非线性

Taking the nonlinear refraction and the nonlinear absorption into account simultaneously, this paper investigated the diffraction theory model of the Z-scan technique, and analyzed the features of Z-scan curves and their variation rules.

在同时考虑非线性折射和非线性吸收的情况下，借助光的衍射理论，研究了Z-扫描技术的衍射理论模型，分析了非线性折射和非线性吸收同时存在时Z-扫描曲线的形状特征和变化规律。

Then, the relations between the general nonlinear systems and its adjoint system were discussed, from which the sufficient and necessity conditions for exact linearization of general nonlinear control systems were obtained. The conclusions include the corresponding results of the affine nonlinear systems.

引入一类相关的仿射非线性系统，通过研究一般非线性系统与其伴随系统的关系，利用伴随系统的精确线性化结论，获得一般非线性系统精确线性化的充要条件，其结果包含了仿射非线性系统的已有结果。

A ship course controller is designed for Norrbin nonlinear ship mathematical model with matching uncertainty. Combining the backstepping algorithm with the nonlinear damping algorithm to design controller, the nonlinear damping is used to cancel the uncertainty. The integral item is introduced in the design to improve the performance of the controller. Now, general ships can only use the electric gyrocompass to measure the course angle, but they have no equipments to measure the angular velocity, so in this article another ship course controller of output feedback is designed for Norrbin nonlinear ship, firstly the angular velocity is estimated by the observer and then the ship course controller is designed.

本文基于含有匹配不确定项的Norrbin非线性船舶数学模型，将backstepping算法和非线性阻尼算法相结合设计船舶航向控制器，利用非线性阻尼来抵消系统的不确定项，同时为了更好地改善系统的性能，在设计过程中引入了积分项；由于目前一般船舶只有电罗经用于测量船舶的航向角，还没有测量船舶航向角速度的设备，因此，针对Norrbin非线性船舶模型设计了一种输出反馈控制器，首先利用观测器对船舶航向角速度进行估计，然后再设计船舶航向控制器。

By virtue of method of continuum approximate limit, we obtained the solitons of the vibration of lattice in one-dimensional harmonic and inharmonic chains of polarized molecule, under the conditions considering and inconsidering the interaction of exciton with phonon, through solving moving equations of exciton and phonon.

运用连续极限近似方法，通过求解声子和激子的运动方程，得到了在不考虑激子与声子的相互作用和考虑激子与声子相互作用两种情况下的极性分子简谐链和非简谐链中晶格振动的孤子解，并得出了激子与声子的相互作用的非线性效应类似于晶格三次势的非线性效应，以及相同的非线性效应不论是同时作用还是单独作用都具有相同的非线性效应的结论。

For a nonlinear course keeping system for ships, a kind of nonlinear robust PID is presented, which is based on an exact feedback linearization and a closed-loop gain shaping algorithm. The nonlinear PID controller is constituted of a nonlinear items with a robust PID controller.

针对非线性船舶航向保持系统，给出一种基于精确反馈线性化和闭环增益成形算法的非线性鲁棒PID控制器，该非线性PID控制器由非线性函数项和鲁棒PID控制器组成。

After comparing nonlinear simulation with linear, the results indicate that: Weak nonlinearity has definite and apparent influence on the distribution of acoustic fields and focused gain of array, which cause the distribution of waveform is closer to the array and the focused gain deteriorate ; the strong nonlinearity have a strong waveform aberration, because the other waves of non-fundamental frequency appear . No evident distinction is found in the effects between the oblique propagation and the vertical propagation, though less focused gain and influence caused by strong nonlinear produced by the acoustic diffraction which results in more attenuation in terms of oblique propagation.

将线性条件下的模拟结果与非线性条件下的模拟结果进行比较发现：弱非线性会对声场的分布和阵列聚焦增益产生一定的影响，使得声场分布波形比线性条件下的更加靠近阵列，聚焦效果变差；强非线性会使波形发生更严重畸变，这是由于产生了基频以外的其他频率声波引起的；非线性对斜向传播时声场分布的影响与垂直传播时的影响效果基本相同，但由于斜向辐射时的声波衍射造成的衰减要大于垂直辐射时的，因此聚焦增益和强非线性的影响都将小于垂直辐射时的情况。

At the beginning of 1990"s, backstepping was developed by Kokotovic and his copartners, it is a kind of circulative nonlinear design method that uses systematic way to construct feedback method and simultaneous correlative control Lyapunov function and so more and more scholars pay attention to it. Because it has very good flexibility, people can use "good" nonlinear item through introducing nonlinear damping to control "bad nonlinear item. Now backstepping design method is one of the most effective methods to settle control problems in nonlinear system with uncertainty.

20世纪90年代初，出现了以Kokotovic及其合作者发展起来的backstepping设计方法，它是一种运用系统化的方式同时构造反馈控制律和相关联的控制李雅普诺夫函数的循环非线性设计方法，近年来引来了越来越多的学者的高度重视，它具有很好的设计柔韧性，设计者可利用&好的&非线性项，通过增加非线性阻尼来控制&坏的&非线性项，是目前解决不确定非线性系统控制问题的最有效途径之一。

To the nonlinear plants, the shortage of normal inverse control method for nonlinear plants is discussed in chapter 6. ANFIS is effectively applied to nonlinear inverse dynamic control system. A project about how to design nonlinear inverse dynamic controller is also discussed here. It effectively avoid the inherent imperfects in the normal inverse control methods. These methods show a great promise.

对于非线性被控对象，本文在第六章分析了通常非线性逆控制方法的不足，并将自适应模糊神经推理系统用于非线性逆动态控制中，讨论了ANFIS非线性逆动态控制器的设计方案，有效地克服了在常规逆控制方法中所固有的缺陷，在非线性控制中很有应用前途。

From the curve, we linearised the CCS nonlinear model and constructed the T-S fuzzy model of the unit by linking together the linear models of the unit with membership functions. A kind of fuzzy supervisory control system in which using the multi-variable inner model controller or robust controller as its local controller and T-S fuzzy model as the inner model of the supervisory controller has been proposed.

本文的研究内容集中在如下几个方面：根据非线性系统平衡流型和非线性测度的定义，提出了关于平衡流型参数的相对非线性测度的概念，据此绘出了一个具体单元机组机炉协调控制系统模型的相对非线性测度曲线，对此协调控制系统非线性模型进行了线性化，并用隶属度加权的方法将各线性化模型连接成协调控制系统T-S模糊模型。

Our study addresses the following topics:A conception of relative nonlinear measure on the equilibrium manifold parameter has been derived based on the definitions of equilibrium manifold and nonlinear measure about nonlinear system.And the nonlinear measure curve of a material boiler-turbine CCS model has been drawn.From the curve, we linearised the CCS nonlinear model and constructed the T-S fuzzy model of the unit by linking together the linear models of the unit with membership functions.

本文的研究内容集中在如下几个方面：根据非线性系统平衡流型和非线性测度的定义，提出了关于平衡流型参数的相对非线性测度的概念，据此绘出了一个具体单元机组机炉协调控制系统模型的相对非线性测度曲线，对此协调控制系统非线性模型进行了线性化，并用隶属度加权的方法将各线性化模型连接成协调控制系统T-S模糊模型。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。