THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS

This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=0.The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions satisfy.Furthermore,the exact bound of a special case is given using the Chebyshev system.At the end,some numerical simulations are given to illustrate the existence of limit cycles.

Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

The Rotary Inverted Pendulum(RIP)is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge.Despite the implementation of various control strategies to maintain equilibrium,optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive.Existing methods frequently rely on extensive experimental data or the designer’s expertise,presenting a notable drawback.This paper proposes a novel tracking control approach for RIP,utilizing a Linear Quadratic Regulator(LQR)in combination with a reduced-order observer.Initially,the RIP system is mathematically modeled using the Newton-Euler-Lagrange method.Subsequently,a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states.This approach enhances the controller’s robustness by eliminating differential terms from the observer,thereby attenuating unknown disturbances.Thorough numerical simulations and experimental evaluations demonstrate the system’s capability to maintain balance below50Hz and achieve precise tracking below1.4 rad,validating the effectiveness of the proposed control scheme.

Program structures and synchronization schemes in numerical coordinate controllers of three-wire welding

In the three-wire welding system, a welding process consists of the operations of four devices, namely three welding machines and one bogie. The operations need to be synchronized by a numerical coordinate controller （ NCC ）. In this paper, we will discuss a tnsk-job-procedure cubic program structure. Under this structure, the devices are synchronized and isolated at the same time. This cubic program structure can also be used as a reference for other multi-device or multi-unit manufacturing processes.

Measurement of remanent magnetic moment using a torsion pendulum with single frequency modulation method

In Tian Qin spaceborne gravitational-wave detectors, the stringent requirements on the magnetic cleanliness of the test masses demand the high resolution ground-based characterization measurement of their magnetic properties. Here we present a single frequency modulation method based on a torsion pendulum to measure the remanent magnetic moment mr of 1.1 kg dummy copper test mass, and the measurement result is(6.45 ± 0.04(stat) ± 0.07(syst)) × 10^(-8)A · m^(2). The measurement precision of the mr is about 0.9 n A · m^(2), well below the present measurement requirement of Tian Qin. The method is particularly useful for measuring extremely low magnetic properties of the materials for use in the construction of space-borne gravitational wave detection and other precision scientific apparatus.

Inexplicable Multi-Annual Astral Action on the Precession of Allais Pendulum: An Influence of the Solar System (and Especially of Jupiter?)

Between 1954 and 1961, Allais conducted 6 one-month observations of the azimuth of the plane of oscillation of a pendulum installed in his laboratory. That of 1958 also implemented a second pendulum, identical to the first, located 6 km away in an underground quarry. Although, over these 6 years, the average azimuth of each observation, the amplitude of the 24 h 50 min and 24 h waves, as well as certain other quantities, have evolved considerably, in 1958 their values were very close to those of the second pendulum. The analysis shows that these evolutions could only result from an action external to the pendulum, that no classical phenomenon seems to be able to explain, and which appears, at least mainly, to be an astral action. The evolution of the average azimuth of the pendulum and of the amplitudes of the 24 h and 24 h 50 min components can be decomposed into a component associated with the annual revolution of the Earth around the Sun, and a multi-annual component, whose harmonic 1 has a period which was estimated to 5.74 years. An action of Jupiter is an excellent candidate to explain a large part of the multi-annual action: everything happens as if there were an important action of the modulus of its declination on the multi-annual component, and an important daily action of its hour angle on the azimuth of the pendulum. We cannot exclude an action of the solar cycle, whose period was then about 11 years. The main results were obtained by Allais himself, but this was only published in his book “The Anisotropy of Space”, and remained very little known. Starting from the raw data of Allais, the author of this article found them again, and completed them on certain points.

The Extended Non-Elementary Amplitude Functions as Solutions to the Damped Pendulum Equation, the Van der Pol Equation, the Damped Duffing Equation, the Lienard Equation and the Lorenz Equations

In this paper, we define some non-elementary amplitude functions that are giving solutions to some well-known second-order nonlinear ODEs and the Lorenz equations, but not the chaos case. We are giving the solutions a name, a symbol and putting them into a group of functions and into the context of other functions. These solutions are equal to the amplitude, or upper limit of integration in a non-elementary integral that can be arbitrary. In order to define solutions to some short second-order nonlinear ODEs, we will make an extension to the general amplitude function. The only disadvantage is that the first derivative to these solutions contains an integral that disappear at the second derivation. We will also do a second extension: the two-integral amplitude function. With this extension we have the solution to a system of ODEs having a very strange behavior. Using the extended amplitude functions, we can define solutions to many short second-order nonlinear ODEs.

