A new method based on two freedom-degree PD-P flow rate controller for congestion control in computer networks

The rate-based feedback PD-P controller of two freedom-degrees is proposed for the congestion control in computer networks to improve the abilities against disturbance. Moreover, the Dahlin algorithm is used for setting the controller to overcome the adverse effect caused by the propagation delay effectively. The research results show that the proposed scheme not only can make sources respond to the changes of network state more quickly, but also has a good robustness against estimated error of the delay. Then the packet queue level in buffer will be stabilized on the set-point quickly, and the delay and its jitter of the packet queuing will also become smaller. Besides, the flexible bandwidth allotment can be obtained by setting the weight coefficients.

Modified Two-Degrees-of-Freedom Internal Model Control for Non-Square Systems with Multiple Time Delays

A modified two-degrees-of-freedom( M-TDOF) internal model control( IMC) method is proposed for non-square systems with multiple time delays and right-half-plane( RHP) zeros. In this method,pseudo-inverse is introduced to design the internal model controller,and a desired closed-loop transfer function is designed to eliminate the unrealizable factors of the derived controller. In addition,set-point tracking and load-disturbance rejection of each process are separately controlled by two controllers. The simulation results show that in addition to high decoupling performance and robustness,the proposed control method also effectively improves loaddisturbance rejection and simultaneously optimizes the input tracking performance and disturbance rejection performance by selecting the parameters of controllers. Furthermore,the higher tolerance of model mismatch is achieved in this paper.

A novel two-degree-of-freedom spherical ultrasonic motor using three travelling-wave type annular stators

In order to promote the tolerance and controllability of the multi-degree-of-freedom(M-DOF) ultrasonic motor, a novel two-degree-of-freedom(2-DOF) spherical ultrasonic motor using three traveling-wave type annular stators was put forward. Firstly,the structure and working principle of this motor were introduced, especially a spiral spring as the preload applied component was designed for adaptive adjustment. Then, the friction drive model of 2-DOF spherical motor was built up from spatial geometric relation between three annular stators and the spherical rotor which was used to analyze the mechanical characteristics of the motor.The optimal control strategy for minimum norm solution of three stators' angular velocity was proposed, using Moore-Penrose generalized inverse matrix. Finally, a 2-DOF prototype was fabricated and tested, which ran stably and controllably. The maximum no-load velocity and stall torque are 92 r/min and 90 m N·m, respectively. The 2-DOF spherical ultrasonic motor has compact structure, easy assembly, good performance and stable operation.

Two freedom linear parameter varying μ synthesis control for flight environment testbed

To solve the problem of robust servo performance of Flight Environment Testbed(FET)of Altitude Ground Test Facilities(AGTF) over the whole operational envelope, a two-degree-offreedom μ synthesis method based on Linear Parameter Varying(LPV) schematic is proposed, and meanwhile a new structure frame of μ synthesis control on two degrees of freedom with double integral and weighting functions is presented, which constitutes a core support part of the paper. Aimed at the problem of reference command's rapid change, one freedom feed forward is adopted, while another freedom output feedback is used to meet good servo tracking as well as disturbance and noise rejection; furthermore, to overcome the overshoot problem and acquire dynamic tuning,the integral is introduced in inner loop, and another integral controller is used in outer loop in order to guarantee steady errors; additionally, two performance weighting functions are designed to achieve robust specialty and control energy limit considering the uncertainties in system. As the schedule parameters change over large flight envelope, the stability of closed-loop LPV system is proved using Lyapunov inequalities. The simulation results show that the relative tracking errors of temperature and pressure are less than 0.5% with LPV μ synthesis controller. Meanwhile, compared with non-LPV μ synthesis controller in large uncertainty range, the proposed approach in this research can ensure robust servo performance of FET over the whole operational envelope.

Nonlinear dynamics of two degree of freedom systems with linear and nonlinear stiffnesses

In this study, a new analytical approach is developed to analyze the free nonlinear vibration of conservative two-degree-of-freedom （TDOF） systems. The mathematical models of these systems are governed by second--order nonlinear partial differential equations. Nonlinear differential equations were transferred into a single equation by using some intermediate variables. The single nonlinear differential equations are solved by using the first order of the Hamiltonian approach （HA）. Different parameters, which have a significant impact on the response of the systems, are considered and discussed. Some comparisons are presented to verify the results between the Hamiltonian approach and the exact solution. The maximum relative error is less than 2.2124 % for large amplitudes of vibration. It has been established that the first iteration of the Hamiltonian approach achieves very accurate results, does not require any small perturbations, and can be used for a wide range of nonlinear problems.

