A combined finite element-stiffness equation transfer method for steady state vibration response analysis of structures

An extended finite element transfer matrix method, in combination with stiffness equation transfer, is applied to dynamic response analysis of the structures under periodic excitations. In the present method, the transfer of state vectors from left to right in a combined finite element-transfer matrix (FE-TM) method is changed into the transfer of general stiffness equations of every section from left to right. This method has the advantages of reducing the order of standard transfer equation systems, and minimizing the propagation of round-off errors occurring in recursive multiplication of transfer and point matrices. Furthermore, the drawback that in the ordinary FE-TM method, the number of degrees of freedom on the left boundary be the same on the right boundary, is now avoided. A FESET program based on this method using microcomputers is developed. Finally, numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for steady state vibration response analysis of structures.     

A stiffness equation transfer method for natural frequencies of structures

A stiffness equation transfer method is proposed for obtaining vibration frequencies of structures. This method is an extension of the finite element-transfer matrix (FE-TM) method. In the present method, the transfer of state vectors from left to right in the ordinary FE-TM method is changed into the transfer of stiffness equations of every section from left to right. This method reduces the propagation of round-off errors produced in the ordinary transfer matrix method. Furthermore, the drawback that the number of degrees of freedom on the left boundary must be the same as that on the right boundary in the ordinary FE-TM method, is now avoided. Besides, this method finds out the values of the frequency by Newton-Raphson iteration method, so no plotting of the value of the determinant versus assumed frequency is necessary. An IFETM—W program based on this method for use on an IBM PC586 microcomputer is developed. Finally, numerical examples are presented to demonstrate the accuracy as well as the potential of the proposed method for free vibration analysis of structures.     

基于时延补偿机理的网络化输出反馈控制器设计

本文考虑前向和反馈通道均存在网络时延的网络化控制系统,提出了一种新的动态输出反馈控制器的设计方法.针对状态可测和不可测两种情况,整个设计过程采用不同的时延补偿机理,来主动地消除网络时延的影响.同时,讨论了闭环网络化控制系统的稳定性.最后的仿真实例表明了该方法的有效性.     

A CFD assisted control system design with applications to NO x control in a FGR furnace

In this paper, a novel technique to design control systems for industrial processes with non-linear distributed parameters is proposed. The technique utilizes computational fluid dynamics (CFD) simulation to extract the most essential characteristics from the non-linear industrial process, and then represent them as a set of linear dynamic models around a specific operating point. Based on the linear dynamic representation, a closed-loop feedback linear control system can be designed to maintain the desired performance for the system around the chosen operating point. To illustrate such a design process, an industrial reheating furnace with flue gas recirculation (FGR) is selected herein. The method involves the numerical solution of the partial differential equations describing the fluid flow, heat transfer and combustion process in the furnace. The resulting dynamic relations between the furnace inputs and outputs can then be represented in terms of a multi-input and multi-output transfer function matrix. The objective of the control system is then to maintain the optimally selected furnace operating conditions and compensate for any deviations caused by disturbances to minimize the nitric oxides (NO _x ) emission through feedback mechanisms. The performance of the closed-loop controlled furnace is evaluated not only in the linear domain, but also with the detailed full-scale non-linear CFD model. The results have shown that the proposed method is viable and the designed control system can indeed minimize the deviation of the furnace from the desired operating conditions and hence to prevent any excessive NO _x formation in the combustion process.     

Adaptive modification of the delayed feedback control algorithm with a continuously varying time delay

We propose a simple adaptive delayed feedback control algorithm for stabilization of unstable periodic orbits with unknown periods. The state dependent time delay is varied continuously towards the period of controlled orbit according to a gradient-descent method realized through three simple ordinary differential equations. We demonstrate the efficiency of the algorithm with the Rössler and Mackey-Glass chaotic systems. The stability of the controlled orbits is proven by computation of the Lyapunov exponents of linearized equations.     

双环掺铒光纤激光器混沌耦合反馈相移控制

提出双环单模掺铒光纤激光器激光混沌耦合反馈相移控制方法和物理模型,利用耦合器将系统的输出量反馈到系统中,选取适当的反馈系数,并在反馈通道上加入相移控制器PC控制反馈光的相移,通过对反馈系数和反馈光相移的控制,实时、动态、有效地控制激光混沌到稳定态和周期态;分析了系统输出状态随着控制参数变化的演化规律,控制参数的变化可以使得系统的输出产生丰富的有一定规律性的激光动力学现象;讨论了混沌被控制到单周期态时系统输出的振荡周期的变化规律与控制量的关系。     

Vibration analysis of liquid-filled pipelines with elastic constraints

In this paper, a transfer matrix method (TMM) in frequency domain considering fluid-structure interaction of liquid-filled pipelines with elastic constraints is proposed. The time-domain equations considering fluid-structure interaction, are transformed into frequency domain by Laplace transformation, and then twelve fourth-order ordinary differential equations and two second-order ordinary differential equations are deduced from the frequency-domain equations. The results of the fourteen frequency-domain equations are assembled into a transfer matrix, which represents the motion of a single pipe section. Combined with point matrices that describe specified boundary conditions, an overall transfer matrix for liquid-filled pipeline system can be assembled. Using the method, all the pipeline with no and rigid constraints can be easily calculated by simply setting the stiffness of the restraining springs from zero to a large number. Taking into account the longitudinal vibration, transverse vibration and torsional vibration, the proposed method can be used to analyze the pipelines with bends. Several numerical examples with different constraints are presented here to illustrate the application of the proposed method. The results are validated by measured and simulation data. Through the numerical examples, it is shown that the proposed method is efficient.     