Project-Based Teaching in Control Theory Education Based on V-REP: A Cart Inverted Pendulum Case

This paper provides a teaching concept for control theory education based on Virtual Robot Experimentation Platform(V-REP).A cart inverted pendulum virtual physical model is developed on V-REP.Students must analyze,design,and implement a suitable controller for the cart inverted pendulum system using their knowledge of the control theory.Different from traditional experiment and numerical simulation,virtual experiment is safe and less constrained.Moreover,the experiment results are more intuitive and obvious.This study can improve students’interest in learning the control theory and help students understand the relevant content better.

一种摆式谐振加速度计的微杠杆结构设计与分析

为提升摆式谐振式加速度计性能,设计了一种将质量块与微杠杆结构一体化的摆式微杠杆结构,实现惯性力的敏感与放大,提升结构的鲁棒性。首先建立了微杠杆结构力学模型,并进行了关键参数计算。其次,根据微杠杆结构放大倍数影响机理,分析了质量块、支撑梁及微杠杆结构尺寸参数对放大倍数的影响;理论分析与有限元仿真结果均表明,支点梁与输出梁的宽度应作为该类微杠杆的关键优化参数。最后,根据上述结论对现有结构尺寸进行优化,优化后的微杠杆放大倍数为15.68,系统放大倍数为12.88,标度因数为70.52 Hz/g,较优化前分别提升了36.94%、36.87%和36.88%,验证了优化方法的有效性。

基于LQR对直线倒立摆的稳摆控制研究及实现

针对倒立摆的稳摆控制问题,研究设计了一个LQR控制器。首先,考虑摆杆摆动的阻力矩,采用牛顿力学分析方法推导出直线倒立摆的数学模型,建立了其线性状态空间模型,并分析了系统的稳定性、能控性与能观性。通过采用仿真试凑确定加权矩阵Q、R,得到状态反馈增益矩阵K,完成LQR控制器的设计。之后,搭建了以开放式运动控制器为核心的倒立摆实验平台,在计算机上开发了实时人机交互程序,在运动控制器里编写了倒立摆控制算法。最后,进行了仿真与实测实验,验证了所设计的LQR控制器的有效性和可行性。

新型万向球摆式隔震装置的设计与应用

针对浮放物体防震保护的迫切需求,研发了一款基于万向球的摆式隔震装置。首先介绍了它的构造特征与运行原理,并以某陈列佛塔为对象进行方案设计,利用有限元软件模拟万向球与圆盘间的接触关系,评估该装置的承载能力;然后通过试验验证了内部阻尼机构力学模型的准确性,采用时程分析法检验了该装置在8度极罕遇地震作用下的隔震效果,并与传统滑动摩擦摆的减震性能进行了对比。结果表明,该隔震装置不仅结构简单、性能可靠,而且具有摩擦系数低,起滑加速度阈值小,阻尼灵活可调的特点。装置中的点面接触具有一定的承载能力,能够满足设计需求。端部设置黏滞阻尼器的阻尼机构表现出明显的速度相关性,阻尼力会随速度的增大而增大。该装置隔震性能良好,在满足位移限值的情况下达到了设定的隔震目标,而且相比于传统型,在位移和加速度响应均需兼顾的情况下,通过合理调整阻尼机构的性能参数,该装置在各地震工况中能够取得更优的综合隔震效果。

