Control of a Nonlinear System Using the Saturation Phenomenon

In this paper, a theoretical investigation of nonlinear vibrations of a 2 degrees of freedom system when subjected to saturation is studied. The method has been especially applied to a system that consists of a DC motor with a nonlinear controller and a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. It is shown that the closed-loop system exhibits different response regimes. The nature and stability of these regimes are studied and the stability boundaries are obtained. The effects of the initial conditions on the response of the system have also been investigated. Furthermore, the second-order solution is presented and the corresponding results are compared with those of the first-order solution. It is shown that by increasing the amplitude of the excitation voltage, the higher-order term in the solution becomes significant and causes a drift in the response. In order to verify the obtained theoretical results, they are compared with the corresponding numerical results. Good agreement between the two sets of results is observed.     

Nonlinear Vibration Control of a System with Dry Friction and Viscous Damping Using the Saturation Phenomenon

Application of saturation to provide active nonlinear vibration control was introduced not long ago. Saturation occurs when two natural frequencies of a system with quadratic nonlinearities are in a ratio of around 2:1 and the system is excited at a frequency near its higher natural frequency. Under these conditions, there is a small upper limit for the high-frequency response and the rest of the input energy is channeled to the low-frequency mode. In this way, the vibration of one of the degrees of freedom of a coupled 2 degrees of freedom system is attenuated. In the present paper, the effect of dry friction on the response of a system that implements this vibration absorber is discussed. The system is basically a plant with a permanent magnet DC (PMDC) motor excited by a harmonic forcing term and coupled with a quadratic nonlinear controller. The absorber is built in electric circuitry and takes advantage of the saturation phenomenon. The method of multiple scales is used to find approximate solutions. Various response regimes of the closed-loop system as well as the stability of these regimes are studied and the stability boundaries are obtained. Especial attention is paid on the effect of dry friction on the stability boundaries. It is shown that while dry friction tends to shrink the stable region in some parts, it enlarges other parts of the stable region. To verify the theoretical results, they have been compared with numerical solution and good agreement between the two is observed.This work was done while the authors were associated with the Mechanical Engineering Department, Sharif University of Technology, Tehran, Iran.     

含饱和作动器的基准建筑物混合控制研究

当作动器所提供的控制力小于所需控制力时会出现控制力饱和现象,这一现象在大型结构的实际控制过程中经常出现,为此,本文根据饱和控制力,采用线性矩阵不等式来设计控制器。考虑作动器饱和时,单纯采用作动器来控制结构在地震作用下的响应往往不足于保护结构,此时需附加阻尼器。最优阻尼的确定需要大量的计算,为了减少计算量,本文借鉴临界激励的概念来简化最优阻尼的选择。最后,以三层非线性基准结构为例来说明本文方法的可行性。     

有界随机噪声激励下一类非线性系统的共振与饱和现象

研究了二自由度非线性系统在有界随机噪声激励下,系统响应的共振与随机饱和现象。用多尺度法分离了系统的快变项,用线性化方法求出了系统响应幅值的一、二阶矩,并给出了系统优化设计的一些建议。数值模拟表明本文提出的方法是有效的。     

弹性板振动的多模态主动控制

采用多对压电片对板振动的多阶模态进行主动控制。为了改善结构振动控制的效果，本文对选用结构振动能量和控制信号能量作为控制目标函数的LQR控制算法作了初步研究。首先，按能量准则推导了控制目标函数中权系数矩阵(Q矩阵和R矩阵)的理论计算公式，为权系数矩阵的选取提供了一定的理论依据。然后，运用该算法，在研究了单对压电片进行振动主动控制的基础上．本文深入分析了压电层合板振动的多阶模态控制的问题，用Matlab进行系统仿真，得到了压电层合板受到初始位移激励下板中心点的位移和控制电压大小随时间变化的曲线。数值模拟的结果表明，该方法能达到更有效控制结构振动和减小控制能量消耗的目的．进一步验证了该方法能达到有效控制结构振动和减小控制能量消耗的目的。     