An experimental investigation of one-and two-degree of freedom VIV of cylinders

In the paper,an experiment investigation was conducted for one-and two-degree of freedom vortex-induced vibration（VIV） of a horizontally-oriented cylinder with diameter of 11 cm and length of 120 cm.In the experiment,the spring constants in the cross-flow and in-line flow directions were regulated to change the natural vibration frequency of the model system.It was found that,in the one-degree of freedom VIV experiment,a ＂double peak＂ phenomenon was observed in its amplitude within the range of the reduced velocities tested,moreover,a ＂2T＂ wake appeared in the vicinity of the second peak.In the two-degree of freedom VIV experiment,the trajectory of cylinder exhibited a reverse ＂C＂ shape,i.e.,a ＂new moon＂ shape.Through analysis of these data,it appears that,besides the non-dimensional in-line and cross-flow natural vibration frequency ratios,the absolute value of the natural vibration frequency of cylinder is also one of the important parameters affecting its VIV behavior.

Physical Modeling and Parametric Study on Two-Degree-of-Freedom VIV of A Cylinder near Rigid Wall

Unlike most previous studies on the transverse vortex-induced vibration（VlV） of a cylinder mainly under the wallfree condition （Williamson ＆ Govardhan, 2004）, this paper experimentally investigates the vortex-induced vibration of a cylinder with two degrees of freedom near a rigid wall exposed to steady flow. The amplitude and frequency responses of the cylinder are discussed. The lee wake flow patterns of the cylinder undergoin^g VIV were visualized by employing the hydrogen bubble technique. The effects of the gap-to-diameter ratio （eo/D） and the mass ratio on the vibration amplitude and frequency are analyzed. Comparisons of VIV response of the cylinder are made between one degree （only transverse） and two degrees of freedom （streamwise and transverse） and those between the present study and previous ones. The experimental observation indicates that there are two types of streamwise vibration, i.e. the first streamwise vibration （FSV） with small amplitude and the second streamwise vibration （SSV） which coexists with transverse vibration. The vortex shedding pattern for the FSV is approximately syrmnetric and that for the SSV is ahernate. The first streamwise vibration tends to disappear with the decrease of eo/D. For the case of large gap-to-dianeter ratios （ e.g. eo/D = 0. 54 ～ 1.58）, the maximum amplitudes of the second streamwise vibration and transverse one increase with the increasing gap- to-diameter ratio. But for the case of small gap-to-diameter ratios （e. g. eo/D= 0. 16, 0.23）, the vibration amplitude of the cylinder increases slowly at the initial stage （i.e. at small reduced velocity Vr）, and across the maximum amplitude it decreases quickly at the last stage （i.e. at large Vr）. Within the range of the examined small mass ratio （m 〈 4）, both streamwise and transverse vibration amplitude of the cylinder decrease with the increase of mass ratio for the fixed value of Vr- The vibration range （ in terms of Vr） tends to widen with the decrease of the mass ratio. In the second streamwise vibration region, the vibration frequency of the cylinder with a small mass ratio （ e.g. mx = 1.44） undergoes a jump at a certain Vr＋ The maximum amplitudes of the transverse vibration for two-degree-of-freedom case is larger than that for one-degree-of-freedom case, but the transverse vibration frequency of the cylinder with two degrees of freedom is lower than that with one degree of freedom（transverse）.

Behavior of Vortex-Induced Vibration of A Circular Cylinder Near A Deformable Wall with Two Degrees of Freedom in Steady Flow

The behavior of vortex-induced vibration of a two-degree-of-freedom cylinder near a deformable wall in steady flow is investigated experimentally. The typical phenomenon of the two-degree-of-freedom cylinder＇s VIV is discussed. The influences of initial gap between the cylinder and the wall on the dynamic responses of the cylinder are analyzed. The comparison is made about dynamic responses of the cylinder with one and two degrees of freedom. Experimental results show that the vibration of the cylinder near a deformable wall with a small value of initial gap-to-diameter ratios can generally be divided into two phases. The initial gap-to-diameter ratios have a noticeable influence on the occurrence of transverse vibration. The transverse maximum amplitude of the cylinder with two degrees of freedom is larger than that of the cylinder with one degree of freedom under the condition with the same values of other parameters. However, the vibration frequency of the cylinder for the two degrees of freedom case is smaller than that for the one degree of freedom case at the same value of Vr number

