Fuzzy logic cross-coupling controller for precision contour machining

This paper introduces a new cross-coupling controller with a rule-based fuzzy logic control. It is asserted that (i) fuzzy logic controllers provide a better transient response (which is essential for better contour accuracy during transient motions) than the conventional controllers, such as PID controllers, and (ii) cross-coupling controllers perform better than axial controllers in trajectory tracking by machine tools. In this paper, a fuzzy logic controller and a cross-coupling controller are combined to reduce contour errors. A simulation of the FLCCC was performed and the FLCCC was implemented on a CNC milling machine. The simulation and the experimental results show improved contour accuracy over the conventional cross-coupling controller.     

Robust contouring control for biaxial feed drive systems

Contouring control is an effective method of providing precision machine tool control, and various such methods have been proposed to date. However, most existing methods require prior exact knowledge of feed drive dynamics. This paper presents a robust contouring control system design that takes into account dynamics modelling errors and disturbances such as friction. We first present a controller design for biaxial feed drive systems that enables assignment of controller gains, for reducing the error component orthogonal to the desired contour curve, independent of the tangential error component. Although this design provides better control performance with small control input variance, an inherent contour error exists because of the difficulty in calculating the exact contour error for any contour curve in real time. To address this problem, a reference adjustment method is used to estimate the actual contour error. A robust contouring controller is proposed based on the variable structure control. The effectiveness of the robust controller is demonstrated by experimental results using circular and non-circular contour curves.     

Adaptive contouring of three-dimensional surfaces

An adaptive method of contouring a bivariate surface defined over arbitrarily spaced data in two dimensions is introduced. The method has two stages: 1. Produce a Bézier polynomial surface defined over a union of triangles. 2. Use this surface to compute the required contour levels. Using positional data only, this method produces a C¹-continuous surface and contours which can be made arbitrarily close to being C¹-continuous. The contour is represented as a piecewise linear approximation to the C¹-continuous contour.The method computes a linear representation of the surface in the neighborhood of the contour using an adaptive degree reduction algorithm. This algorithm is used to minimize the number of subdivisions necessary to obtain the desired smoothness of the contour. As a result of this adaptive subdivision, no contours are missed due to the coarseness of the original data points.     

A computer procedure to analyze seismic data to estimate outcome probabilities in oil exploration,with an initial application in the tabasco region of southeastern Mexico

The Tabasco region contains a number of major oilfields, including some of the emerging “giant” oil fields which have received extensive publicity. Fields in the Tabasco region are associated with large geologic structures which are detected readily by seismic surveys. The structures seem to be associated with deepseated movement of salt, and they are complexly faulted. Some structures have as much as 1000 milliseconds relief of seismic lines. A study, interpreting the structure of the area, used initially only a fraction of the total seismic linesThat part of Tabasco region that has been studied was surveyed with a close-spaced rectilinear network of seismic lines. A, interpreting the structure of the area, used initially only a fraction of the total seismic data available. The purpose was to compare “predictions” of reflection time based on widely spaced seismic lines, with “results” obtained along more closely spaced lines. This process of comparison simulates the sequence of events in which a reconnaissance network of seismic lines is used to guide a succession of progressively more closely spaced lines. A square gridwork was established with lines spaced at 10 km intervals, and using machine contour maps, compared the results with those obtained with seismic grids employing spacings of 5 and 2.5 km respectively.The comparisons of predictions based on widely spaced lines with observations along closely spaced lines provide information by which an error function can be established. The error at any point can be defined as the difference between the predicted value for that point, and the subsequently observed value at that point. Residuals obtained by fitting third-degree polynomial trend surfaces were used for comparison. The root mean square of the error measurement, (expressed in seconds or milliseconds reflection time) was found to increase more or less linearly with distance from the nearest seismic point. Oil-occurrence probabilities were established on the basis of frequency distributions of trend-surface residuals obtained by fitting and subtracting polynomial trend surfaces from the machine-contoured reflection time maps. We found that there is a strong preferential relationship between the occurrence of petroleum (i.e. its presence versus absence) and particular ranges of trend-surface residual values. An estimate of the probability of oil occurring at any particular geographic point can be calculated on the basis of the estimated trend-surface residual value. This estimate, however, must be tempered by the probable error in the estimate of the residual value provided by the error function.The result, we believe, is a simple but effective procedure for estimating exploration outcome probabilities where seismic data provide the principal form of information in advance of drilling. Implicit in this approach is the comparison between a maturely explored area, for which both seismic and production data are available, and which serves as a statistical “training area”, with the “target” area which is undergoing exploration and for which probability forecasts are to be calculated.     

