Thermal error measurement and modelling in machine tools.: Part I. Influence of varying operating conditions

Thermal error in machine tools has been observed to be closely linked to the temperature of critical elements of the machine. It was found, in the experiments conducted herein, that there was a significant increase in the axis positioning error on account of an increase in the temperature of the machine elements due to continuous operation. However, it was also observed that the specific operating parameters of the test cycles carried out also significantly affected the positioning error. Different sets of operating parameters generated significantly different error values even though the temperature of the machine elements generated by those operating conditions was similar. As such, this observation forms a very important consideration in the development of a generic thermal error compensation system. It appears to indicate that such a system needs to be capable of evaluating the compensation depending upon the temperature values of the machine elements as well as account for the effect that different operating parameters induce upon the positioning error under the same thermal condition of the machine. This paper attempts to analyse the thermal behaviour of a three-axis vertical machining centre under the influence of various operating parameters and, through the experimental results obtained, point out and explain the effect of these parameters on the axis positioning error. This behaviour forms the basis of an improved modelling methodology that is presented separately in Part II of this paper.     

A new high accuracy method for two-dimensional biharmonic equation with nonlinear third derivative terms: application to Navier–Stokes equations of motion

In this paper, we propose a new compact fourth-order accurate method for solving the two-dimensional fourth-order elliptic boundary value problem with third-order nonlinear derivative terms. We use only 9-point single computational cell in the scheme. The proposed method is then employed to solve Navier–Stokes equations of motion in terms of streamfunction–velocity formulation, and the lid-driven square cavity problem. We describe the derivation of the method in details and also discuss how our streamfunction–velocity formulation is able to handle boundary conditions in terms of normal derivatives. Numerical results show that the proposed method enables us to obtain oscillation-free high accuracy solution.     

基于逻辑回归模型的木片和树皮的图像识别

为了提高木片生物能的利用率,需要除去木片中的树皮杂质。识别木片和树皮的图像对于实现二者分离具有重要作用。提出一种基于逻辑回归模型来对木片和树皮进行图像识别的算法。算法流程包括计算各种可以描述木片和树皮纹理的参数,利用SAS统计分析出最佳参数,将最佳参数计算所得的样本数据用于SAS LOGISTIC过程得到预测方程,再将预测方程用于逻辑回归模型来实现木片和树皮的图像识别。通过实验可知,最佳参数为灰度方差,该图像识别算法的正确率能达到97.4%。     

Leader-following consensus for uncertain second-order nonlinear multi-agent systems

This paper studies the leader-following consensus problem for a class of second-order nonlinear multi-agent systems subject to linearly parameterized uncertainty and disturbance. The problem is solved by integrating the adaptive control technique and the adaptive distributed observer method. The design procedure is illustrated by an example with a group of Van der Pol oscillators as the followers and a harmonic system as the leader.     

On input‐to‐state stability‐based design for leader/follower formation control with measurement delays

This paper addresses the design of low‐level controllers for leader–follower formations of nonholonomic vehicles in the presence of bounded measurement delays. The concept of input‐to‐state stability is extended to encompass the effect of bounded delays and restrictions on the input. A method is proposed to integrate a Smith predictor in a backstepping design on the basis of nested saturations and nonlinear small‐gain assignment, which allows for time delays in the feedback loop. Robustness analysis under uncertain bounded time delays is provided, and design tradeoffs resulting from the use of bounded controls are discussed. Illustrative simulations are shown to validate the design and robustness analysis in the context of a simple leader–follower trailing control problem. Copyright © 2012 John Wiley & Sons, Ltd.     

Limit load and shakedown analysis of plastic structures under stochastic uncertainty

Problems from plastic analysis are based on the convex, linear or linearised yield/strength condition and the linear equilibrium equation for the stress (state) vector. In practice one has to take into account stochastic variations of several model parameters. Hence, in order to get robust maximum load factors, the structural analysis problem with random parameters must be replaced by an appropriate deterministic substitute problem. A direct approach is proposed based on the primary costs for missing carrying capacity and the recourse costs (e.g. costs for repair, compensation for weakness within the structure, damage, failure, etc.). Based on the mechanical survival conditions of plasticity theory, a quadratic error/loss criterion is developed. The minimum recourse costs can be determined then by solving an optimisation problem having a quadratic objective function and linear constraints. For each vector a(·) of model parameters and each design vector x, one obtains then an explicit representation of the “best” internal load distribution F^∗. Moreover, also the expected recourse costs can be determined explicitly. Consequently, an explicit stochastic nonlinear program results for finding a robust maximal load factor μ^∗. The analytical properties and possible solution procedures are discussed.     

Robust Kalman filtering for uncertain discrete-time systems with probabilistic parameters bounded within a polytope

We consider the problem of finite horizon discrete-time Kalman filtering for systems with parametric uncertainties. Specifically, we consider unknown but deterministic uncertainties where the uncertain parameters are assumed to lie in a convex polyhedron with uniform probability density. The condition and a procedure for the construction of a suboptimal filter that minimizes an expected error covariance over-bound are derived.     

Stability and control of nonlinear systems described by retarded functional equations: a review of recent results

This paper reports on recent results in a series of the work of the authors on the stability and nonlinear control for general dynamical systems described by retarded functional differential and difference equations. Both internal and external stability properties are studied. The corresponding Lyapunov and Razuminkhin characterizations for input-to-state and input-to-output stabilities are proposed. Necessary and sufficient Lyapunov-like conditions are derived for robust nonlinear stabilization. In particular, an explicit controller design procedure is developed for a new class of nonlinear time-delay systems. Lastly, sufficient assumptions, including a small-gain condition, are presented for guaranteeing the input-to-output stability of coupled systems comprised of retarded functional differential and difference equations.     

Matlab遗传算法工具箱在非线性优化中的应用

投影寻踪是一种降维处理技术,通过它可以将多维分析问题通过投影方向转化为一维问题分析。应用该法的关键在于寻求最佳投影方向,这可以转化为一个复杂的非线性优化问题来进行解决。选取某地区大气环境质量评价的投影寻踪评价模型,编制相关的目标函数和约束函数,应用基于MATLAB的遗传算法和直接搜索工具箱进行优化求解。结果表明：该工具箱在求解此类非线性优化问题上的有效性和方便性,从而为各领域应用投影寻踪模型提供了强有力的优化工具。     

Error compensation in machine tools: a neural network approach

For a non-idealized machine tool, each point in the workspace is associated with a tool point positioning error vector. If this error map can be determined, then it is possible to substantially improve the positioning performance of the machine by introducing suitable compensation into the control loop. This paper explores the possibility of using an artifical neural network (ANN) to compute this mapping. The training set for the ANN is obtained by mounting a physical artifact whose dimensions are precisely known in the machine's workspace. The machine, equipped with a touch trigger probe, measures the positions of features on the artifact. The difference between the machine reading and the known dimension is the machine error at that point in the workspace. Using standard modeling techniques, the kinematic error model for a CNC turning center was developed. This model was parameterized by measurement of the parametric error functions using a laser interferometer, electronic levels and a precision square. The kinematic model was then used to simulate the artifact-measuring process and develop the ANN training set. The effect of changing artifact geometry was explored and a machining operation was simulated using the ANN output to provide compensation. The results show that the ANN is capable of learning the error map of a real machine, and that ANN-based compensation can significantly reduce part-dimensional errors.