Type Synthesis of Two-Degrees-of-Freedom Rotational Parallel Mechanism with Two Continuous Rotational Axes

The two-rotational-degrees-of-freedom（2R） parallel mechanism（PM） with two continuous rotational axes（CRAs） has a simple kinematic model.It is therefore easy to implement trajectory planning,parameter calibration,and motion control,which allows for a variety of application prospects.However,no systematic analysis on structural constraints of the 2R-PM with two CRAs has been performed,and there are only a few types of 2R-PM with two CRAs.Thus,a theory regarding the type synthesis of the 2R-PM with two CRAs is systematically established.First,combining the theories of reciprocal screw and space geometry,the spatial arrangement relationships of the constraint forces applied to the moving platform by the branches are explored,which give the 2R-PM two CRAs.The different distributions of the constraint forces in each branch are also studied.On the basis of the obtained structural constraints of branches,and considering the geometric relationships of constraint forces in each branch,the appropriate kinematic chains are constructed.Through the reasonable configuration of branch kinematic chains corresponding to every structural constraint,a series of new 2R-PMs with two CRAs are finally obtained.

PSO-based Parameter Tuning for a TwoDegree-of-Freedom IMC Scheme and Its Application to Paper Basis Weight Control

Basis weight is an important indicator for evaluating paper quality and a major factor directly affecting the economic benefits of enterprises.Focusing on the large time-delay,time-varying,and nonlinear characteristics of a basis weight control system,a two-degree-of-freedom(TDF)internal model control(IMC)method based on a particle swarm optimization(PSO)algorithm was proposed.The method took the integral of time multiplied by the absolute error(ITAE)as the objective function,and the PSO algorithm was used to optimize the time constant of the tuning IMC filter.The simulation results for the control system under the proposed TDF-IMC method based on the PSO algorithm demonstrate good set-point tracking performance,strong anti-interference capabilities,and good robustness properties.The application results revealed that the basis weight fluctuation range of the paper was±2 g/m2,which significantly improved both the control quality and the product quality.

Manufacture of End－micro－manipulator with Two Degrees of Freedom and its Driving System for Robot

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ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS

A class of two-degree-of-freedom systems in resonance with an external, parametric excitation is investigated, the existence of the periodic solutions locked to Omega is proved by the use of the method of multiple scales. This systems can be transformed into the systems of Wiggins under some conditions. A calculating formula which determines the existence of homoclinic orbits of the systems is given.

HAMILTONIANS WITH TWO DEGREES OF FREEDOM ADMITTING A SINGLEVALUED GENERAL SOLUTION

Following the basic principles stated by Painlevé, we first revisit the process of selecting the admissible time-independent Hamiltonians H = （p1^2 ＋ p2^2）/2 ＋ V（q1, q2） whose some integer power qj^nj （t） of the general solution is a singlevalued function of the complez time t. In addition to the well known rational potentials V of Hénon-Heiles, this selects possible cases with a trigonometric dependence of V on qj. Then, by establishing the relevant confluences, we restrict the question of the explicit integration of the seven （three “cubic” plus four “quartic”） rational Hénon-Heiles cases to the quartic cases. Finally, we perform the explicit integration of the quartic cases, thus proving that the seven rational cases have a meromorphic general solution explicitly given by a genus two hyperelliptic function.

Set-point Filter Design for a Two-degree-of-freedom Fractional Control System

This paper focuses on a new approach to design(possibly fractional) set-point filters for fractional control systems.After designing a smooth and monotonic desired output signal,the necessary command signal is obtained via fractional input-output inversion.Then,a set-point filter is determined based on the synthesized command signal.The filter is computed by minimizing the 2-norm of the difference between the command signal and the filter step response.The proposed methodology allows the designer to synthesize both integer and fractional setpoint filters.The pros and cons of both solutions are discussed in details.This approach is suitable for the design of two degreeof-freedom controllers capable to make the set-point tracking performance almost independent from the feedback part of the controller.Simulation results show the effectiveness of the proposed methodology.

