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.

Astral Actions on Allais’ Pendulum Apparently Inexplicable by Classical Factors: A Point of the Situation

1) The observation by Allais of the precession of pendulums from 1954 to 1960 highlighted regularities of astral origin an in-depth analysis of which showed that, apparently, no classical phenomenon can explain them. These regularities were diurnal waves whose periods are characteristic of astral influence (the main ones being 24 h and 24 h 50 min), annual and semi-annual components, and a multi-annual component of approximately 6 years, an influence of Jupiter being a very good candidate to explain it. 2) Allais had experimentally established that all these astral influences were expressed globally on the pendulum by an action tending to call back its plane of oscillation towards a direction variable in time, and which ovalized its trajectory. In 2019 the observation of 2 pendulums in Horodnic (Romania), thanks to the use of an automatic alidade, made it possible to identify the main mechanism that, very probably, acted on the pendulum to achieve this result. This perturbation model, called “linear anisotropy”, is characterized by its “coefficient of anisotropy” η, and by the azimuth of its “direction of anisotropy”. The composition of 2 linear anisotropies is always a linear anisotropy. 3) In the search for the phenomena which could be at the origin of all what precedes, the fact that they must create an ovalization immediately eliminates some of them. 4) We have calculated the values of η corresponding to the 24 h and 24 h 50 min waves both for the observations in Horodnic and the Allais observations. The order of magnitude (some 10−7) is effectively the same in both cases. 5) Mathematically, the regularities discovered may result of a new force field but also, as Allais proposes, from the creation, under the astral influences, of a local anisotropy of the medium in which the pendulum oscillates. In the first case the length of the pendulum is involved, in the second one not. The data available do not make it possible to decide. 6) The joint exploitation, in mechanics and optics, of Allais observations and of observations by other experimenters provides additional information: a) Allais, and after him several other scientists, discovered also marked anomalies in the precession of pendulums during certain eclipses, and maybe certain other syzygies. For the few eclipses for which both something was observed and sufficient data were available (one of them being a lunar eclipse for which nothing had been published until now), it was always the above perturbation model which acted on the pendulum, but sometimes with quite exceptional magnitude. b) There are quite possible links with optics. During the observation campaign of August 1958, which had implemented both two pendulums and an optical device, all the 24 h 50 min waves were almost in phase. In the precession of the Allais pendulum, in Miller’s interferometric observations in Mont Wilson, and in Esclangon’s observations in Strasbourg, a same peculiarity is found: the extrema of the annual influence are at the equinoxes, not at the solstices.

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.

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。

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.

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。

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。

某型摆式加速度计自动盖总成装配系统

摆式加速度计广泛应用于航空航天、船舶等领域的惯性导航系统中,其装配作业目前主要依赖于人工操作,产品一致性难以保证。鉴于此,本文针对某型摆式加速度计研制了一套自动装配系统。基于宏微结合的设计策略,搭建基于高精度运动滑台的微动平台,以及基于单轴机器人的宏动平台。确立了以微动平台为精调核心,以宏动平台辅助压装并实现不同功能模块工作位置调整的装配机制,同时设计功能模块上中下三层的立体分层式结构,在保证精度的同时避免作业空间的拥挤。引入六轴协作机器人并集成视觉系统,实现作业空间的全覆盖识别和自动化上下料功能。针对磁钢零件磁性力对装配精度的影响,采用零件内部辅助限位的方式,实现零件装配精度的保持。基于刚体变换,对系统进行误差分析并推导了误差补偿模型。实验结果验证,该装配系统的角度装配精度优于±0.03°,压装力精度优于±0.5 N,扭力精度优于±0.003 N·m,满足装配要求,为该型摆式加速度计的批量化生产提供了有力保障。

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。

基于遗传模糊PID算法的倒立摆稳摆抑噪抗扰实验与分析

倒立摆稳摆控制原理应用的实际工程需求牵引,使倒立摆成为检验各类控制算法的理想替代实验研究平台。因此,将倒立摆摆杆的姿态稳定控制和抑噪抗扰作为研究内容,以理论分析、编程实现、仿真实验和实物实验验证作为研究手段,聚焦控制器设计的优化。首先,引入模糊控制对PID参数调节进行优化,改固定参数调节为在线参数调节,旨在提高系统的鲁棒性与抗扰性;然后,运用遗传算法的量化因子和比例因子完成调节参数的在线寻优,通过设计适应度函数和选择算子,经过选择、交叉、变异不断演化迭代,最终获取最佳适应度个体、找到最优解,通过仿真验证遗传模糊PID算法突出的抑噪抗扰优势;最后,基于该控制策略进行倒立摆实物实验,验证了其指令跟踪有效性的结论。该研究表明:遗传模糊PID算法具有良好的指令跟踪和抑噪抗扰性能,具有一定的工程应用价值。

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。

圆形截面罐体液体晃动的摆锤模型可行性研究

为研究圆形截面罐体液罐车液体晃动等效摆锤模型的可行性,运用非惯性系下流体Euler方程和均质平面体质心计算公式,构建了液体自由液面倾斜率和质心坐标精确计算模型。得出圆形截面罐体液罐车在横向加速度作用下,液体质心运动轨迹是以罐体截面中心为圆心的一段圆弧,在此基础上提出了一种以液体质心与罐体中心连线为等效摆长的摆锤模型。采用理论计算与计算流体力学(computational fluid dynamics, CFD)仿真技术,分别得到相对应条件下的摆锤振动曲线图像。摆锤振动曲线图像表明,将圆形截面罐体液罐车液体晃动视为摆锤振动具有可行性,可以较好地反映出液体晃动变化规律,方便计算液体晃动时对罐体内壁的反作用力。研究结论可为开展液罐车横向稳定性研究提供理论参考。

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。

铁路标准桥梁典型减隔震体系响应行为与谱分析方法

基于铁路标准桥梁3种典型减隔震设计体系,分析了结构的地震响应行为,重点研究了墩身质量的动力效应和减隔震体系的振型效应.结果显示:铁路标准桥梁墩身质量对桥墩的地震响应存在显著的动力效应,忽视该效应会导致墎顶位移和墎底弯矩的平均相对误差约达11%~32%,对主梁的地震位移影响较小,平均相对误差不超过5%;桥墩的地震响应主要受计算方向上的前2阶振型控制,其中第2阶振型以桥墩自振形态为主,振型阻尼可偏于安全地按结构阻尼比考虑;基于2阶振型效应的SRSS组合可以较好地考虑减隔震铁路标准桥梁的墩身质量动力效应,其预测墩底弯矩平均相对误差可下降至7.5%;AASHTO规范建议的多振型反应谱法适用于铁路标准桥梁典型减隔震体系的地震响应分析.

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。