超晶格分层与断裂的相平面分析

在经典力学框架内和位错线整体运动的假设下,把Seeger方程化为具有固定力矩的摆方程。引入相面积概念描述了位错的能量转移和释放机制,并导出了能量释放系数。分析表明,同宿轨道很难完成能量传递,周期轨道也不能实现大范围内的能量转移。但是,只要适当控制超晶格的生长温度和速度,就可实现系统能量的有效释放。     

The nonlinear wave equation for higher harmonics in free-electron lasers

The nonlinear wave equation and self-consistent pendulum equation are generalized to describe free-electron laser operation in higher harmonics; this can significantly extend their tunable range to shorter wavelengths. The dynamics of the laser field's amplitude and phase are explored for a wide range of parameters using families of normalized gain curves applicable to both the fundamental and harmonics. The electron phase-space displays the fundamental physics driving the wave, and we use this picture to distinguish between the effects of high gain and Coulomb forces.     

基于扩张状态观测器的直线倒立摆状态反馈控制研究

针对直线倒立摆的控制问题,利用拉格朗日方法对实际物理模型进行线性化处理建立数学模型,为了提高控制精度,将不确定外扰和未建模动态视为一个综合扰动项,运用扩张状态观测器对系统状态和综合扰动项进行观测,设计了基于扩张状态观测器的直线倒立摆状态反馈稳摆控制器;用能量反馈方法和bang-bang控制器实现倒立摆起摆到稳摆的切换。通过无干扰和有干扰状态直线倒立摆起摆到稳摆过程的实验研究,表明系统能够有效的抑制外界干扰,具有较强的鲁棒性。     

Balancing of an inverted pendulum with a SCARA robot

The balancing act of an inverted pendulum with a robotic manipulator is a classical benchmark for testing modern control strategies in conjunction with fast sensor-guided movements. From the control design perspective, it presents a challenging and difficult problem, as the system is open-loop instable and includes nonlinear effects in the actuators, such as friction, backlash, and elasticity. In addition, the necessity of a sensor system that can measure the inclination angles of the pendulum contributes to the complexity of the balancing problem. The pendulum is projected onto the xz and yz planes of the inertial coordinate system. These projections are treated independently from each other and are controlled individually by a state-space controller in the x and y axes, respectively. The nonlinearities of the robot are compensated by using inverse dynamics and inverse kinematics. A specially developed sensor system allows the contactless measurement of the inclination angles of the pendulum. This system consists of a small magnet, placed at the bottom of the pendulum, and Hall-effect sensors placed inside the end effector     

Identification of human postural dynamics

Human postural dynamics was investigated for six healthy subjects using a force platform recording body sway induced by vibrators attached to the calf muscles. The model of body mechanics adopted was that of an inverted pendulum, the dynamics of postural control being assumed to be reflected in the stabilizing forces exerted on the platform by the feet as a result of complex muscular activity subject to state feedback of body sway and position. The approach to signal processing has been that of parametric identification of a transfer function representing the stabilized inverted pendulum. Posture control was quantified in three variables: swiftness, stiffness, and damping. It is shown that the identification fulfils ordinary statistical validation criteria, and it is conjectured that the state feedback parameters identified are suitable for use in assessing ability to maintain posture     

BO方程的同宿呼吸波和有理波及其扰动动力学行为

针对(1+1)维Benjamin-Ono(BO)方程,应用初值扰动双线性变换,结合同宿测试法获得了新的初值扰动周期呼吸波解和扭结呼吸波解,结合二次函数拟设法获得了初值扰动有理波解及其动力学分叉点.直观展示了一些动力学局域扰动结构,结果表明了该方程动力学行为对初值的敏感性.     

由单变量受扰观测序列估计非线性系统重影轨迹

同宿切面和同宿截面的存在使得非双曲线型非线性系统重影轨迹的估计变得十分困难。该文在充分挖掘非线性系统本身特性的基础上,提出了一种估计非双曲线型非线性系统重影轨迹的新方法。不同于以往算法,该方法首先计算受扰序列的局部稳定流和不稳定流方向,进而确定同宿切面存在的位置,很大程度上降低了同宿切面对算法性能的影响,并可精确确定重影轨迹的长度;也不同于现有文献忽视同宿截面对算法性能影响的做法,该文研究得出同宿截面点间的最小距离和干扰噪声幅度二者间的关系,首次定量地估计了同宿截面点可能对算法造成的影响,这无疑对其它算法也将是一个有益的启示。     

