基于最优控制的仿人机器人行走振动抑制

针对仿人机器人行走过程中由腿部非刚性特性引起的振动,提出了一种基于最优控制的行走振动抑制方法．首先对振动进行建模,并将这一模型加入到原有机器人动力学模型中去．然后基于拓展的动力学模型,使用预观控制方法求取一条符合质心加速度约束的控制轨迹,作为求解最优控制问题的初始解．进而由此初始解出发,迭代求解此带约束的最优控制问题,利用得到的最优控制轨迹即能以前馈方式抑制行走过程中的振动．最后,使用预观控制方法和本文方法在仿人机器人“空”上进行行走对比实验．实验结果表明提出的方法显著减小了机器人行走过程中零力矩点（ZMP）的振荡和躯干的晃动．该方法对行走振动抑制的有效性得到了验证．     

正交各向异性叠层板的非线性主共振分析

研究了在四边简支的边界条件下,正交各向异性矩形叠层板在横向简谐激励作用下的非线性主共振及其稳定性问题．在给出了正交各向异性叠层板的振动微分方程的基础上,利用伽辽金法导出了相应的达芬型非线性强迫振动方程．应用平均法对主共振问题进行求解,得到了系统在稳态运动下的幅频响应方程．基于李雅普诺夫稳定性理论,得到了解的稳定性判定条件．作为算例,分别给出了不同条件下,系统运动的幅频响应曲线图、振幅-激励幅值响应曲线图和动相平面图,并对解的稳定性进行了分析,讨论了各参数对系统非线性振动特性的影响．     

双参数弹性地基上板的自由振动

建立了双参数弹性地基上的正交异性矩形薄板自由振动位移函数微分方程,并得到其一般解．这可用以精确地求解板在任意边界条件下的自由振动问题．以四边固定的正方形板为例进行了分析,计算过程简单,便于实际应用．亦适用于求解单参数弹性地基和各向同性板情形。     

基于特征模型的挠性结构自适应振动控制

航天器是一种由中心刚体和挠性附件组成的刚柔耦合复杂系统，由于系统调姿或外部扰动作用时将引起振动，尤其是在平衡位置的小幅度振动对姿态稳定度和指向控制精度严重影响，并且难以控制．为了解决该问题，采用基于特征模型的黄金分割自适应控制方法，并引入逻辑微分阻尼项进行振动主动控制．建立了刚柔耦合结构实验平台，进行了包括位置设定点及转动振动主动控制的算法实验比较，结果表明，采用的基于特征模型的方法得到了比较理想的振动抑制效果，尤其是对低频小幅值振动的抑制，在相同条件下，与传统控制方法相比，大大减少了振动抑制的时间．实验研究表明采用的算法快速抑制振动的有效性．     

压电智能挠性悬臂板主动振动控制试验研究

航天器上太阳帆板这种悬臂外伸薄板结构的挠性附件，存在有扰动条件下引起的振动，可采用压电智能结构对悬臂板进行主动振动控制。文章对设计的挠性悬臂板系统进行系统辨识，得到板系统的前三阶模态频率及阻尼比，并采用PD控制和PPF控制算法对板的前三阶模态(包括弯曲模态和扭转模态)进行主动振动控制。试验结果表明，采用压电智能结构可以抑制挠性悬臂板的振动．效果明显。     

矩形中厚板自由振动问题的哈密顿体系与辛几何解法

以矩形中厚板的胡海昌方程为基础,将中厚板自由振动问题导入哈密顿体系,然后利用辛几何中的分离变量和本征函数展开的方法求出了对边简支板自由振动的精确解．文中采用的辛方法不必事先人为地引入试函数,而是通过完全理性的推导,从而突破了传统半逆解法的限制,使得问题的求解更加合理,易于推广．计算实例证明了本文推导结果的正确性．     

非线性地基上正交异性矩形板的非线性热振动

研究了非线性地基上正交异性矩形板的非线性固有热振动.采用常规的L-P法分析非线性地基上正交异性矩形板的非线性热振动难以得到高精度的近似解,为此,先对该强非线性振动系统进行参数变换,将该强非线性振动系统转化为弱非线性振动系统.然后采用改进的L-P法进行求解,得到了强非线性振动系统的高精度近似解.此外,讨论了温度、地基特征参数、长宽比等因素对非线性地基上正交异性矩形板非线性热振动固有频率的影响,得到了非线性地基上正交异性矩形板热振动频率随温度下降、地基特征参数变大、长宽比变大而增大的结论.     