Response control for the externally excited van der Pol oscillator with non-local feedback

A non-local control force is introduced in such a way to obtain a third-order nonlinear differential equation (jerk dynamics) and to control nonlinear vibrations in an externally excited van der Pol oscillator. Two first-order nonlinear ordinary differential equations governing the modulation of the amplitude and the phase of solutions are derived and subsequently the performance of the control strategy is investigated. Excitation amplitude–response and frequency–response curves are shown. In certain cases when the excitation amplitude is very low an approximate analytic solution corresponding to a modulated two-period quasi-periodic motion can be obtained for the uncontrolled system. Uncontrolled and controlled systems are compared and the appropriate choices for the feedback gains are found in order to reduce the amplitude peak of the response and to exclude the possibility of quasi-periodic motion. Numerical simulation confirms the validity of the new method.     

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system. The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics, and a new algorithm—algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method. In the new algorithm, the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator. The exact analytical piece-like solution of the ordinary differential equations is expressed in terms of Taylor series with a local convergent radius, and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.     

Manipulation of Multi‐Level Quantum Systems via Unsharp Measurements and Feedback Operations

The recently proposed quantum control method called self‐fulfilling prophesy is investigated in multi‐level cases, based on a sequence of measurement‐feedback operations. The feedback operation is elaborately designed with respect to the eigenstates of the density matrix of the target state and its post‐measurement state. This design procedure is suitable for the generation of any predefined coherent superpositions of multiple quantum states and elicitation of desired quantum dynamics. For the sake of clearness, arbitrarily prescribed superposition states in three‐ and four‐level systems are prepared, and quantum dynamics achieved as desired. The simulation results indicate that the scheme tolerates modest imprecisions of feedback operation and is robust against sudden perturbations. Thus, the scheme enables new insight on quantum manipulations in a variety of multi‐level systems to be achieved.     

BOOST变换器延迟反馈混沌控制及其优化

引入输出延迟反馈控制(time-delay feedback control, TDFC)到峰值电流控制BOOST变换器中，构建了被控系统的离散迭代模型，获取相应的Jacobian矩阵表达式.通过分析变换器在平衡点的变化规律及Jacobian矩阵特征值轨迹，确定出控制系统混沌到单周期态的TDFC反馈增益范围，并依据状态变量和占空比的收敛情况讨论了系统的稳态和动态性能，实现了对TDFC控制参数优化选择.仿真结果证实了所提控制方式的有效和理论分析的正确.     

Stabilization of an axially moving web via regulation of axial velocity

In this paper, a novel control algorithm for suppression of the transverse vibration of an axially moving web system is presented. The principle of the proposed control algorithm is the regulation of the axial transport velocity of an axially moving beam so as to track a profile according to which the vibration energy decays most quickly. The optimal control problem that generates the proposed profile of the axial transport velocity is solved by the conjugate gradient method. The Galerkin method is applied in order to reduce the partial differential equation describing the dynamics of the axially moving beam into a set of ordinary differential equations (ODEs). For control design purposes, these ODEs are rewritten into state-space equations. The vibration energy of the axially moving beam is represented by the quadratic form of the state variables. In the optimal control problem, the cost function modified from the vibration energy function is subjected to the constraints on the state variables, and the axial transport velocity is considered as a control input. Numerical simulations are performed to confirm the effectiveness of the proposed control algorithm.     

A Novel Low-Dimensional Method for Analytically Solving Partial Differential Equations

This paper is concerned with a low-dimensional dynamical system model for analytically solving partial differential equations (PDEs). The model proposed is based on a posterior optimal truncated weighted residue (POT-WR) method, by which an infinite dimensional PDE is optimally truncated and analytically solved in required condition of accuracy. To end that, a POT-WR condition for PDE under consideration is used as a dynamically optimal control criterion with the solving process. A set of bases needs to be constructed without any reference database in order to establish a space to describe low-dimensional dynamical system that is required. The Lagrangian multiplier is introduced to release the constraints due to the Galerkin projection, and a penalty function is also employed to remove the orthogonal constraints. According to the extreme principle, a set of ordinary differential equations is thus obtained by taking the variational operation of the generalized optimal function. A conjugate gradient algorithm by FORTRAN code is developed to solve the ordinary differential equations. The two examples of one-dimensional heat transfer equation and nonlinear Burgers’ equation show that the analytical results on the method proposed are good agreement with the numerical simulations and analytical solutions in references, and the dominant characteristics of the dynamics are well captured in case of few bases used only.     