基于能量准则的板振动控制的LQR法

针对压电层合结构振动的主动控制问题，为了优化控制效果，本文基于现代控制理论提出了选用结构振动能量和控制信号能量作为控制目标函数的LQR法。首先，按能量准则推导了控制目标函数中权系数矩阵(Q矩阵和R矩阵)的理论计算公式，为权系数矩阵的选取提供了一定的理论依据。然后，运用该算法，分析了压电层合板受到初始位移激励和冲击载荷作用下的控制过程，用Matlab进行系统仿真，得到了板中心点的位移和控制电压大小随时间变化的曲线。数值模拟的结果表明，该方法能达到更有效控制结构振动和减小控制能量消耗的目的，与一般的LQR控制方法相比，能满足系统多方面的设计要求且控制效果更优，从而验证了该LQR方法运用到结构振动主动控制中的可行性。     

Theoretical and Experimental Study of Multimodal Targeted Energy Transfer in a System of Coupled Oscillators

The purpose of this study is the theoretical and experimental investigation of targeted energy transfers from a two-degree-of-freedom primary structure to a nonlinear energy sink (NES). It is demonstrated that an NES can resonate with and extract energy from both modes of the primary structure. By facilitating these energy transfers, notably through excitation of appropriate periodic and quasi-periodic orbits, one can promote dissipation of a major portion of externally induced energy in the nonlinear attachment.     

An Integral Method to Calculate Water Saturation in a Centrifuge Experiment to Determine Capillary Pressure

The centrifuge method is commonly used to determine the capillary pressure of a porous medium, and the original approximating method for data analysis developed by Hassler and Brunner is still being used. Its limitations are, however, not well understood. Application to analyze experiments where one of the assumptions was obviously violated had been given in the literature. While the result appeared to be quite reasonable, it was not clear how close was it to reality. One of the objectives of this paper is to review the assumptions that is required to develop this method, so that the experimental condition in which it is applicable can be established. The other objective is to derive a completely different solution technique to this problem. There is no need to assume that the ratio of the inlet radius to the exit radius of the core to the center of the centrifuge be close to 1. With the freedom from this limitation it is, therefore, possible to construct machines at lower cost and to improve on the data quality by allowing longer cores.     

Development of a generalised active vibration suppression strategy for a cantilever beam using internal resonance

In this paper, the potential to utilise modal coupling effects in the formulation of a generalised vibration suppression algorithm is investigated. The plant, a flexible cantilever beam undergoing first mode oscillation, is modelled by a second order differential equation with a spring constant and damping coefficient that are representative of the first mode flexibility and material damping of the beam, respectively.In order to establish an internal resonance condition, a second equation, designated the supplementary equation or controller, is appended to the plant to render a two-degree-of-freedom system. The objective is to generate an internally resonant pair. Upon successful completion of this task, a suppression technique is implemented whereby energy is removed from the plant via the supplementary system.The introduction of the supplementary system results in a set of design parameters which are employed to realise a state of internal resonance and to establish the desired dynamic response. The choice of 2:1 internal resonance models results in a unidirectional control torque making this technique particularly attractive for systems using thrusters or tendons as actuators. A similar structural configuration regulated under a PD (Proportional-Derivative) control law is compared to the proposed control scheme via simulation.     

A theoretical and experimental investigation of a three-degree-of-freedom structure

The response of a structure to a simple-harmonic excitation is investigated theoretically and experimentally. The structure consists of two light-weight beams arranged in a T-shape turned on its side. Relatively heavy and concentrated weights are placed at the upper and lower free ends and at the point where the two beams are joined. The base of the T is clamped to the head of a shaker. Because the masses of the concentrated weights are much larger than the masses of the beams, the first three natural frequencies are far below the fourth; consequently, for relatively low frequencies of the excitation, the structure has, for all practical purposes, only three degrees of freedom. The lengths and weights are chosen so that the third natural frequency is approximately equal to the sum of the two lower natural frequencies, an arrangement that produces an autoparametric (also called an internal) resonance. A linear analysis is performed to predict the natural frequencies and to aid in the design of the experiment; the predictions and observations are in close agreement. Then a nonlinear analysis of the response to a prescribed transverse motion at the base of the T is performed. The method of multiple scales is used to obtain six first-order differential equations describing the modulations of the amplitudes and phases of the three interacting modes when the frequency of the excitation is near the third natural frequency. Some of the predicted phenomena include periodic, two-period quasiperiodic, and phase-locked (also called synchronized) motions; coexistence of multiple stable motions and the attendant jumps; and saturation. All the predictions are confirmed in the experiments, and some phenomena that are not yet explained by theory are observed.     

Engine Control using Neural Networks: A New Method in Engine Management Systems

To be able to meet the demands of low emissions and fuel consumption ofmodern combustion engines, new ways have to be found to control thecombustion. We use new sensors to measure the pressure in the combustionchamber and analyze this signal with a neural network in order to receiveseveral form factors which can be used to control the ignition timing. Theneural network is trained off line with measured data and used on line toderive the form factors. The proposed algorithm can be computed in real timeon conventional digital signal processors and adapted to new engines withvery little effort.     

一种基于SMR主动隔振模型的功率流控制方法

用功率流指标描述主动隔振系统中能量的传输，以传输到接受性的功率流最小为最优化控制目标，推导主动隔振系统中功率流传递的最优控制表达式，提出一种基于SMR主动隔震模型的主动功率流的最优化控制策略，对比分析了被动和主动模型下总功率流的传递特性以及主动控制时传递到基础的各功率流分量的分布特征。针对工程实际中的柔性安装问题，对四边筒支矩形薄板扩动隔振进行了研究。     

Fractional Order Control of a Hexapod Robot

This paper studies the performance of integer and fractional order controllers in a hexapod robot with joints at the legs having viscous friction and flexibility. For that objective the robot prescribed motion is characterized in terms of several locomotion variables. The walking performance is analysed through the Nyquist stability criterion and several indices that reflect the system dynamical properties. A set of model-based experiments reveals the influence of the different controller implementations upon the proposed metrics.     

不同水合物饱和度下注热水开采实验研究

为研究不同水合物藏饱和度对注热开采动态的影响,采用自制的一维天然气水合物(NGH)开采模拟实验装置,模拟地层多孔介质的条件,首先在填砂模型中生成不同饱和度的NGH,然后进行注热盐水分解实验。结果表明:不同饱和度的NGH注热分解产气都可划分为三个阶段,不同的是NGH饱和度越高,水合物分解阶段的产气速率越大,且该阶段持续的时间越长;NGH饱和度越高,注热分解阶段电阻率增大的幅度越大,系统各测点温度升高的幅度越小。注热分解过程中产水速率围绕注水速率而上下波动,且NGH饱和度越高,产水速率波动幅度越大;在实验研究范围内,随初始水合物饱和度的升高,注热开采的能量效率逐渐升高。因此,从能量效率来说,高饱和度的水合物藏更适宜于注热开采。     

泡沫铝填充金属薄壁圆管的实验和理论研究

利用实验研究与理论分析相结合的方法研究了泡沫铝填充金属薄壁圆管在准静态侧向压缩下的力学响应.基于能量法,建立了泡沫铝填充圆管和金属薄壁圆管在侧向均匀压缩时的瞬时侧向力、平均侧向力和总吸能的理论公式.对泡沫铝填充管与金属薄壁圆管进行了准静态侧向压缩实验,并且将实验结果与理论公式进行了对比,结果表明理论预测值与实验结果吻合较好.基于建立的理论分析模型,研究了管的几何尺寸以及泡沫铝材料的密度对结构的瞬时侧向力、平均侧向力、总吸能和比吸能的影响.结果表明,在准静态侧向压缩下,泡沫铝填充管的总吸能大于对应的金属薄壁圆管;泡沫铝填充管的侧向压缩力和总吸能随管长度、壁厚和直径的增加而增大;当填充材料泡沫铝密度增大时,填充管的总吸能与侧向压缩力均增加.     

