Group delay induced instabilities and Hopf bifurcations, of a controlled double pendulum

Digital filters, frequently used in active control of mechanical systems, enable one to improve the signal-to-noise ratio and the control performance, but introduce group delays into the control loops simultaneously. In order to gain an insight into the effects of a digital filter on a controlled mechanical system, this paper presents the stability switches and the corresponding Hopf bifurcations of a double pendulum system with the linear quadratic control having a digital filter via theoretical analysis, numerical simulations and experiments. In this study, the digital filters are used to remove the undesired noise of high frequency, which is embedded in the control signal, and are modeled as the components of pure time delay during the theoretical analysis and numerical simulations. The study shows that a digital filter with moderate specifications can not only improve the vibration reduction effectively, but also save the energy consumption of the servo-motor remarkably. However, over demanding specifications will make the group delay of the filter exceed a critical value and cause either a divergent motion or a self-excited vibration through a Hopf bifurcation, the occurrence of which depends on both the stability and the size of the basin of attraction of the bifurcating periodic motion. The experimental results well coincide with the theoretical and numerical ones, and strongly support the simplification of the digital filters as the components of pure time delay. Finally, some suggestions are made to avoid the group delay induced instability.     

普物实验中调动学生主动思维的尝试

介绍了在目前的物理实验课中如何能够调动学生主动性思维的方法 ,并在这种初步的尝试中取得了良好的效果。     

复摆振动中的混沌现象

利用组合物理实验仪,研究了复摆振动中的混沌现象,分析了产生混沌的物理条件,并给出不同条件下的混沌图形.     

东北地区普通高等学校医药类专业物理实验课教学现状调查

通过问卷方式,调查了东北地区8所普通高等学校医药专业(本科)物理实验课教学情况。     

Measurement and analysis of complex modulated motions in a weakly nonlinear system

The two-timing dynamics of a forced, weakly nonlinear system are considered. Experimental results on a roll-forced spherical pendulum verify the occurrence of slow-time, subharmonically and chaotically modulated oscillations in a frequency band near resonance; the modulatory behavior follows the occurrence of a Hopf bifurcation in the slow-time coordinates. A phase-sensitive detection method for experimentally isolating the slow-time behavior is described. A Lagrangian model for the pendulum is developed, and slow-time equations are presented. A two-thirds power scalling law relating roll angle to the appearance of the modulations is derived from the slow-time equations and tested with experimental results.     

对耦合摆实验中耦合弹簧的改进

以悬细线拉拽小重物作为等效耦合弹簧，可实现2个一维单摆之间的耦合．通过改变重物的质量或细线的长度，实现等效耦合弹簧的劲度系数的改变．     

装饰光学涂层的研究和进展

对装饰硬涂层目前的研究动态和应用作了评论，论述了颜色的产生和颜色变化的基本原理以及为了研究涂层颜色与涂层其它性质之间关系所需要的特殊技术。文中给出了化学计量、结构以及表面粗糙度对物理蒸汽淀积（PVD）的硬涂层颜色的影响，对于最佳标准的PVD装饰涂层和具有最新抗腐蚀性能、最新颜色的涂层系统作了评论。应用NiPd和CuSn(Zn）代替Ni电镀涂层作为中间层，使涂层系统得到了改进，大大减小了变态反应的危险性。     

体育系新生运动损伤调查与分析

对新生进校后第一学期运动损伤的情况，采用问卷调查法进行分析研究．意在揭示体育教育专业学生运动损伤的规律及损伤原因，剖析运动损伤的机理．为预防运动损伤提供依据．     

Application of vibrational control to linear-quadratic control problems

The application of the theory of vibrational control to linear-quadratic control problems is developed. The solution of the matrix Riccati differential equation (RDE) and the optimal trajectory are found approximately as power series of a small parameter. The minimizing effect of vibrations on the maximal solution of RDE and the cost functional is studied. The region of attraction of the maximal solution of RDE for the case of Hamiltonian matrix with imaginary axis eigenvalues is found. Special attention is paid to the application of vibrations to the linear-quadratic problem of stabilization with respect to a part of variables and transfer of the other variables to a given position. A problem of vibrational stabilization and optimal control of a carriage with an inverted pendulum is solved as an example.     

对CMOS门电路的物理参数基于理想化的分析

以CMOS门电路元件产品为例，提出了如何从理想化出发，对元件产品的物理参数进行设定与正确解读．讨论表明该分析方法可以澄清一些以往对参数的误解，并能有助于指导该型元件产品的正确应用。