运动阻尼对晶体摆动场辐射稳定性的影响

从势和场的观点出发,考虑电子多重散射和晶格热振动的影响,在经典力学框架内,把粒子的运动方程化为广义摆方程;在线性近似下,把摆方程化为带有阻尼项的Mathieu方程。用变形参数方法求出了Mathieu方程的过渡曲线,讨论系统阻尼对稳定性的影响。结果表明,系统的稳定性与阻尼有关,阻尼越大稳定性越好。为晶体摆动场辐射的获得提供了较为宽松的物理条件。     

LQR在单级倒立摆系统中的应用

单级倒立摆控制是一个即复杂而又对准确性、快速性要求很高的非线性不稳定系统控制问题。单级倒立摆数学模型的建立对研究其稳定性具有指导作用。针对多变量、非线性、强耦合性的倒立摆系统,运用牛顿动力学方法建立其动力学方程,并进行线性化处理,得到状态空间模型。然后对该模型分别进行LQR控制,在MATLAB环境下进行仿真。实验结果表明,二次型最优控制具有良好的响应性能和算法简单等特点,在实际应用中具有重要意义。     

Some tools for analyzing chaos

Although computer simulation and physical experiment are probably the most widely used techniques for understanding complex dynamical behavior in nonlinear systems, these are seldom adequate for full understanding unless they are used in conjunction with analytical techniques. In this paper we describe two such techniques, the Melnikov and Shiinikov bifurcation theorems, both of which deal with homoclinic orbits; that is, with trajectories which, in a suitable sense, contain both the unstable and stable dynamics of generalized saddle points. To understand why homoclinic orbits are important, we show how they are related to Smale's famous horseshoe map and thence to shifts operating on sequences of symbols. This makes it easy to understand why the Melnikov and Shilnikov results describe complex, unpredictable motion of the kind usually called chaotic. Our exposition of the theorems is aimed at someone who wants to understand why they are true, and to be able to use them, but is not concerned with the full technicalities.     

Development and control of a bicycle robot based on steering and pendulum balancing

This research focuses on the development of an electric bicycle robot which balances itself while moving at a constant forward speed. The bicycle robot is balanced by applying a pendulum mass moving together with heading steering to share the balancing load. The nonlinear dynamics model of a bicycle along with a pendulum is derived from the Euler-Lagrange equation of motion and nonholonomic constraints with respect to translation and rotation relative to the ground plane. This nonlinear model is then linearized around the upright position and combined with the DC motor model to obtain the completed linearized dynamics model. The robot's prototype is designed and built. The linear quadratic regulator (LQR) is implemented on the system to control its balance. The simulation results show that, by varying the control weighting matrix to increase the use of the pendulum's input, the system obtains better performance in both balancing and straight-line path tracking. In addition, the state weighting matrix can be varied to further improve the path tracking performance while still keeping the stability. Real experimental results are also in line with the simulation results.     

Mechatronics by analogy and application to legged locomotion

A new design methodology for mechatronic systems, dubbed as Mechatronics by Analogy (MbA), is introduced. It argues that by establishing a similarity relation between a complex system and a number of simpler models it is possible to design the former using the analysis and synthesis means developed for the latter. The methodology provides a framework for concurrent engineering of complex systems while maintaining the transparency of the system behavior through making formal analogies between the system and those with more tractable dynamics. The application of the MbA methodology to the design of a monopod robot leg, called the Linkage Leg, is also presented. A series of simulations show that the dynamic behavior of the Linkage Leg is similar to that of a combination of a double pendulum and a spring-loaded inverted pendulum, based on which the system kinematic, dynamic, and control parameters can be designed concurrently.     

基于单片机实现的二级倒立摆控制系统

倒立摆控制系统是一个典型的多阶次、强耦合的时变复杂系统,并且系统阶次高,且存在一定的非线性因素,使得倒立摆系统难以用精确数学模型描述。用经典法设计控制器存在较大的局限性。分析倒立摆控制系统的运动模态,根据人控制倒摆的经验,得到倒立摆系统的控制规律。并利用MCS 52单片机对倒立摆实施控制,实验结果表明该方法控制精度高,能满足预期目的。     

Galvanic vestibular stimulation for analysis of postural adaptationand stability

Human postural dynamics was investigated in 12 normal subjects by means of a force platform recording body sway, induced by bipolar transmastoid galvanic stimulation of the vestibular nerve and labyrinth. The model adopted was that of an inverted segmented pendulum, the dynamics of postural control being assumed to be reflected in the stabilizing forces actuated by the feet as a result of complex muscular activity subject to state feedback of body sway and position. Time-series analysis demonstrates that a transfer function from stimulus to sway-force response with specific parameters can be identified. In addition, adaptation to the vestibular stimulus is demonstrated to exist, and the authors describe this phenomenon using quantification in terms of a postural adaptation time constant in the range of 40-50 s. The results suggest means to evaluate adaptive behavior and postural control in the erect human being which may be useful in the rehabilitation of individuals striving to regain upright stance     

