Time-optimal interpolation for CNC machining along curved tool pathes with confined chord error

In this paper, two new interpolation algorithms lot CNC machining along curve~l tom pathes are proposed： a time-optimal interpolation algorithm under chord error, feedrate, and tangential acceleration bounds, and a greedy interpolation algorithm under the chord error and tangential jerk bounds. The key idea is to reduce the chord error bound to a centripetal acceleration bound which leads to a velocity limit curve, called the chord error velocity limit curve. Then, the velocity planning is to find the proper velocity curve governed by the acceleration or jerk bounds ＇~under＂ the chord error velocity limit curve. For two types of simple tool pathes, explicit formulas for the velocity curve are given and the methods are implemented in commercial CNC controllers.     

基于模糊辨识的混合鲁棒自适应控制

针对一类多输入多输出不确定非线性系统,提出一种基于模糊辨识的混合鲁棒自适应控制方法。该方法探讨了自适应模糊控制器的参数自适应律由跟踪误差和逼近误差共同进行调节,并从理论分析和仿真角度证明了该方法比参数自适应律仅用跟踪误差进行调节的控制器具有更好的跟踪效果,该方法加快了系统跟踪误差的收敛速度。将该算法用于两连杆机械手轨迹跟踪,仿真结果表明该算法具有跟踪精度高,收敛速度快的优点。     

带有误差补偿的非线性系统自适应模糊控制

针对一类非线性系统提出了间接自适应模糊控制方法,该方法用模糊逻辑系统逼近未知函数,并设计误差补偿器来减少逼近误差对跟踪精度的影响。在设计等效控制时考虑其存在性,仿真证明该方法不但能使跟踪误差收敛到原点的小邻域内,而且通过适当调整设计参数,可使跟踪误差减小,收敛速度加快。仿真结果验证了此方法的有效性。     

Variable feedrate interpolation of NURBS Toolpath with geometric and kinematical constraints for five-axis CNC machining

Variable feedrate interpolation algorithms for five-axis parametric toolpath are very promis- ing but still rather limited currently. In this paper, an off-line feedrate scheduling method of dual NURBS curve is presented with geometric and kinematical constraints. For a given dual parametric curve, the feedrates of sampling points are first scheduled sequent with confined feedrate of cutter tip and machine pivot, chord error, normal acceleration and angular feedrate. Then, the feedrate profiles of angular feed acceleration sensitive regions of the path are adjusted using a bi-directional scanning algorithm. After that, a linear programming method is used to adjust the feedrate profiles of linear feed acceleration sensitive regions and control the linear feed acceleration of both cutter tip and machine pivot within preset values. Further, a NURBS curve is used to fit the feedrates of sampling points. Finally, illustrative examples are carried out to validate the feasibility of the proposed feedrate schedul- ing method. The results show that the proposed method has the ability of effectively controlling the angular feed characters of cutter axis as well as the chord error and linear feed characters of cutter tip and machine pivot, and it has potential to be used in high accuracy and high quality five-axis machining.     

一类不确定非线性系统的自适应模糊控制

对一类不确定非线性系统提出自适应模糊控制方法。此方法用模糊逻辑系统设计自适应模糊监督控制器和自适应模糊控制器,且设计补偿器对逼近误差进行补偿,以此来减少逼近误差对跟踪精度的影响,同时对自适应模糊监督控制器和自适应模糊控制器中的未知参数设计了自适应学习律。证明了该方法不但能保证闭环系统稳定,而且可使跟踪误差收敛到原点的邻域内。仿真结果验证了此方法的有效性。     

切向加速度与弦误差约束的CNC系统时间最优轨迹规划

针对计算机数控(CNC)系统给定参数化路径, 给出了一种求解时间最优轨迹规划问题的凸优化方法. 轨迹规划问题考虑切向加速度约束与弦误差约束. 通过建立两种约束下的状态容许空间, 分析约束对时间最优轨迹的影响. 通过非线性变量代换, 时间最优轨迹规划问题被表述为一个与时间无关的凸最优控制问题. 基于控制向量参数化(CVP)方法, 问题被进一步转化为易于求解的凸优化问题. 以路径参数对时间的二阶导数(参数加速度)为优化变量, 序列二次规划(SQP)方法获得问题数值解. 文末通过求解两个测试路径的时间最优轨迹规划问题, 验证方法的有效性.     

Finite element approximation for a class of parameter estimation problems

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.The authors derive some a priori error estimates for both the control and state approximations.Finally,the numerical experiments verify the theoretical results.     

Robust adaptive neural network control with supervisory controller

The problem of direct adaptive neural network control for a class of uncertain nonlinear systems with unknown constant control gain is studied in this paper. Based on the supervisory control strategy and the approximation capability of multilayer neural networks (MNNs), a novel design scheme of direct adaptive neural network controller is proposed.The adaptive law of the adjustable parameter vector and the matrix of weights in the neural networks and the gain of sliding mode control term to adaptively compensate for the residual and the approximation error of MNNs is determined by using a Lyapunov method. The approach does not require the optimal approximation error to be square-integrable or the supremum of the optimal approximation error to be known. By theoretical analysis, the closed-loop control system is proven to be globally stable in the sense that all signals involved are bounded, with tracking error converging to zero.Simulation results demonstrate the effectiveness of the approach.     

Study on High-Speed Magnitude Approximation for Complex Vectors

Abstract: High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The perfor-mance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, theapproximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modifiedCORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to bewith a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finiteregister length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practicalapplications.     

多星载光学传感器系统误差极大似然配准算法

针对低轨星座协同探测弹道目标过程中存在系统误差的问题，提出多星载光学传感器系统误差极大似然配准（maximum likehood registration，MLR）算法。通过一阶Taylor近似对非线性量测转换线性化，推导出目标状态的误差协方差与卫星轨道定向、姿态角测量和传感器测量等随机误差的关系，并基于视线交叉获得观测在状态空间中的近似投影，从而将MLR算法扩展到低轨星座多光学传感器的误差配准。通过引入各类测量误差的先验信息对目标状态的误差协方差进行修正，利用期望极大化迭代，实现了对系统误差的无偏有效估计及目标轨迹的融合估计。仿真验证了所提算法的有效性，且配准性能优越。     

直接鲁棒自适应模糊控制

针对一类不确定非线性系统 ,基于监督控制方案并利用第二类模糊系统的逼近能力 ,提出了一种直接鲁棒自适应模糊控制器设计的新方案。该方案通过引入最优逼近误差的自适应补偿项来消除建模误差的影响 ,从而在稳定性分析中取消了要求逼近误差平方可积或逼近误差的上确界已知的条件。理论分析证明了闭环控制系统是全局稳定的 ,跟踪误差收敛到零。仿真结果表明了该方法的有效性。     

增益符号未知的鲁棒自适应模糊控制

针对一类具有函数控制增益符号未知的不确定非线性系统,根据滑模控制原理和模糊系统的逼近能力,提出了一种自适应模糊控制器设计新方案。该方案利用Nussbaum函数的性质,取消了常用的函数控制增益符号已知这一条件。并通过引入最优逼近误差的自适应补偿项来消除建模误差和参数估计误差的影响。理论分析证明了闭环系统的有界性和跟踪误差收敛到零。仿真结果表明了该方法的有效性。     

CONVERGENCE RATE ANALYSIS OF MULTIPLICATIVE SCHWARZ ALGORITHM FOR ELLIPTIC VARIATIONAL INEQUALITIES

1 IntroductionWith the development of computer science, decomposition methods have been widely usedin solving large sparse lineax systems arising from the discretization of seifadjoint or nonseifad-joint elliptic boundary value problems (see, e.g., [1--6]). These methods have also been used tosolve variational inequalities (see [7--13] and the references therein). Recently, decompositiontechniques have been introduced to solve discrete problems of variational inequalities. An algthrithm of thi…     

MULTILEVEL CORRECTION FOR COLLOCATION SOLUTIONS OF VOLTERRA NONL INEARINTEGRO-DIFFERENTIAL EQUATIONS

1. IntroductionWe consider a Volterra integro-differential equationwith initial condition u(0) = not where f, P, k are continuous on their respective domainsJ, JxR and axs (n:~ {(t,s): 05s5t5T}) such that (1.l) possesses a unique solutionu E C'(J).It has been shown in [1] that the collocation approximation for (1.1) by discolltinuous piece--wise polynomial spline collocation at the Gauss points restore optimal local superconvergenceat the knots but does not yield global superconvergence on…     

