A modified dynamic surface approach for control of nonlinear systems with unknown input dead zone

This paper focuses on the robust output precise tracking control problem of uncertain nonlinear systems in pure‐feedback form with unknown input dead zone. By designing an extended state observer, the states unmeasurable problem in traditional feedback control is solved, and the lumped uncertainty, which is caused by system unknown functions and input dead zone, is estimated. In order to apply separation principle, finite‐time extended state observer is designed to obtain system states and estimate the lumped uncertainty. Then, by introducing tracking differentiator, a modified dynamic surface control approach is developed to eliminate the ‘explosion of complexity’ problem and guarantee the tracking performance of system output. Because tracking differentiator is a fast precise signal filter, the closed‐loop control performance is significantly improved when it is used in dynamic surface control instead of first‐order filters. The L _∞ stability of the whole closed‐loop system, which guarantees both the transient and steady‐state performance, is shown by the Lyapunov method and initialization technique. Numerical and experiment examples are performed to illustrate our proposed control scheme with satisfactory results. Copyright © 2013 John Wiley & Sons, Ltd.     

基于改进型精密整流电路的电容式微位移传感器设计

介绍了一种改进型精密整流电路,该电路基于一个模拟多路复用器,无需二极管和匹配电阻,克服了传统整流电路中的非线性问题。同时基于该精密整流电路设计了一种电容式微位移传感器。测试结果表明,在0～1.6mm的量程内,该电容式微位移传感器的非线性误差小于0.6‰,灵敏度约为4.3V/mm。     

悬臂梁大变形的向量式有限元分析

为分析悬臂梁的几何非线性行为,用向量式有限元法将结构离散成质点系以及质点间的连接单元.根据牛顿第二定律得到每个质点在内力和外载荷作用下的运动方程以及悬臂梁在每个时刻的变形用该时刻质点系的运动表示.结合刚架元的节点内力和等效质量得出质点位移的迭代计算公式,采用FORTRAN编制计算程序,对悬臂梁分别承受集中载荷和弯矩下的大变形进行算例分析.计算结果与理论解吻合较好,表明该方法能很好地模拟分析悬臂梁的大变形.     

考虑非线性项的卫星编队保持

针对低轨道运行的编队卫星在非线性项作用下,伴随卫星运行的相对运动轨道发生偏移的情况,传统的李亚普诺夫方法能较好地控制轨道的初始偏移,使系统达到李亚普诺夫大范围一致稳定,但长期项误差震荡较大.本文提出了一种多回路结构的卫星轨道保持的控制方法,内回路选取使系统满足李亚普诺夫大范围一致稳定的控制律,外回路选取LQR线性状态调节器.此内外回路调节器能更好地抑制环绕卫星相对于基准轨道的误差漂移,更好地稳定编队队形.最后,数值仿真结果验证了此方法比传统的李亚普诺夫方法具有使编队更稳定的效果.     

Geometric nonlinear effects on the planar dynamics of a pivoted flexible beam encountering a point-surface impact

Flexible-body modeling with geometric nonlinearities remains a hot topic of research by applications in multibody system dynamics undergoing large overall motions. However, the geometric nonlinear effects on the impact dynamics of flexible multibody systems have attracted significantly less attention. In this paper, a point-surface impact problem between a rigid ball and a pivoted flexible beam is investigated. The Hertzian contact law is used to describe the impact process, and the dynamic equations are formulated in the floating frame of reference using the assumed mode method. The two important geometric nonlinear effects of the flexible beam are taken into account, i.e., the longitudinal foreshortening effect due to the transverse deformation, and the stress stiffness effect due to the axial force. The simulation results show that good consistency can be obtained with the nonlinear finite element program ABAQUS/Explicit if proper geometric nonlinearities are included in the floating frame formulation. Specifically, only the foreshortening effect should be considered in a pure transverse impact for efficiency, while the stress stiffness effect should be further considered in an oblique case with much more computational effort. It also implies that the geometric nonlinear effects should be considered properly in the impact dynamic analysis of more general flexible multibody systems.     

Stabilization of geometrically nonlinear topology optimization by the Levenberg–Marquardt method

This paper deals with the design of compliant mechanisms in a continuum-based finite-element representation. Because the displacements of mechanisms are intrinsically large, the geometric nonlinearity is essential for designing such mechanisms. However, the consideration of the geometric nonlinearity may cause some instability in topology optimization. The problem is in the analysis part but not in the optimization part. To alleviate the analysis problem and eventually stabilize the optimization process, this paper proposes to apply the Levenberg–Marquardt method to the nonlinear analysis of compliant mechanisms.     

Stability analysis of a class of digital filters utilizing single saturation nonlinearity

A novel criterion for the global asymptotic stability of a class of digital filters utilizing single saturation nonlinearity is presented. An example showing the effectiveness of the present criterion is given.     

On the lower bounds of the second order nonlinearities of some Boolean functions

The rth order nonlinearity of a Boolean function is an important cryptographic criterion in analyzing the security of stream as well as block ciphers. It is also important in coding theory as it is related to the covering radius of the Reed-Muller code R(r,n). In this paper we deduce the lower bounds of the second order nonlinearities of the following two types of Boolean functions:

1.

with d=2^2r+2^r+1 and , where n=6r.

2.

, where x,y∈F_2^t,n=2t,n?6 and i is an integer such that 1?i<t,gcd(2^t-1,2ⁱ+1)=1.

For some λ, the functions of the first type are bent functions, whereas Boolean functions of the second type are all bent functions, i.e., they possess the maximum first order nonlinearity. It is demonstrated that in some cases our bounds are better than the previously obtained bounds.     

Adaptive predistortion using threshold decomposition‐based piecewise linear modeling

A new adaptive predistortion approach for nonlinear power amplifiers based on the piecewise linear (PWL) approximation of nonlinear functions is presented. The PWL model is obtained using threshold decomposition (TD) of the input‐output characteristics. The TD based PWL model is used to develop a baseband predistorter using both the direct and the indirect learning architectures. The proposed predistorter is proved to provide a better performance in suppressing nonlinear distortion than conventional polynomial predistorters and a reduced hardware complexity as compared to lookup table (LUT) approach. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

The complex local mean decomposition

The local mean decomposition (LMD) has been recently developed for the analysis of time series which have nonlinearity and nonstationarity. The smoothed local mean of the LMD surpasses the cubic spline method used by the empirical mode decomposition (EMD) to extract amplitude and frequency modulated components. To process complex-valued data, we propose complex LMD, a natural and generic extension to the complex domain of the original LMD algorithm. It is shown that complex LMD extracts the frequency modulated rotation and envelope components. Simulations on both artificial and real-world complex-valued signals support the analysis.