带两个区域的平面分段光滑系统的非双曲极限环分岔

本文讨论了一类含有两条切换线的平面分段光滑系统的非双曲极限环的分岔.假设该系统的未扰系统含有一个非双曲极限环且它分别与每一条切换线横截相交一次,本文应用Diliberto定理和由此引出的变分引理导出了极限环的Poincaré映射,并讨论了极限环的稳定性及其在扰动下的分岔.

俯仰角对鸭式布局飞机摇滚运动的影响与机理分析

为了研究鸭式布局飞机的摇滚运动,设计了一种包括鸭翼、脊型前体、边条翼、主翼和垂尾的模型,进行滚转自由度释放、静态测力、动导数试验和烟线流场显示多种技术手段相结合的风洞试验。首先为了得到摇滚从发生到消失的全过程,进行了俯仰角范围为12°~52°、间隔1°测量的滚转自由度释放试验;结果表明对应于不同的俯仰角,鸭翼布局飞机的摇滚运动也具有不同的性质,其平衡点和运动形式均发生变化。接着静态测力和动导数试验证实:在翼体结构的多涡系影响下,摇滚可在零度平衡点和非零平衡点位置处发生;且运动可为极限环和非极限环形式。最后通过流场显示,分析了在不同迎角时鸭式布局飞机形成翼体摇滚的可能的流动机理。

Backlash Nonlinear Compensation of Servo Systems Using Backpropagation Neural Networks

Aim To eliminate the influences of backlash nonlinear characteristics generally existing in servo systems, a nonlinear compensation method using backpropagation neural networks(BPNN) is presented. Methods Based on some weapon tracking servo system, a three layer BPNN was used to off line identify the backlash characteristics, then a nonlinear compensator was designed according to the identification results. Results The simulation results show that the method can effectively get rid of the sustained oscillation(limit cycle) of the system caused by the backlash characteristics, and can improve the system accuracy. Conclusion The method is effective on sloving the problems produced by the backlash characteristics in servo systems, and it can be easily accomplished in engineering.

Non-linear 2-DOF model and centre manifold theory to study limit cycle oscillations caused by drum-brake judder

This paper presents the research on the laws of systematic-parameter dependent variation in the vibration amplitude of drum-brake limit cycle oscillations (LCO). We established a two-degree non-linear dynamic model to describe the low-frequency vibration of the drum brake, applied the centre manifold theory to simplify the system, and obtained the LCO amplitude by calculating the normal form of the simplified system at the Hopf bifurcation point. It is indicated that when the friction coefficient is smaller than the friction coefficient at the bifurcation point, the amplitude decreases; whereas with a friction coefficient larger than the friction coefficient of bifurcation point, LCO occurs. The results suggest that it is applicable to suppress the LCO amplitude by changing systematic parameters, and thus improve the safety and ride comfort when applying brake. These findings can be applied to guiding the design of drum brakes.

鸭式布局飞行器的翼体摇滚特性风洞试验

为研究鸭式布局飞行器摇滚特性,设计了一种包括鸭翼、脊型前体、边条翼、主翼和垂尾的模型,进行了自由滚转、扰动滚转、静动态测力和烟线流场显示多种技术手段相结合的风洞试验。通过自由滚转和扰动滚转试验得到了该模型翼体摇滚的时间历程,静态测力和动导数测定验证了非极限环运动形式摇滚的发生。结果表明该鸭式布局模型摇滚不仅同侧存在多个摇滚平衡点,而且在临界俯仰角,摇滚过程中可能出现从一摇滚平衡点跳动至同侧另一摇滚平衡点的突变。通过流场显示技术得到该鸭式布局模型复杂流场的基本形态分布,并对滚转角为0°时的全机涡系干扰和摇滚形成机理进行了简要分析。

Calculations of the bounds on limit cycle oscillations in nonlinear aeroelastic systems based on equivalent linearization

The nonlinear aeroelastic system of an airfoil with an external store was investigated,with emphasis on the bounds of limit cycle oscillations(LCOs).Based on the equivalent linearization,an approach was proposed to calculate the bounds on LCOs over the full flight envelope.The bounds are determined directly without solving LCOs one by one as the flow speed varies.The presented approach can provide us with the maximal LCO amplitudes and the lower threshold for flow speed beyond which LCOs may arise.Numerical examples show that the obtained bounds are in nice agreement with numerical simulation results.The speed threshold can be predicted to a relative error less than 0.1%,and the maximal LCO amplitude to about 3%.The influences of the system parameters on the speed threshold for speed were investigated efficiently by the proposed approach.

EXISTENCE AND ANALYTICAL APPROXIMATIONS OF LIMIT CYCLES IN A THREE-DIMENSIONAL NONLINEAR AUTONOMOUS FEEDBACK CONTROL SYSTEM

This paper is concerned with the existence and the analytical approximations of limit cycles in a three-dimensional nonlinear autonomous feedback control system.Based on three-dimensional Hopf bifurcation theorem,the existence of limit cycles is first proved.Then the homotopy analysis method(HAM) is applied to obtain the analytical approximations of the limit cycle and its frequency.In deriving the higher-order approximations,the authors utilized the idea of a perturbation procedure proposed for limit cycles' approximation in van der Pol equation.By comparing with the numerical integration solutions,it is shown that the accuracy of the analytical results obtained in this paper is very high,even when the amplitude of the limit cycle is large.

Identification and robust limit-cycle-oscillation analysis of uncertain aeroelastic system

Model uncertainty directly affects the accuracy of robust flutter and limit-cycle-oscillation (LCO) analysis. Using a data-based method, the bounds of an uncertain block-oriented aeroelastic system with nonlinearity are obtained in the time domain. Then robust LCO analysis of the identified model set is performed. First, the proper orthonormal basis is constructed based on the on-line dynamic poles of the aeroelastic system. Accordingly, the identification problem of uncertain model is converted to a nonlinear optimization of the upper and lower bounds for uncertain parameters estimation. By replacing the identified memoryless nonlinear operators by its related sinusoidal-input describing function, the Linear Fractional Transformation (LFT) technique is applied to the modeling process. Finally, the structured singular value(μ) method is applied to robust LCO analysis. An example of a two-degree wing section is carded out to validate the framework above. Results indicate that the dynamic characteristics and model uncertainties of the aeroelastic system can be depicted by the identified uncertain model set. The robust LCO magnitude of pitch angle for the identified uncertain model is lower than that of the nominal model at the same velocity. This method can be applied to robust flutter and LCO prediction.