Force Control Compensation Method with Variable Load Stiffness and Damping of the Hydraulic Drive Unit Force Control System

Each joint of hydraulic drive quadruped robot is driven by the hydraulic drive unit（HDU）, and the contacting between the robot foot end and the ground is complex and variable, which increases the difficulty of force control inevitably. In the recent years, although many scholars researched some control methods such as disturbance rejection control, parameter self-adaptive control, impedance control and so on, to improve the force control performance of HDU, the robustness of the force control still needs improving. Therefore, how to simulate the complex and variable load characteristics of the environment structure and how to ensure HDU having excellent force control performance with the complex and variable load characteristics are key issues to be solved in this paper. The force control system mathematic model of HDU is established by the mechanism modeling method, and the theoretical models of a novel force control compensation method and a load characteristics simulation method under different environment structures are derived, considering the dynamic characteristics of the load stiffness and the load damping under different environment structures. Then, simulation effects of the variable load stiffness and load damping under the step and sinusoidal load force are analyzed experimentally on the HDU force control performance test platform, which provides the foundation for the force control compensation experiment research. In addition, the optimized PID control parameters are designed to make the HDU have better force control performance with suitable load stiffness and load damping, under which the force control compensation method is introduced, and the robustness of the force control system with several constant load characteristics and the variable load characteristics respectively are comparatively analyzed by experiment. The research results indicate that if the load characteristics are known, the force control compensation method presented in this paper has positive compensation effects on the load characteristics variation, i.e., this method decreases the effects of the load characteristics variation on the force control performance and enhances the force control system robustness with the constant PID parameters, thereby, the online PID parameters tuning control method which is complex needs not be adopted. All the above research provides theoretical and experimental foundation for the force control method of the quadruped robot joints with high robustness.

Numerical Research on The Nozzle Damping Effect by A Wave Attenuation Method

Nozzle damping is one of the most important factors in the suppression of combustion instability in solid rocket motors.For an engineering solid rocket motor that experiences combustion instability at the end of burning,a wave attenuation method is proposed to assess the nozzle damping characteristics numerically.In this method,a periodic pressure oscillation signal which frequency equals to the first acoustic mode is superimposed on a steady flow at the head end of the chamber.When the pressure oscillation is turned off,the decay rate of the pressure can be used to determine the nozzle attenuation constant.The damping characteristics of three other nozzle geometries are numerically studied with this method under the same operating condition.The results show that the convex nozzle provides more damping than the conical nozzle which in turn provides more damping than the concave nozzle.All the three nozzles have better damping effect than that of basic nozzle geometry.At last,the phase difference in the chamber is analyzed,and the numerical pressure distribution satisfies well with theoretical distribution.

A time domain induced polarization relaxation time spectrum inversion method based on a damping factor and residual correction

Relaxation time spectra （RTS） derived from time domain induced polarization data （TDIP） are helpful to assess oil reservoir pore structures. However, due to the sensitivity to the signal-to-noise ratio （SNR）, the inversion accuracy of the traditional singular value decomposition （SVD） inversion method reduces with a decrease of SNR. In order to enhance the inversion accuracy and improve robustness of the inversion method to the SNR, an improved inversion method, based on damping factor and spectrum component residual correction, is proposed in this study. The numerical inversion results show that the oscillation of the RTS derived from the SVD method increased with a decrease of SNR, which makes it impossible to get accurate inversion components. However, the SNR has little influence on inversion components of the improved method, and the RTS has high inversion accuracy and robustness. Moreover, RTS derived from core sample data is basically in accord with the pore-size distribution curve, and the RTS derived from the actual induced polarization logging data is smooth and continuous, which indicates that the improved method is practicable.

Stability of average acceleration method for structures with nonlinear damping

The energy approach is used to theoretically verify that the average acceleration method （AAM）, which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.

A Damping Characteristics Calculation Method of Metal Dry Friction Isolators

The dry friction ring-type vibration isolator is considered as an isotropic continuous medium. A method of dry friction hysteresis loop calculation is proposed based on friction force analysis of contact beam. The friction force is modeled as an equivalent distributed moment to use the finite element method （FEM） to calculate the dry friction vibration isolator hysteresis loop, so the damping characteristics can be obtained. A comparison of the hysteresis loop calculation results and the experimental results shows the average relative error is 2.7 %, it proves the calculation method is feasible.

Second order conformal multi-symplectic method for the damped Korteweg–de Vries equation

A conformal multi-symplectic method has been proposed for the damped Korteweg–de Vries(DKdV) equation, which is based on the conformal multi-symplectic structure. By using the Strang-splitting method and the Preissmann box scheme,we obtain a conformal multi-symplectic scheme for multi-symplectic partial differential equations(PDEs) with added dissipation. Applying it to the DKdV equation, we construct a conformal multi-symplectic algorithm for it, which is of second order accuracy in time. Numerical experiments demonstrate that the proposed method not only preserves the dissipation rate of mass exactly with periodic boundary conditions, but also has excellent long-time numerical behavior.

Moving-Particle Semi-Implicit Method for Vortex Patterns and Roll Damping of 2D Ship Sections

A meshless method, Moving-Particle Semi-hnplicit Method （MPS） is presented in this paper to simulate the rolling of different 2D ship sections. Sections S. S. 0.5, S.S. 5.0 and S. S. 7.0 of series 60 with CB = 0.6 are chosen for the simulation. It shows that the result of MPS is very close to results of experiments or mesh-numerical simulations. In the simulation of MPS, vortices are found periodically in bilges of ship sections. In section S. S. 5.0 and section S. S. 7.0, which are close to the middle ship, two little vortices are found at different bilges of the section, in section S. S. 0.5, which is close to the bow, only one big vortex is found at the bottom of the section, these vortices patterns are consistent with the theory of Ikeda. The distribution of shear stress and pressure on the rolling hull of ship section is calculated. When vortices are in bilges of the section, the sign clmnge of pressure can be found, but in section S. S. 0.5, there is no sign change of pressure because only one vortex in the bottom of the section. With shear stress distribution, it can be found the shear stress in bilges is bigger than that at other part of the ship section. As the free surface is considered, the shear stress of both sides near the free surface is close to zero and even sign changed.

Accuracy of the half-power bandwidth method with a third-order correction for estimating damping in multi-DOF systems

A third-order correction was recently suggested to improve the accuracy of the half-power bandwidth method in estimating the damping of single DOF systems.This paper analyzes the accuracy of the half-power bandwidth method with the third-order correction in damping estimation for multi-DOF linear systems.Damping ratios in a two-DOF linear system are estimated using its displacement and acceleration frequency response curves,respectively.A wide range of important parameters that characterize the shape of these response curves are taken into account.Results show that the third-order correction may greatly improve the accuracy of the half-power bandwidth method in estimating damping in a two-DOF system.In spite of this,the half-power bandwidth method may significantly overestimate the damping ratios of two-DOF systems in some cases.

THE AUTO-ADJUSTABLE DAMPING METHOD FORSOLVING NONLINEAR EQUATIONS

The general approach for solving the nonlinear equations is linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For the strongly nonlinear problems, the solution obtained in the iterative process is always difficult, even divergent due to the numerical instability. It can not fulfill the engineering requirements. Newton's method and its variants can not settle this problem. As a result, the application of numerical simulation for the strongly nonlinear problems is limited. An auto-adjustable damping method has been presented in this paper. This is a further improvement of Newton's method with damping factor. A set of vector of damping factor is introduced. This set of vector can be adjusted continuously during the iterative process in accordance with the judgement and adjustment. An effective convergence coefficient and quichening coefficient are employed to relax the restricted requirements for the initial values and to shorten the iterative process. Then, the numerical stability will be ensured for the solution of complicated strongly nonlinear equations. Using this method, some complicated strongly nonlinear heat transfer problems in airplanes and aeroengines have been numerically simulated successfully. It can be used for the numerical simulation of strongly nonlinear problems in engineering such as nonlinear hydrodynamics and aerodynamics, heat transfer and structural dynamic response etc.

A CLASS OF r-POINT (r+1)ST-ORDER A-STABLE ONE-BLOCK METHODS WITH DAMPING AT THE INFINITE POINT

This paper presents a class of r-point (r+1)st-order A-stable one-block methods with damping at the infinite point (DIAOB r,r+1 ). Under the conditions of the same order, A-stability, operation count (at each iterative step) and storage space are the same as the methods in , the methods in the paper improve the stability in a neighborhood at the infinite point. And, by using the OOPI method , it possesses much faster rate of convergence for solving systems of nonlinear equations produced by the DIAOB r,r+1 .

Numerical Integration of Forced and Damped Oscillators through a New Multistep Method

Forced and damped oscillators appear in the mathematical modelling of many problems in pure and applied sciences such as physics, engineering and celestial mechanics among others. Although the accuracy of the T-functions series method is high, the calculus of their coefficients needs specific recurrences in each case. To avoid this inconvenience, the T-functions series method is transformed into a multistep method whose coefficients are calculated using recurrence procedures. These methods are convergent and have the same properties to the T-functions series method. Numerical examples already used by other authors are presented, such as a stiff problem, a Duffing oscillator and an equatorial satellite problem when the perturbation comes from zonal harmonics J2.

Mixed Finite Volume Element Method for Vibration Equations of Beam with Structural Damping

In this paper, for the initial and boundary value problem of beams with structural damping, by introducing intermediate variables, the original fourth-order problem is transformed into second-order partial differential equations, and the mixed finite volume element scheme is constructed, and the existence, uniqueness and convergence of the scheme are analyzed. Numerical examples are provided to confirm the theoretical results. In the end, we test the value of δ to observe its influence on the model.

Application of the Homotopy Perturbation Method to Nonlinear Heat Conduction and Fractional Van der Pol Damped Nonlinear Oscillator

In this paper, a powerful analytical method, called He’s homotopy perturbation method is applied to obtaining the approximate periodic solutions for some nonlinear differential equations in mathematical physics via Van der Pol damped non-linear oscillators and heat transfer. Illustrative examples reveal that this method is very effective and convenient for solving nonlinear differential equations. Comparison of the obtained results with those of the exact solution, reveals that homotopy perturbation method leads to accurate solutions.

一种虚拟同步发电机自适应阻尼补偿方法

针对系统电感对虚拟同步发电机控制系统存在等效负阻尼效应的问题,提出了一种自适应阻尼补偿方法。首先,基于虚拟同步发电机控制技术,通过dq变换和小信号分析建立系统的动态电磁方程和动态小信号模型。然后利用电磁转矩偏差分解出同步力矩系数和等效阻尼系数。最后根据等效负阻尼的产生机制,在有功-频率调节器中加入以系统频率、虚拟阻抗为自适应控制变量的阻尼补偿模块,实现对虚拟同步发电机阻尼的自适应补偿。通过MATLAB/Simulink仿真,并与基于传统的虚拟同步发电机控制方法及基于虚拟阻抗补偿方法等方法所获得的结果进行比较,表明文章所提出的自适应阻尼补偿方法具有更强的稳定性和更快的响应速度,验证了方法的有效性。

基于电气转矩法的VSC-HVDC系统直流电压振荡稳定性评估

文章采用电气转矩法分析了VSC-HVDC系统的直流电压振荡稳定性。首先,基于电压源型换流器的平均值模型,分别研究了基于功率控制的换流器及基于电压控制的换流器的动态响应特征以得到适用于电气转矩法的并网换流器模型。基于提出的评估模型,建立了双端VSC-HVDC系统的Phillips-Heffron模型并推导出系统的阻尼系数和同步系数。经典电气转矩法指出:电力系统稳定性与系统阻尼系数高度相关。因此,基于电气转矩法推导出的稳定条件揭示了系统直流电压振荡失稳机理,量化了直流网络动态及换流器控制动态对直流电压振荡稳定性的影响。当由基于电压控制的换流器及直流网络提供的正阻尼无法抵消由基于功率控制的换流器产生的负阻尼时,系统直流电压振荡稳定性将无法得到保证。此外,合理设置电压控制器的比例增益能够使系统获得足够的稳定裕度。最后,通过仿真验证了电气转矩法在分析VSC-HVDC系统直流电压振荡稳定性问题时的可行性及所得稳定条件的正确性。

