Dynamic analysis and fractional-order adaptive sliding mode control for a novel fractional-order ferroresonance system

Ferroresonance is a complex nonlinear electrotechnical phenomenon, which can result in thermal and electrical stresses on the electric power system equipments due to the over voltages and over currents it generates. The prediction or determination of ferroresonance depends mainly on the accuracy of the model used. Fractional-order models are more accurate than the integer-order models. In this paper, a fractional-order ferroresonance model is proposed. The influence of the order on the dynamic behaviors of this fractional-order system under different parameters n and F is investigated.Compared with the integral-order ferroresonance system, small change of the order not only affects the dynamic behavior of the system, but also significantly affects the harmonic components of the system. Then the fractional-order ferroresonance system is implemented by nonlinear circuit emulator. Finally, a fractional-order adaptive sliding mode control(FASMC)method is used to eliminate the abnormal operation state of power system. Since the introduction of the fractional-order sliding mode surface and the adaptive factor, the robustness and disturbance rejection of the controlled system are enhanced. Numerical simulation results demonstrate that the proposed FASMC controller works well for suppression of ferroresonance over voltage.     

Theoretical analysis of the experimental UV-Vis absorption spectra of some phenolic Schiff bases

The time-dependent density functional theory (TDDFT) was applied in conjunction with the natural bond orbital analysis to examine the UV-Vis properties of 10 phenolic Schiff bases. The calculations were performed with different functionals, but main discussion refers to results obtained at the B3LYP/6-311+G(d,p) level of theory. The approach based on the natural localised molecular orbital clusters indicates similar behaviour for majority of examined compounds. The HOMO (“highest occupied molecular orbital”) cluster is delocalised over the ring which is electron richer, the HOMO-1 cluster is spread over the other ring, whereas the LUMO (“lowest unoccupied molecular orbital”) cluster is situated on the imino group. The two bands at long wavelengths correspond to the HOMO → LUMO and HOMO-1 → LUMO transitions, i.e. from both A and B rings to the imino group. The next band originates from a transition from the imino group to the imino group. The band at the smallest wavelengths originates from a transition from the A ring to the A ring, or from the B ring to the B ring. Our findings are in very good agreement with the existing literature data.     

Solution of the reduced occupation-number equation for a fermion system

Using the thin target — thin catchers techniques, masses, mean recoil energies and angular distributions of target residues have been measured for 86 MeV/nucleon¹²C induced reactions. Several different nuclear reaction processes, from peripheral to central collisions have been observed. Experimental results are partly reproduced by intranuclear cascade+evaporation calculations. Up to now, the production of the lightest masses (44<A<71) recoiling with high kinetic energies is not correctly understood by theoretical models. More exclusive experiments are needful to check if the formation of a highly excited quasi-compound nucleus could be a possible explanation of the phenomena.     

Movement dynamics analysis for an optical pickup head lens actuator in a digital versatile disc system

With the rapid development of CD/DVD(compact disc/digital versatile disc)technology,the disc rotation speed and the information density have increased greatly to fulfil the demand of high informatiopn bit rate transfer,As one of the most important elements in a DVD pickup head,objective lens actuators are required to provide a more precise means to accurately follow the disc deviation.The design of the lens actuator becomes all the more important and critical.In order to give complete suggestion to the design of the lens actuator,we put forward the movement differnetial equations as a new theoretical means to analyse the characteristics of the lens actuator reliably and rigorously.Based on the theoretical analyses,many important and effective methods are propsed.A typical experiment verifies that the performance of our lens actuator head,which adopts these methods,can satisfy the high speed and high density requirement of DVD systems.     

Techniques for analysis of stability of non-equilibrium system dynamics

Two techniques for practical analysis of non-equilibrium system stability, which were demonstrated using an example of dynamics of a charged subsystem in an electrical field, are presented. Analytical formulas of possible instabilities determining their well-known and unknown mechanisms are derived. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 34–39, October, 2006.     

A finite element analysis for the vibration modes of a bladed disc

The coupled vibration modes of a rotating blade-disc system are calculated by a finite element method. It is assumed that a large number of identical blades are present, such that the resulting blade loadings on the disc can be considered continuously distributed around the rim of the disc. The disc may have arbitrary profile, and the blades may be tapered and twisted, thus closely representing practical axial flow turbomachine configurations. The effects of rotation, thermal stress, and transverse shear and rotatory inertia in discs of moderately thick profile are readily incorporated into the finite element model. Calculated values of frequencies are compared with experimental data obtained on non-rotating models, and the convergence of the solution is examined by comparison with exact solutions, which can be obtained for configurations of simple geometry. Excellent agreement with experimental data is obtained when using remarkably few elements in the mathematical model, and convergence of the solution is extremely rapid.     

一种分数阶非线性系统稳定性判定定理的问题及分析

分数阶非线性系统稳定性理论的研究对于分数阶混沌系统同步控制的应用具有重要价值,将分数阶非线性系统稳定性判断转化为相应整数阶非线性系统稳定性判断的探讨很有意义.通过实例表明了:对于时变系数矩阵,如果整数阶系统稳定,其对应的阶次小于1的分数阶系统也稳定的判定定理是错误的,并分析了问题产生的原因.     

