the safety and reliability of the power system. The traditional centralized control method of the distribution network has the problem of low efficiency, which is not practical enough in engineering practice. To address the problems, this paper proposes a cluster voltage control method for distributed photovoltaic grid-connected distribution network. First, it partitions the distribution network into clusters, and different clusters exchange terminal voltage information through a “virtual slack bus.” Then, in each cluster, based on the control strategy of “reactive power compensation first, active power curtailment later,” it employs an improved differential evolution (IDE) algorithm based on Cauchy disturbance to control the voltage. Simulation results in two different distribution systems show that the proposed method not only greatly improves the operational efficiency of the algorithm but also effectively controls the voltage of the distribution network, and maximizes the consumption capacity of DPVs based on qualified voltage.

关键词： distributed photovoltaics (DPVs)     cluster partitioning     improved differential evolution algorithm     voltage control     consumption capacity of distributed photovoltaics    

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标题 作者 时间 类型 操作

Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

null

期刊论文

Velocity gradient elasticity for nonlinear vibration of carbon nanotube resonators

Hamid M. SEDIGHI, Hassen M. OUAKAD

期刊论文

Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes

M.R. AKBARI,D.D. GANJI,A.R. AHMADI,Sayyid H. Hashemi KACHAPI

期刊论文

Scrutiny of non-linear differential equations Euler-Bernoulli beam with large rotational deviation by

M. R. AKBARI,M. NIMAFAR,D. D. GANJI,M. M. AKBARZADE

期刊论文

非线性系统高阶微分反馈控制

齐国元,陈增强,袁著祉

期刊论文

Stability and coupling dynamic behavior of nonlinear journal active electromagnetic bearing rotor system

LU Yanjun, HEI Di, WANG Yuan, DAI Rong, LU Yanjun, LIU Heng, YU Lie

期刊论文

Analytical method of capsizing probability in the time domain for ships in the random beam seas

LIU Liqin, TANG Yougang, LI Hongxia

期刊论文

Classical state feedback controller for nonlinear systems using mean value theorem: closed loop-FOC of

Abrar ALLAG,Abdelhamid BENAKCHA,Meriem ALLAG,Ismail ZEIN,Mohamed Yacine AYAD

期刊论文

Robust nonlinear control via feedback linearization and Lyapunov theory for permanent magnet synchronous

Ridha CHEIKH, Arezki MENACER, L. CHRIFI-ALAOUI, Said DRID

期刊论文

基于大气阻力的立方星编队飞行非线性规划控制算法

Sheng-chao DENG, Tao MENG, Zhong-he JIN

期刊论文

Tuned reactive power dispatch through modified differential evolution technique

S. BISWAS (RAHA), N. CHAKRABORTY

期刊论文

Review of MEMS differential scanning calorimetry for biomolecular study

Shifeng YU, Shuyu WANG, Ming LU, Lei ZUO

期刊论文

Precision analysis of a weakly-coupled parallel mechanism with three translational degrees of freedom

MA Lv-zhong, GUO Zong-he, YANG Qi-zhi, YIN Xiao-qin, HAN Ya-li, SHEN Hui-ping

期刊论文

Solving multi-objective optimal power flow problem considering wind-STATCOM using differential evolution

Belkacem MAHDAD, K. SRAIRI

期刊论文

Cluster voltage control method for “Whole County” distributed photovoltaics based on improved differential

期刊论文