基于负刚度装置的超长联大跨连续梁桥地震反应控制研究

为完善超长联大跨连续梁桥的减、隔震技术,将负刚度装置引入到超长联大跨隔震连续梁桥中组成新型减、隔震系统,并与黏滞阻尼器-摩擦摆支座组合减震系统进行比较。基于CSiBridge软件建立全桥有限元模型,负刚度装置采用弹性多段线模拟,摩擦摆支座采用双线性恢复力模型,黏滞阻尼器采用Maxwell模型,输入3条地震波进行非线性时程分析,考查两种新型减、隔震系统下桥梁结构的地震反应,探究负刚度系统及黏滞阻尼器系统对超长联大跨连续梁桥地震反应的控制效果。研究结果表明:负刚度装置与黏滞阻尼器均可以有效地减小超长联大跨隔震连续梁桥的支座位移。负刚度装置对桥墩内力反应及梁体加速度反应的控制优于黏滞阻尼器。负刚度装置在超长联大跨连续梁桥地震反应控制中有较好的应用前景。

水平偏心摆波能装置运动获能特性研究

以水平偏心摆波能装置为对象,通过物理模型试验和数值模拟,对装置在单自由度和多自由度下的运动和获能规律进行研究。不同波周期下,摆体出现小幅振荡、旋转和振荡旋转三种运动状态。研究表明,装置在单自由度下出现对获能不利的“锁停”现象,而多自由度的获能相对较好,平均功率随波浪周期出现两次峰值。第一次峰值对应波周期与能量输出(PTO)阻尼和摆臂长度正相关,峰值与PTO阻尼正相关;第二次峰值及对应波周期与外浮体轴比正相关。

基于柔性铰链结构的大口径压电快摆镜

为了解决压电作动器驱动的快速反射镜因压电作动器伸长量较小,导致快速反射镜偏转角过小的问题,该文提出了一款新型快速反射镜设计方案。采用三级杠杆式柔性铰链放大机构实现压电作动器位移的放大,采用柔性轴承作为快摆镜的运动关节实现快摆镜的大角度定轴偏转。通过理论推导和有限元仿真对快摆镜的最大偏转角度、等效应力、谐振频率以及振型进行分析。实验结果表明,所设计的快摆镜可以实现大于2 mrad的镜面偏转,满足大范围、高精度的光束定位要求。

罕遇地震下高速铁路大跨矮塔斜拉桥减隔震性能研究

为研究不同减隔震装置对高速铁路大跨矮塔斜拉桥的减隔震机理,以某(90+180+90)m矮塔斜拉桥为研究背景,基于非线性时程分析建立有限元模型,研究摩擦摆支座、黏滞阻尼器和减隔震组合装置的减震效果及桥梁的抗震性能。结果表明:罕遇地震作用下,全桥主塔处采用摩擦摆支座和黏滞阻尼器的组合装置可以有效解决抗震问题,优化后选取摩擦系数为0.06、曲率半径为2 m的摩擦摆支座和阻尼系数为12000 kN·(m·s^(-1))-α、阻尼指数α为0.8的黏滞阻尼器;相比于单独使用摩擦摆支座或黏滞阻尼器,减隔震组合装置可大幅度减小全桥各关键截面的内力、桥墩位移及梁端转角,显著提升桥梁的抗震性能,剪力和弯矩的减震率分别达70.85%和76.94%,桥墩墩顶位移减震率达76.08%;各关键截面安全系数均大于1,结构均处于弹性范围,满足桥梁抗震性能的要求。

基于磁悬浮理论的自适应抗拔摩擦摆隔震支座力学性能研究

为解决摩擦摆隔震支座抗拔能力不足的问题并优化其隔震性能,将传统的摩擦摆支座(FPB)和半主动控制思想相结合,提出一种自适应磁悬浮抗拔摩擦摆隔震支座(AMFPB)。基于磁路理论进行理论分析,推导出U型电磁铁的电磁力公式,以及AMFPB刚度、周期和等效阻尼比计算公式;对U型电磁铁进行位移-电磁力试验分析,建立AMFPB有限元模型,并对不同位移幅值、不同电磁铁匝数和输入电流下支座的滞回特性和抗拔性能进行分析。研究结果表明:U型电磁铁的位移-电磁力试验结果与理论结果吻合度较好,计算得到的AMFPB滞回曲线与数值模拟结果基本相同。AMFPB随滑动位移的增加可调节自身的刚度及耗能,有利于支座位移的控制。