Biaxial contouring control with friction dynamics using a contour index approach

In conventional designs, contouring control is usually decomposed into independent tracking tasks of axes. Its success relies on good tracking performance of each axis, which is difficult to achieve when the dynamics of each axis is different from each other and subjected to nonlinear frictions and load variations. Additionally, another difficulty in contouring control is the formulation of a contouring error model and real-time estimation of contouring error. Therefore, in this paper, a contour following strategy was developed to improve contouring accuracy without depending on axial tracking performance. The proposed contouring error model is formulated systematically based on the coordinated transformation scheme. A contour index (CI) is evaluated geometrically, which can be treated as an equivalent contour error such that a reduction in CI implies a reduction in contour error. With the proposed approach, the resulting contour performance will not be degraded if the tracking task of each axis is not carried out precisely. Experiments were conducted using a bi-axial linear stage and the results demonstrate that the contouring qualities were still maintained at high feed-rates even in the presence of undesirable tracking lags.     

Contouring controller design based on iterative contour error estimation for three-dimensional machining

Recently, there has been a growth of interest in high precision machining in multi-axis feed drive systems, subjected to problems such as friction, cutting force and incompatibility of individual driving axis dynamics. To guarantee high precision machining in modern computer numerical controlled (CNC) machines, CNC's controllers do its control efforts to reduce contour error. One of the common approaches is to design a controller based on the estimation of contour error in real time. However, for complex contours with severe curvatures, there is a lack of effective algorithms to calculate contour errors accurately. To address this problem, this paper proposes an accurate contour error estimation procedure for three-dimensional machining tasks. The proposed method is based on an iterative estimation of the instantaneous curvature of the reference trajectory and coordinates transformation approach, and hence, it is effective for complex reference trajectories with high curvatures. In addition, contour error controller is presented to reduce the estimated contour error. The feasibility and superiority of the proposed model as well as contour error controller are demonstrated through experimental system using a desk-top three-axis CNC machine.     

A contouring program based on dual kriging interpolation

For contouring very large data sets, such as those arising from 3-D finite element computations, for instance, or in numerical cartography, a computer program based on dual kriging interpolation was developed at École Polytechnique for the Castor project (a multidisciplinary research and development work in computational software for hydroelectric projects). The dual kriging technique presented here simplifies considerably the handling of interpolated data and is especially useful for 3-D applications. It also containsspline interpolation as a particular case and theleast squares method as a limit case. In order to minimize the computational effort, several original features have been incorporated in this program: (1) the concept ofdistance of influence was introduced to allow the algorithm, when evaluating the interpolation value at a given location, to discard data points that are situated too far apart; (2)arbitrary geometric domains are decomposed into simpler regions, inside which the requested contours are drawn directly by scanning vertical slices from left to right, instead of building each contour line sequentially as in direct contouring; (3) contour lines may also be stored in arandom access database (this last feature was added to enable the automatic assembly of isovalue surfaces in 3-D applications such as stress analysis); and (4) contours can be smoothed by interpolating separately the sequences ofX andY coordinates for each contour line. This process, calledparametric kriging, permits the efficient compression of the number of data points necessary to record contours.     

Integrated direct/indirect adaptive robust contouring control of a biaxial gantry with accurate parameter estimations

This paper presents an integrated direct/indirect adaptive robust contouring controller (DIARC) for an industrial biaxial high-speed gantry that achieves not only excellent contouring performance but also accurate parameter estimations for secondary purposes such as machine health monitoring and prognosis. Contouring control problem is first formulated in a task coordinate frame. A physical model-based indirect-type parameter estimation algorithm is then developed to obtain accurate on-line estimates of unknown model parameters. A DIARC controller possessing dynamic-compensation-like fast adaptation is subsequently constructed to preserve the excellent transient and steady-state contouring performance of the direct adaptive robust controller (DARC) designs. The proposed DIARC along with previously developed DARC contouring controllers are implemented on a high-speed industrial biaxial gantry to test their achievable performance in practice. Comparative experimental results verify the improved contouring performance and the accurate physical parameter estimates of the proposed DIARC algorithm.