也谈刚体在固定曲面上作纯滚动时接触点的加速度

用矢量分析的方法求出刚体在固定曲面上作纯滚动时接触点、即速度瞬心的加速度的表示式.     

Soliton solutions and stability analysis for some conformable nonlinear partial differential equations in mathematical physics

This research presents soliton solutions and stability analysis to some conformable nonlinear partial differential equations (CNPDEs). The CNPDEs equations in this paper are conformable Cahn–Allen and conformable Zoomeron equations. The powerful sine-Gordon method is used to carry out the soliton solutions for these equations. The aspects of stability analysis for the considered equations is investigated using the linear stability technique. The sine-Gordon method proves to be efficient and effective for the extraction of soliton solutions for different types of CNPDEs.     

Ultrasonic-assisted top-down preparation of NbSe2 micro/nanoparticles and hybrid material as solid lubricant for sliding electrical contact

2H-NbSe₂ single crystal flake (ca. 2 × 2 × 0.5 mm in size) by chemical vapor transport is employed as the precursor for a top-down preparation of NbSe₂ micro/nanoparticles by two kinds of processes, i.e. (1) mechanical exfoliation; (2) ultrasonic-assisted exfoliation in ethanol without ageing and with ageing for 210 days. NbSe₂ micro/nanoparticles are applied on top of a Cu disk by a drop-casting process and the tribological property in sliding against a Cu pin under sliding electrical contact is investigated at room temperature. Mechanical exfoliation produces NbSe₂ microplatets with typical sizes of 1 μm to 30 μ m with a thickness less than 2 μm. Ultrasonic-assisted exfoliation without aging facilitates the formation of NbSe₂ micro/nanoplatets with sizes of 0.1 μm to 25 μm and nano-whiskers with 100 nm in diameter and 1 ~ 3 μm in length, but Nb₂O₅ and Se are also found on the basis of XPS results. Prolonged aging of the suspensions modifies the morphology by converting platets and whiskers into corrugated floccules (hybrid material), which are composed of Nb₂O₅, Se, NbSe₂, and graphene. Notably, NbSe₂ micro/nanoparticles by ultrasonic-assisted exfoliation without ageing exhibit an excellent lubricating property with low friction coefficient (0.3), mild wear, and longer wear lifetime (120 min) than that of mechanical exfoliated NbSe₂ microplatets (10 min). The wear lifetime for the aged NbSe₂ micro/nanoparticles can be as long as 504 min and are 4.2 times of the sample without aging, which can be a good solid lubricant for sliding electrical contact     

大型固体激光器光束定位稳定性分析

 根据ICF驱动器系统工程的要求,建立光学元件运动量与靶点光束定位之间关系,对稳定性进行初估。运用B类评定方法、光线追迹方法和有限元数值模拟方法进行检验和校正,使其更具有可行性。并从结构随机振动理论出发,将结构用单自由度线性系统的平稳随机振动模拟,实现稳定性值激励源的重分。     

大型固体激光器光束定位稳定性分析

根据ICF驱动器系统工程的要求,建立光学元件运动量与靶点光束定位之间关系,对稳定性进行初估。运用B类评定方法、光线追迹方法和有限元数值模拟方法进行检验和校正,使其更具有可行性。并从结构随机振动理论出发,将结构用单自由度线性系统的平稳随机振动模拟,实现稳定性值激励源的重分。     

大型固体激光器光束定位稳定性分析

根据 ICF驱动器系统工程的要求 ,建立光学元件运动量与靶点光束定位之间关系 ,对稳定性进行初估。运用 B类评定方法、光线追迹方法和有限元数值模拟方法进行检验和校正 ,使其更具有可行性。并从结构随机振动理论出发 ,将结构用单自由度线性系统的平稳随机振动模拟 ,实现稳定性值激励源的重分。     

Test of the stability of a three-phase contact line with negative line tension

The equilibrium structure of a three-phase contact line with negative line tension using a mean-field free-energy functional is calculated in the square-gradient approximation. The equilibrium density profiles are found by solving the Euler—Lagrange equations on a square grid of N ² points covering an area of L ². The fluctuations about the equilibrium structure are analysed via the spectrum of the free energy's second functional derivative. The equilibrium configuration is found to be stable with respect to fluctuations in the structure of the three-phase line and of the interfaces that meet at this line. In addition, the behaviour is investigated numerically of the lowest eigenvalue as the area of the grid is increased. The lowest eigenvalue is always positive and vanishes as 1/L ².     

半导体激光自混合干涉仪稳定性的仿真分析

利用半导体激光器的Lang-Kobayashi方程,对半导体激光自混合干涉系统的动力学特性进行了仿真分析。研究结果表明,当光反馈系数较小时,激光器处于稳定状态,外腔长度不影响系统的稳定性;当光反馈系数较大时,激光器将进入不稳定状态,对于不同的外腔长度,激光器的稳定状态将发生变化。为实现大量程的位移或距离测量,光反馈系数必须足够小才能保证在较大外腔长度变化范围内,激光器始终处于稳定状态。     

Spectral stability of periodic waves in the generalized reduced Ostrovsky equation

We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations of the reduced Ostrovsky equations to the semi-linear equations of the Klein–Gordon type.