Design for Two-degree-of-freedom PID Regulator Based on Improved Generalized Extremal Optimization Algorithm

A kind of new design method for two-degree-of-freedom(2DOF)PID regulator was presented,in which,a new global search heuristic--improved generalized extremal optimization(GEO)algorithm is applied to the parameter optimization design of 2DOF PID regulator.The simulated results show that very good dynamic response performance of both command tracking and disturbance rejection characteristics can be achieved simultaneously.At the same time,the comparisons of simulation results with the improved GA,the basic GEO and the improved GEO were given.From the comparisons,it is shown that the improved GEO algorithm is competitive in performance with the GA and basic GEO and is an attractive tool to be used in the design of two-degree-of-freedom PID regulator.

Asymptotic dynamics of the alternate degrees of freedom for a two-mode system:An analytically solvable model

The composite systems can be non-uniquely decomposed into parts（subsystems）.Not all decompositions（structures） of a composite system are equally physically relevant.In this paper we answer on theoretical ground why it may be so.We consider a pair of mutually un-coupled modes in the phase space representation that are subjected to the independent quantum amplitude damping channels.By investigating asymptotic dynamics of the degrees of freedom,we find that the environment is responsible for the structures non-equivalence.Only one structure is distinguished by both locality of the environmental influence on its subsystems and a classical-like description.

双自由度D形截面柱体流致振动的二维数值模拟

本文研究了D形截面柱体在顺流向和横流向两个自由度下的流致振动特性,迎流角为90°,质量比为2.6,雷诺数为370~3685,应用RANS方程采用SST k-ω湍流模型和Newmark-β法求解水流运动和柱体运动,入口流速采用匀加速法,检验了数值模型的网格和时间步长敏感性,并与相关文献的实验结果进行对比,验证了数值模型的可靠性。基于计算结果,系统分析了D形截面柱体的振幅、振动频率、水动力系数、尾涡脱落模式,以及平均位置偏移情况。结果表明,双自由度D形截面柱体在约化速度为8~14的区间内表现为涡激振动-驰振模式,尾涡多为2S和S+2S交替脱落,双自由度振幅比单自由度有显著的增大。升力主要偏向截面的直线边一侧,且升力出现了多个倍频。横流向和顺流向平均偏移量最大都可达到一倍特征长度以上。

CYLINDRICAL WORM MACHINED BY THE CONE GRINDING WHEEL WITH TWO DEGREE－OF－FREEDOM AND MESHING THEORY OF ITS DRIVE①

The characteristics of novel cone-generated cylindrical worm and the machining princi- ple of using a grinding wheel with two degree-of-freedom motions are described. A systematic study is made on the first enveloping process of the grinding wheel forming a worm and the second enveloping process of the worm forming a worm wheel with the meshing theory of kinematic method. Some numerical calculation formulas and important conclusions are obtained.

基于双自由度转台的全向空间单目视觉室内定位测量方法

针对传统单目视觉测量系统测量视场有限的问题,本文提出一种基于双自由度旋转平台的全向空间单目视觉测量方法。首先,对双自由度旋转平台的转轴参数进行标定,用副相机拍摄固定在双自由度转台上的棋盘格标定板,提取棋盘格角点的位置坐标,并将其转化到同一相机坐标系下。利用PCA(主成分分析)平面拟合得到初始位置转轴参数中的方向向量,使用空间最小二乘圆拟合方法得到初始位置下转轴参数中的位置参数。然后,通过转台转动的角度以及罗德里格斯公式将不同位置下相机获取的数据进行坐标系统一,实现水平和竖直方向全向空间下的目标测量。最后,通过高精度激光测距仪验证了本方法的测量精度,并通过与双目视觉测量系统、wMPS测量系统进行比对实验,验证了本方法的全向空间测量能力。实验结果表明,本方法测量精度基本达到双目视觉测量系统水平,但测量范围远大于双目视觉测量,可以满足全向空间测量要求。

基于LMI的二自由度飞行器多变量控制

针对二自由度飞行器存在非线性特性、强耦合性以及易受外界干扰等问题,提出了基于LMI的二自由度飞行器多变量控制方法。首先,根据二自由度飞行器系统的输入和输出变量,结合空间动力学方程建立了系统的状态空间模型;其次,设计满足静态输出反馈稳定的多变量控制律;然后,通过李亚普托夫稳定性定理与极点配置法,将控制系统稳定性问题转化为优化问题,利用线性矩阵不等式(LMI)求解满足最优性能指标的多变量控制器参数;最后,通过对比仿真分析与单变量PID,表明该方法能有效提升二自由度飞行器的轨迹跟踪精度。