反应扩散模型在图灵斑图中的应用及数值模拟

反应扩散方程模型常被用于描述生物学中斑图的形成.从反应扩散模型出发,理论推导得到GiererMeinhardt模型的斑图形成机理,解释了非线性常微分方程系统的稳定常数平衡态在加入扩散项后会发生失稳并产生图灵斑图的过程.通过计算该模型,得到图灵斑图产生的参数条件.数值方法中采用一类有效的高精度数值格式,即在空间离散条件下采用Chebyshev谱配置方法,在时间离散条件下采用紧致隐积分因子方法.该方法结合了谱方法和紧致隐积分因子方法的优点,具有精度高、稳定性好、存储量小等优点.数值模拟表明,在其他条件一定的情况下,系统控制参数κ取不同值对于斑图的产生具有重要的影响,数值结果验证了理论结果.     

Real-Time Quantum Feedback Control: ManipulatingQuantum State in Non-Markovian System

In this paper, we propose a closed-loop real-time feedback design for manipulating a quantum state to a target eigenstate via sequential measurements. To this end, based on the Lyapunov stability theorem, considering the controllability and convergence of the system, we select one measured observable and two control channels, which feedback part of the output signal to the input end, forming a closed-loop control. By dynamical programming, we find the optimal parameters to achieve state transfer with a high probability by real-time feedback control. Numerical simulation experiments show that, in a stochastic quantum system with non-Markovian noise, the real-time control strategy moves the system from initial state to the target eigenstate with fast convergence.

     

Analytical method for steady state vibration of system with localized non-linearities using convolution integral and Galerkin method

The analytical method using transfer function or impulse response is very effective for analyzing non-linear systems with localized non-linearities. This is because the number of non-linear equations can be reduced to that of the equations with respect to points connected with the non-linear element. In the present paper, analytical method for the steady state vibration of non-linear system including subharmonic vibration is proposed by utilizing convolution integral and the impulse response. The Galerkin method is introduced to solve the non-linear equations formulated by the convolution integral, and then the steady state vibration is obtained. An advantage of the present method is that stability or instability of the steady state vibration can be discriminated by the transient analysis from convolution integral. The three-degree-of-freedom mass-spring system is shown as a numerical example and the proposed method is verified by comparing with the result by Runge-Kutta-Gill method.     

电磁波导的辛分析与对偶棱边元

将电磁波导的控制方程导向了Hamilton体系、辛几何的形式.以电磁场的横向分量组成对偶向量并采用分离变量法，可以得到Hamilton算子矩阵的辛本征值问题.共轭辛正交归一关系、辛本征解展开定理等均可在此应用.对于复杂横截面和填充非均匀材料的电磁波导，提出对偶棱边元，对截面半解析离散后即可进行数值求解.对偶棱边元克服了结点基有限元求解电磁场问题的困难，与常规棱边元相比在某些方面具有一定的优势. 关键词： 电磁波导 Hamilton体系 对偶变量 棱边元     

OPTIMAL CONTROL METHOD WITH TIME DELAY IN CONTROL

Optimal control method for active vibration control of linear time-delay systems is investigated in this paper. In terms of two cases that time delay is integer and non-integer times of sampling period, motion equation with time delay is transformed as standard discrete forms which contain no time delay by using zero order holder respectively. Discrete quadratic function is used as objective function in design of controller to guarantee good control efficiency on sampling points. In every step of computation of the deduced controller, it contains not only current step of state feedback but also linear combination of some former steps of control. Because the controller is deduced directly from time-delay differential equation, system stability can be guaranteed easily, thus this method is generally applicable to ordinary control systems. The performance of the control method proposed and system stability when using this method are all demonstrated by numerical simulation results. Simulation results demonstrate that the presented method is a viable and attractive control strategy for applications to active vibration control. Instability in responses occurs possibly if the systems with time delay are controlled using controller designed in case of no time delay.     

Linear-control-based synchronization of coexisting attractor networks with time delays

This paper introduces the concept of linear-control-based synchronization of coexisting attractor networks with time delays.Within the new framework,closed loop control for each dynamic node is realized through linear state feedback around its own arena in a decentralized way,where the feedback matrix is determined through consideration of the coordination of the node dynamics,the inner connected matrix and the outer connected matrix.Unlike previously existing results,the feedback gain matrix here is decoupled from the inner matrix;this not only guarantees the flexible choice of the gain matrix,but also leaves much space for inner matrix configuration.Synchronization of coexisting attractor networks with time delays is made possible in virtue of local interaction,which works in a distributed way between individual neighbours,and the linear feedback control for each node.Provided that the network is connected and balanced,synchronization will come true naturally,where theoretical proof is given via a Lyapunov function.For completeness,several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme.