The fuzzy control algorithms used commonly at present are all regarded as some interpolation functions, which is in essence equivalent to discrete response functions to be fitted. This means that fuzzy control method ...The fuzzy control algorithms used commonly at present are all regarded as some interpolation functions, which is in essence equivalent to discrete response functions to be fitted. This means that fuzzy control method is similar to finite element method in mathematical physics, which is a kind of direct manner or numerical method in control systems.展开更多
In this paper, a kind of rational cubic interpolation function with linear denominator is constructed. The constrained interpolation with constraint on shape of the interpolating curves and on the second-order derivat...In this paper, a kind of rational cubic interpolation function with linear denominator is constructed. The constrained interpolation with constraint on shape of the interpolating curves and on the second-order derivative of the interpolating function is studied by using this interpolation, and as the consequent result, the convex interpolation conditions have been derived.展开更多
5-axis machine tool plays an important role in high-speed and high-precision computer numerical control （CNC） machining of workpieces with complex shapes. A non-uniform rational B-spline （NURBS） interpolation form...5-axis machine tool plays an important role in high-speed and high-precision computer numerical control （CNC） machining of workpieces with complex shapes. A non-uniform rational B-spline （NURBS） interpolation format for 5-axis machining is pro- posed to adapt to the high speed machining （HSM）. With this interpolation format, angles between orientation vectors are chosen as parameters of orientation B-spline constructed by an open controller to achieve reasonable orientation vectors in real-time interpolation process. Coordinated motion between linear axes and rotary axes is achieved by building a polynomial spline which relates interpolation arc lengths of position spline to angles of orientation spline. Algorithm routine of this interpolation format and its realization methods in the supported controller are discussed in detail. Finally, performance of the proposed NURBS in- terpolation format is demonstrated by a practical example.展开更多
文摘The fuzzy control algorithms used commonly at present are all regarded as some interpolation functions, which is in essence equivalent to discrete response functions to be fitted. This means that fuzzy control method is similar to finite element method in mathematical physics, which is a kind of direct manner or numerical method in control systems.
基金Supported by Natural Science Foundation of Shandong Province (Y99A01).
文摘In this paper, a kind of rational cubic interpolation function with linear denominator is constructed. The constrained interpolation with constraint on shape of the interpolating curves and on the second-order derivative of the interpolating function is studied by using this interpolation, and as the consequent result, the convex interpolation conditions have been derived.
文摘5-axis machine tool plays an important role in high-speed and high-precision computer numerical control （CNC） machining of workpieces with complex shapes. A non-uniform rational B-spline （NURBS） interpolation format for 5-axis machining is pro- posed to adapt to the high speed machining （HSM）. With this interpolation format, angles between orientation vectors are chosen as parameters of orientation B-spline constructed by an open controller to achieve reasonable orientation vectors in real-time interpolation process. Coordinated motion between linear axes and rotary axes is achieved by building a polynomial spline which relates interpolation arc lengths of position spline to angles of orientation spline. Algorithm routine of this interpolation format and its realization methods in the supported controller are discussed in detail. Finally, performance of the proposed NURBS in- terpolation format is demonstrated by a practical example.