基于PCA-LM的空战目标威胁评估

空战过程中态势瞬息万变,获取敌目标的威胁是我方取得攻击占位优势和采取战术规避的前提条件。提出主成分分析法和阻尼最小二乘法相结合的回归模型对目标的威胁进行评估。利用主成分分析法,分析指标之间的相关性,转化成相互独立的分量,确定主成分分量,重构目标威胁评估体系;对目标威胁与主成分分量进行回归分析,利用阻尼最小二乘法对回归模型参数进行估计,得到主成分分量与目标威胁之间的统计关系;利用目标威胁估计值与实际值之间的误差大小,验证了回归模型的有效性。消除了指标之间的相关性对评估结果的影响,提高了评估结果的客观性,解决了传统评估方法忽略指标之间耦合性的问题。

A NEW MATRIX PERTURBATION METHOD FOR ANALYTICAL SOLUTION OF THE COMPLEX MODAL EIGENVALUE PROBLEM OF VISCOUSLY DAMPED LINEAR VIBRATION SYSTEMS

A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping matrix is decomposed into the sum of a proportional-and a nonproportional-damping parts, and the solutions of the real modal eigenproblem with the proportional dampings are determined, which are a set of initial approximate solutions of the complex modal eigenproblem. Second, by taking the nonproportional-damping part as a small modification to the proportional one and using the matrix perturbation analysis method, a set of approximate solutions of the complex modal eigenvalue problem can be obtained analytically. The result is quite simple. The new method is applicable to the systems with viscous dampings-which do not deviate far away from the proportional-damping case. It is particularly important that the solution technique be also effective to the systems with heavy, but not over, dampings. The solution formulas of complex modal eigenvlaues and eigenvectors are derived up to second-order perturbation terms. The effectiveness of the perturbation algorithm is illustrated by an exemplar numerical problem with heavy dampings. In addition, the practicability of approximately estimating the complex modal eigenvalues, under the proportional-damping hypothesis, of damped vibration systems is discussed by several numerical examples.

基于附加阻尼的水轮机调速系统优化控制研究

针对水轮机调速系统引发电力系统发生超低频振荡的问题,提出一种调速侧附加阻尼控制策略。首先,基于阻尼转矩法,分析得出水轮机调速系统产生的负阻尼是造成电力系统发生超低频振荡的主要原因;其次,推导调速系统的阻尼转矩系数表达式,证明该系数与水锤效应时间常数及调速器PID参数密切相关;然后,依托附加阻尼控制策略,在系统调速侧引入正阻尼补偿,并采用灰狼优化算法整定调速器PID参数,以进一步改善系统阻尼特性;最后,在Matlab/Simulink仿真平台搭建单机、四机两区域系统进行仿真验证,结果表明所提控制策略能够明显改善调速系统的阻尼特性,有效抑制超低频振荡。

具有局部阻尼的二维Mindlin-Timoshenko板系统的镇定

该文研究了具有局部阻尼的二维Mindlin-Timoshenko板系统,首先将原系统转化成抽象柯西问题,运用算子半群理论得到了系统的适定性.借助系统频域稳定性结果,通过引入几何光学条件结合乘子技巧得到了系统的一致指数稳定性.

非堆积型多颗粒阻尼器等效力学模型及其减振性能分析

为考虑颗粒群碰撞过程中时间效应对非堆积型多颗粒阻尼器(non-packed particle damper, NPPD)减振性能的影响,在现有考虑惯容的等效单颗粒力学模型(equivalent inertia single-particle model, EISM)研究基础上,提出了基于接触单元法的等效单颗粒力学模型(equivalent inertia single-particle model based on contact element method, EISM-CE),并基于Runge-Kutta算法建立了NPPD单自由度结构运动状态求解算法。设计进行附加NPPD单层钢框架结构振动台试验,探究不同填充率对结构顶层位移频响曲线的影响规律,提出了EISM-CE参数取值原则,进而进行力学模型试验验证及模型对比分析。在模型验证合理性基础上,基于EISM-CE依次进行了自由振动、简谐激励及记录强震动下减振性能及能量变化规律分析。研究结果表明,与现有EISM相比,提出的基于接触单元法的EISM-CE模型及参数取值原则更加合理有效。减振性能数值分析结果表明,不同激励下NPPD均具有较好的减振性能;考虑碰撞时间效应后EISM-CE与EISM对应减振性能及机理分析结果存在一定的差异。