载流梁在磁场中的横向固有振动分析

在考虑结构变形对电磁场的影响基础上，假设载流梁的变形为小变形，把变形后载流梁中的电流方向改变看成是电流矢量的刚性旋转．建立了载流梁在磁场中的横向固有振动控制方程．方程表明载流梁在磁场中的横向固有振动是一个典型的非线性问题．采用摄动法求得了其近似解，得到了载流梁在磁场中的横向固有振动频率及位移解析表达式．并通过实例计算讨论分析了导线与载流梁间距、载流梁的电流与导线电流的方向及大小、载流梁梁长及其半径等因素对载流梁横向固有振动的影响，得到了一些有价值的结论．     

哈密顿体系下矩形薄板自由振动的一般解

根据弹性薄板自由振动问题的基本方程，把问题引入到哈密顿对偶体系中．x方向模拟为时间，选取弯矩，等效剪力，转角和挠度为对偶向量，得到了在不同边界条件时关于x轴对称和反对称时的解析解．算例研究了四边固支薄板的自由振动情形，从而推广了哈密顿体系的应用范围，验证了哈密顿体系求解方法在自由振动问题中的有效性．     

显式模型预测控制及其在电梯机械系统振动控制中的应用

基于约束线性优化控制问题的多参数规划方法,分别建立了约束线性时不变和时变系统的显式模型预测控制系统．应用建立的显式模型预测控制系统,对不同运行工况（轻载、重载）下的电梯机械系统的主动振动控制进行了仿真．研究结果表明,电梯机械系统显式模型预测控制的主动振动控制效果明显．     

Vibration analysis of rectangular mindlin plates by the finite strip method

A finite strip analysis of the vibration of rectangular Mindlin plates with general boundary conditions is described. The normal modes of vibration of Timoshenko beams are used to represent the spatial variation along a strip of the deflection and the two cross-sectional rotations. For the crosswise representation equal-order polynomial interpolation is employed for each of these three basic quantities. The accuracy of the approach is demonstrated by the results of a number of applications to square plates with combinations of simply supported, clamped and free edges.     

变摩擦力下板带轧机垂扭耦合振动控制技术

当前对板带轧机垂扭耦合振动的控制过程未考虑变摩擦力的影响，无法对振动特性进行准确分析，导致控制效果不理想。提出一种变摩擦力下基于振动摩擦模型的板带轧机垂扭耦合振动控制技术。将垂扭耦合振动参数作为输入向量，理想状态下变摩擦力作为输出向量，确定垂扭耦合振动参数。采用遗传算法对已确定的最优垂扭耦合振动参数进行辨识，构建振动摩擦模型，完成对垂扭耦合振动特性的准确分析，解决控制过程中的变摩擦力影响问题。利用振动摩擦模型对系统位移响应和频域响应振动特性进行控制，实现板带轧机垂扭耦合振动的控制。与传统控制技术进行对比，得出实验结果，所提控制技术控制精度可达98%，能够减小控制过程的变摩擦影响，可对振动特性进行准确地准确分析，大大提高了控制精度。     

Dynamic analysis of structures using a Reissner-Mindlin finite strip formulation

In this paper a finite strip formulation based on Reissner-Mindlin plate theory for dynamic analysis of prismatic shell type structure is presented. Detailed expressions of the relevant strip matrices for a variety of structures using the simple two node linear strip element are given. Examples of the good performance of the linear strip element for free and forced vibration analysis of plates, bridges and axisymmetric shells are presented.     

Forced vibration analysis of piezoelectric quartz plates in resonance

Quartz is a widely used piezoelectric material and quartz resonators are the primary components in many industrial applications due to the piezoelectric effect. To have a thorough understanding on the vibration characteristics of quartz plates, the experimental measurement of resonant frequencies and mode shapes is indispensable. In this paper, two experimental techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), which are, respectively, full-field and point-wise displacement measurement methods, are used to obtain the out-of-plane vibration characteristics of AT-Cut quartz in real time. The resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time from AF-ESPI method. However, only the resonant frequencies of the out-of-plane vibration modes are determined by the LDV. The cantilever and completely free quartz plates are used in this study and the experimental results are verified by the finite element method (FEM) analysis. The cantilever quartz plates are excited from applying voltage and acoustic waves. Furthermore, three designs of electrode for a quartz plate with free-boundary condition are studied. Excellent agreement between the measured data from the optical method and the numerical results predicted by FEM are found for both resonant frequencies and mode shapes.     