电磁吸盘-摩擦摆复合隔震支座理论分析与试验研究

为解决摩擦摆支座在外部荷载激励下不具备抗拔性的缺点,基于电磁原理和半主动控制思想,提出了一种以电磁力为基础,结合传统摩擦摆的电磁吸盘-摩擦摆复合隔震支座(Electromagnetic Chuck-Friction Pendulum System,ECFPS)。介绍了该复合隔震支座的构造特点和耗能机制,并基于电磁原理推导出电磁吸盘吸力以及ECFPS的等效刚度、周期和等效阻尼比等理论公式,建立了ECFPS计算模型。设计并制作了一个缩尺比为1∶3的ECFPS试件,对不同输入电流、竖向荷载和不同位移幅值下的滞回性能进行了试验研究,探究了不同输入电流对抗拔性能的影响。试验结果表明:理论值与试验值吻合度较高,验证了理论公式推导的正确性;等效刚度和单位循环耗能变化明显,两者最大变化幅度分别为19.81%和28.16%;随着电磁吸盘输入电流的增大,ECFPS支座的抗拔性能提高,实现了支座竖向抗拔的功能。

基于改进SAC的倒立摆控制算法研究

针对倒立摆系统控制过程中易受外界干扰和自然不稳定的特点,以及深度强化学习SAC算法采样数据利用率较低和随机离线策略网络收敛较慢的问题,提出了一种结合近端经验采样和优化策略网络结构的改进算法PRER_SAC。构建神经网络拟合函数,策略网络使用性能更优的Mish函数作为激活函数,设置自调节温度系数以增强智能体的探索能力;设计远、近两个经验池,及一种改变数据存放频率的训练策略,提高数据样本的利用率。通过仿真实验对比,所提方法在同等训练次数下所得回报值和算法收敛速度优于DDPG和SAC算法,同传统控制方法PID和LQR相比,有更好的控制效果。最后,对训练好的智能体加入角度扰动,可在2 s内被消除抑制,证明提出的算法具有较强的适用性。

承德地区摆式仪器观测背景功率谱密度特征分析

为获取承德地区摆式倾斜仪捕捉的地震前兆信息及仪器性能,利用功率谱密度分析方法研究3台VP型垂直摆和1台水平摆倾斜仪的噪声频谱特征。研究结果表明,正常情况下,4台仪器记录的主要背景噪声为0.2 Hz以下的低频自然环境噪声;降雨事件主要影响0.2 Hz以下的低频段;摆式仪器能较好地记录到地震波,近震为更多高频成分,远震以记录面波占主导;地震事件可导致0~0.3 Hz频段的噪声显著增加;仪器标定过程中,低频噪声会显著增加。

马陵山站硐室改造前后VS型垂直摆倾斜仪数据质量分析

利用潮汐分析法,分析和评价了马陵山站VS型垂直摆倾斜仪硐室改造前后数据质量的变化情况,结果表明:(1)历年数据观测精度m_γ均小于0.02,仪器搬迁至改造后硐室又有显著提升,数据质量优于搬迁前,超越全国形变优秀台的标准;(2)搬迁后仪器观测噪声水平M_l始终在0.005″左右,稳定性更好;(3)校正后发现搬迁前仪器安装方位角存在较大偏差,影响M_(2)波相位滞后。硐室环境优化改造是有效改善观测数据精度,提高数据质量的重要保证。

山西垂直摆倾斜仪背景噪声分析

利用山西地区垂直摆倾斜仪正常时段的观测数据,计算功率谱密度PSD和噪声水平SNM,对观测的正常背景特征进行分析和讨论。结果表明,未受任何干扰的观测数据每日PSD变化不大,分钟采样观测数据能反映最大为8.3 mHz的PSD分布,秒采样观测数据能反映最大为0.5 Hz的PSD分布。临汾地震台同址VS型、VP型垂直摆观测数据的噪声水平具有一致性;有2套仪器的背景噪声水平偏高,有4套仪器的背景噪声水平较低;低噪声水平仪器观测曲线光滑、固体潮清晰,运行稳定;高噪声水平仪器观测曲线毛刺多、不光滑。该现象除受观测环境影响以外,主要还受仪器自身的影响。