Adaptive Control of Flexible Structures Using a Nonlinear Vibration Absorber

A nonlinear adaptive vibration absorber to control the vibrations offlexible structures is investigated. The absorber is based on thesaturation phenomenon associated with dynamical systems possessingquadratic nonlinearities and a two-to-one internal resonance. Thetechnique is implemented by coupling a second-order controller with thestructure through a sensor and an actuator. Energy is exchanged betweenthe structure and the controller and, near resonance, the structure'sresponse saturates to a small value.Experimental results are presented for the control of a rectangularplate and a cantilever beam using piezoelectric ceramics andmagnetostrictive alloys as actuators. The control technique isimplemented using a digital signal processing board and a modelingsoftware. The control strategy is made adaptive by incorporating anefficient frequency-measurement technique. This is validated bysuccessfully testing the control strategy for a nonconventionalproblem, where nonlinear effects hinder the application of thenonadaptive controller.     

Theoretical and Experimental Study on the Parametrically Excited Vibration of Mass-Loaded String

The parametrically excited lateral vibration of a mass-loaded string is investigated in this paper. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher-order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieu's equation with cubic nonlinearity. Based on the stability criterion for Mathieu's equation, the critical conditions inducing parametric resonance are clarified. Theoretical analysis shows that when the natural frequency f _s of the string lateral vibration and the vertical excitation frequency f satisfy f _s= (n/2)f, n= 1, 2, 3, ..., parametric resonance occurs in the case of no damping. For a damped system, parametric resonance most likely occurs when f is close to 2f _s, and depends on the damping of the system and the vertical excitation. The critical excitation has been derived at different frequencies. If the natural frequency of the mass vertical vibration happens to be twice that of the string lateral vibration, the parametric resonance may occur due to a small disturbance. Numerical simulations show that the lateral vibration of the string does not increase infinitely at parametric resonance because the parametric excitation is self-tuned due to the coupling between the vertical and lateral vibrations. Finally, the theoretical results are supported by some experimental work.     

A Numerical Study of the Critical Gas Saturation in a Porous Medium

We use porenetwork simulations to study the dependence of the critical gas saturation in solutiongas drive processes on the geometric parameters of the porous medium. We show that for a variety of growth regimes (including global and local percolation, instantaneous and sequential nucleation, and masstransfer driven processes), the critical gas saturation, Sgc, follows a powerlaw scaling with the final nucleation fraction (fraction of sites activated), fq. For 3D processes, this relation reads Sgcfq0.16, indicating a sensitive dependence of Sgc to fq at very small values of fq.     

Coupling between high-frequency modes and a low-frequency mode: Theory and experiment

An analytical and experimental investigation into the response of a nonlinear continuous system with widely separated natural frequencies is presented. The system investigated is a thin, slightly curved, isotropic, flexible cantilever beam mounted vertically. In the experiments, for certain vertical harmonic base excitations, we observed that the response consisted of the first, third, and fourth modes. In these cases, the modulation frequency of the amplitudes and phases of the third and fourth modes was equal to the response frequency of the first mode. Subsequently, we developed an analytical model to explain the interactions between the widely separated modes observed in the experiments. We used a three-mode Galerkin projection of the partial-differential equation governing a thin, isotropic, inextensional beam and obtained a sixth-order nonautonomous system of equations by using an unconventional coordinate transformation. In the analytical model, we used experimentally determined damping coefficients. From this nonautonomous system, we obtained a first approximation of the response by using the method of averaging. The analytically predicted responses and bifurcation diagrams show good qualitative agreement with the experimental observations. The current study brings to light a new type of nonlinear motion not reported before in the literature and should be of relevance to many structural and mechanical systems. In this motion, a static response of a low-frequency mode interacts with the dynamic response of two high-frequency modes. This motion loses stability, resulting in oscillations of the low-frequency mode accompanied by a modulation of the amplitudes and phases of the high-frequency modes.     

基于H∞控制方法的AMD Benchmark主动控制结构的试验研究

针对结构主动控制系统中存在的模型不确定性问题,进行了H∞主动控制策略及实验研究,目的是使控制系统具有良好的鲁棒性.文中首先建立了AMD (active mass damper) Benchmark主动控制结构的试验系统,然后介绍了主动控制试验系统的工作原理,随后提出了基于H∞控制理论的主动控制方法,详细阐述了控制器中有关H∞控制权函数选取的过程以及控制器设计过程,最后通过试验验证了H∞控制器的有效性和鲁棒性.