Nonlinear oscillators, iterated maps, symbolic dynamics, and knotted orbits

We illustrate some recent developments in the theory of dynamical systems. Concentrating on periodically forced second-order ordinary differential equations, and using the Josephson (pendulum) and Duffing equations as examples, we show how the method of symbolic dynamics allows one to study complicated (chaotic) invariant sets in the Poincaré maps of such systems. Under certain conditions, these two-dimensional invertible maps can be reduced to one-dimensional (noninvertible) maps on the interval or circle. In this situation, a fairly complete kneading theory is available and one can use it to study bifurcation sequences occurring as parameters vary. We apply these ideas to the Josephson equation. In contrast to reducing the flow to a lower dimensional Poincaré map, Birman and Williams have exploited reduction to a semiflow on a branched two-dimensional manifold by collapsing orbits along stable contracting directions. Using their fundamental result that the knot types of periodic orbits (closed curves in 3-space) are preserved under this collapse--we study some of the knots arising in the Duffing equation. Since the knot type of a periodic orbit is invariant under continuous deformations, one can use it to characterize families of such orbits in parameterized equations. This notion permits us to follow bifurcating sequences of orbits for Poincaré maps of heavily damped (almost one-dimensional) and lightly damped (almost area-preserving) systems and to show that certain "universal," one-dimensional bifurcation sequences are completely reversed for area-preserving maps.     

High bandwidth tilt measurement using low-cost sensors

In this paper, a state estimation technique is developed for sensing inclination angles using low-cost sensors. A low-bandwidth tilt sensor is used along with an inaccurate rate gyro and a low-cost accelerometer to obtain the measurement. The rate gyro has an inherent bias along with sensor noise. The tilt sensor uses an internal pendulum and therefore has its own slow dynamics. These sensor dynamics were identified experimentally and combined to achieve high-bandwidth measurements using an optimal linear state estimator. Potential uses of the measurement technique range from robotics, to rehabilitation, to vehicle control.     

Caudrey-Dodd-Gibbon-Kotera-Sawada方程的同宿呼吸波解、周期波解和扭结孤立波解

利用Painlevé展开和扩展同宿测试法，获得了CDGKS方程的新的同宿呼吸波解、周期波解和扭结孤立波解，丰富了该方程解的内容及其动力学特征。     

Balancing control of a single-wheel inverted pendulum system using air blowers: Evolution of Mechatronics capstone design

Inverted pendulum systems are one of typical control systems suitable for cross-disciplinary education. This article delivers the historical evolution of inverted pendulum systems as Mechatronics capstone design projects for undergraduate students. A wheeled inverted pendulum system is quite a challenging and interesting system to appeal students as a design project. Several design examples from two-wheel to one-wheel inverted pendulum system are elaborated. As a current design, a one-wheel inverted pendulum system which is our main contribution, is presented to deliver novel ideas of using air power to balance the system. The roll angle is regulated by air pressure generated from ducted fans while the pitch angle is controlled by a dc motor. Air pressure is controlled by linear control methods to keep the balancing in the roll direction. Experimental studies demonstrate the successful balancing performance.     

Stabilizing and Direction Control of Efficient 3-D Biped Walking Based on PDAC

This paper proposes a 3-D biped dynamic walking algorithm based on passive dynamic autonomous control (PDAC). The robot dynamics is modeled as an autonomous system of a 3-D inverted pendulum by applying the PDAC concept that is based on the assumption of point contact of the robot foot and the virtual constraint as to robot joints. Due to autonomy, there are two conservative quantities named “PDAC constant,” which determine the velocity and direction of the biped walking. We also propose the convergence algorithm to make PDAC constants converge to arbitrary values, so that walking velocity and direction are controllable. Finally, experimental results validate the performance and the energy efficiency of the proposed algorithm.      

Single-particle theory of the free-electron laser in a moving frame

We give a summary of the theory of a single electron involved in free-electron laser (FEL) operation. We use the method of transformation to a predetermined moving frame where the wiggler-laser scattering process is elastic. In this paper, we discuss the classical and quantum dynamics of such an electron and evaluate perturbatively the lowest order FEL behavior from the classical pendulum equation. The presentation is tutorial throughout and stresses analytic results and physically significant dimensionless parameters. No results are included for the dynamic evolution of the light during the laser action.