曲面薄壳有限元离散误差分析和修正方法研究

基于曲面薄壳几何/物理方程和有限元离散原理推导,揭示了壳单元离散方法特点、刚度矩阵误差产生机理和范数表示方法。以航空涡轮发动机测压探针为例,深入研究了利用协调平板壳单元、非协调平板壳单元、一次和二次实体退化壳单元等不同类型单元离散曲面薄壳时,应力计算误差影响因素及变化规律,综述了单元的适用条件。基于Boltzmann模型提出了应力计算结果修正通式,通过FORTRAN语言编程修正应力仿真结果和ANSYS二次开发语言APDL命令实现应力修正结果的读取和后处理,应力修正结果与理论解相对误差小于5%,满足曲面薄壳设计和稳定性分析应用要求。

Abstract：

Based on the geometric physical equations and deduction of discrete process of finite element for curved thin-walled structure,characteristics of shell elements for discretion and discrete error for element stiffness matrix were analyzed theoretically,and the norm expression of discrete error for element stiffness matrix was put forward.Then,as an illustration,a probe for detecting the pressure inside turboprops was meshed by curved thin-walled shell element,compatible flat shell element,incompatible flat shell element and 3D degenerated shell element,respectively,and the stress of the probe was numerically calculated by FEM.On the basis of solved results,the stress error was analyzed thoroughly,the influence factors on the error and the applying situations for different elements were determined.Finally,the general form of correctional function was put forward according to the Boltzmann model.The program developed with FORTRAN was used to correct the numerical results and the APDL commands inside ANSYS software were utilized to read and plot the correctional stress results.Through the correction,the discrete error can be reduced within 5% that satisfies the requirement of application for structural design and stability analysis.     

FINITE ELEMENT ERROR EXPANSION FOR NONUNIFORM QUADRILATERAL MESHES

An error expansion for isoparametric bilinear finite element approximation isestablished with some kind of nonuniform quadrilateral mesh constructed in the followingway:We first decompose the considered polygonal domain into several fixed convex macro-quadrilaterals and then link up some equi-proportionate points of the opposite edges in eachmacro-quadrilateral and form a quadrilateral mesh which may not be uniform and so isuseful in the adaptive refinement.     

Investigating the Synthesis of RBF Networks

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ERROR ESTIMATION OF THE APPROXIMATION ALGORITHM FOR THE WINDY POSTMAN PROBLEM

If we restrict the postman to traversing each edge at most twice in the windypostman problem (WPP), we will get a new problem: 2WPP. An approximation algorithmhas been posed by M. Guan for the WPP. In the present paper, we improve the estimatederror given by M. Guan and show that we can estimate the error for the 2WPP by findinga minimum cost circulation. We also pose a new sufficient condition for the equivalencebetween WPP and 2WPP, which can be checked in polynomial time steps.     

一类非线性系统的模型参考自适应模糊控制

针对一类不确定非线性系统 ,基于一种修改的监督控制方案并利用广义多线性模糊逻辑系统的逼近能力 ,提出了一种模型参考自适应模糊控制器设计的新方案。该方案利用参考模型作为性能指标 ,自适应调节模糊控制器的规则库 ,并通过引入最优逼近误差的自适应补偿项来消除建模误差的影响 ,不但能保证闭环系统稳定 ,而且可使跟踪误差收敛到零。仿真结果表明了该方法的有效性     

基于RBF的机械手建模误差补偿自适应控制

针对机械手动力学建模误差,提出了基于RBF神经网络误差补偿的自适应控制策略。在基于逆动力学的计算力矩控制方法的基础上,对系统输入与目标轨迹进行修正,设计了两种误差补偿自适应控制器。利用RBF神经网络对修正项在线自学习,并根据Lyapunov稳定性理论建立了网络权重自适应学习律,保证了跟踪误差的收敛及系统的稳定。以平面转动双臂机械手轨迹跟踪为例进行仿真,结果表明该方法能够有效地补偿建模误差,提高了系统的控制性能并使控制系统具有对参数摄动的鲁棒性,对于机械手自适应控制具有一定的可行性。