Vibration and buckling of skew plates with edges elastically restrained against rotation

This paper deals with vibration and buckling analyses of skew plates with edges elastically restrained against rotation using the spline strip method. The effect of rotational stiffnesses, skew angles and aspect ratios on these problems is analysed, and its characteristic charts are also presented.     

基于Hamilton理论的冷带轧机速度张力系统非奇异 快速终端滑模控制

针对交流异步电机驱动的冷带轧机速度张力系统的跟踪控制问题,给出一种基于Hamilton理论的非奇异快速终端滑模控制器设计方法.首先,设计了一种新型扰动观测器对系统中由参数摄动和负载扰动引起的不确定项进行观测;其次,通过预反馈控制建立了冷带轧机系统速度张力磁链外环的耗散Hamilton模型,进而基于互联–阻尼配置及能量整形方法完成耗散Hamilton控制器的设计;再次,基于串级控制思想完成了冷带轧机系统电流内环非奇异快速终端滑模控制器的设计.通过理论分析证明了所提控制方法能够保证闭环系统全局稳定.最后,基于某交流异步电机驱动的冷带轧机系统的现场实际数据进行仿真对比研究,仿真结果验证了本文所提方法的有效性.     

Buckling of rectangular mindlin plates

The elastic buckling of rectangular Mindlin plates is considered using two related methods of analysis. These methods are the Rayleight-Ritz method and one of its piece-wise forms, the finite strip method. Arbitrary combinations of the standard boundary conditions of clamped, simply-supported and free edges are accommodated by the use in the assumed displacement fields of the normal modes of vibration of Timoshenko beams. The applied membrane stress field leading to buckling can comprise biaxial direct stress plus shear stress. A range of numerical applications is described for isotropic and transversely isotropic plates of thin and moderately thick geometry. The results obtained using the two methods compare closely to one another and to other published results where these are available. A direct relationship between unidirectional buckling stress and frequency of vibration is demonstrated for a category of plates having one pair of opposite edges simply supported.     

Distributed structural identification and control of shells using distributed piezoelectrics: Theory and finite element analysis

Distributed dynamic identification and vibration control of high-performance flexible structures has drawn much attention in recent years. This article presents an analytical and finite-element study on a distributed piezoelectric sensor and distributed actuator coupled with flexible shells and plates. The integrated piezoelectric sensor/actuator can monitor the oscillation as well as actively control the structural vibration by the direct/converse piezoelectric effects, respectively. Based on Maxwell's equations and Love's assumptions, new theories on distributed sensing and active vibration control of a generic shell using the distributed piezoelectrics are derived. These theories can be easily simplified to account for plates, cylinders, beams, etc. A new piezoelectric finite element is also formulated using the variational principle and Hamilton's principle. A piezoelectric micropositioning device was first studied; analytical solutions are compared closely with experimental and finite-element results. Distributed vibration identification and control of a zero-curvature shell-a plate-are also investigated.     

PID sliding mode control for steering of lateral moving strip in hot strip rolling

Lateral movement of a strip in the hot rolling process is an important unsolved technical problem. It results in reduced productivity and, in the extreme case, in strip tearing during tailing out at the finishing mill. Lateral movement of a strip is caused by various asymmetric factors such as mechanical asymmetry of the mill, and different temperatures along the strip width direction. This study aims to understand the influences of these various factors on lateral movement, and to develop a controller that is useful for reducing lateral movement. Mathematical models which consider initial off-center value, leveling error of the mill, and strip tension for lateral movement of the strip are proposed. A Proportional-Integral-Derivative(PID) based sliding mode controller using an observer is also proposed to prevent lateral movement of strips. In addition, a control algorithm is designed to solve the chattering problem of a sliding mode control. The effectiveness of the proposed method is evaluated by numerical simulation of hot rolling by a pinch roll. Recommended by Editor Jae Weon Choi. Yong-Joon Choi received the B.S., M.S., and Ph.D. degrees in Mechanical Engineering from Pusan National University, Pusan, Korea, in 1993, 1995, and 2009, respectively. From 1995 to 2003, he was employed as a Researcher in RIST (Research Institute of Industrial Science and Technology), Pohang, Korea. He has been a Senior Researcher with the technical research laboratory of POSCO, since 2003. His research interests include mechatronics, control, and sensor applications of rolling mill. Min-Cheol Lee received the B.S. in Mechanical Engineering from Pusan National University and M.S. in Engineering Sciences and Ph.D. in Advanced Engineering from the Tsukuba University, Japan, in 1983, 1988, and 1991, respectively. He is now a Professor in the School of Mechanical Engineering, Pusan National University. His research interest includes mechatronics, control of digital servo system, robotics, sensor application, and system identification.