Numerical-control machine tool feeding system modeling method based on improved SVD (singular value decomposition)-Krylov algorithm

Abstract

The invention discloses a numerical-control machine tool feeding system modeling method based on an improved SVD (singular value decomposition)-Krylov algorithm. The method includes creating a state space equation model of a numerical-control machine tool feeding system according to a kinetic equation; acquiring an original system state space matrix, an original system and a transfer function model; setting the order of an order reduction system, and starting a multipoint moment matching SVD-Krylov algorithm for order reduction; outputting a state space matrix of the order reduction system, the order reduction system and a corresponding order reduction transfer function model; performing order reduction algorithm simulation verification according to a orthogonal experiment method and a time response method. Asymptotic stability of the model subjected to order reduction based on an order reducing and modeling algorithm can be guaranteed, and calculation efficiency is high; an iterative algorithm is adopted, moment matching quantity is multiplied, and order reduction accuracy is improved. The numerical-control machine tool feeding system modeling method has the advantages that order reduction accuracy and calculation efficiency are improved remarkably, and modeling and simulating speeds of the numerical-control machine tool feeding system are increased greatly.

Description

Technical field [0001] The invention belongs to the field of model modeling reduction of large-scale complex electromechanical systems, and more specifically, relates to a numerical control machine tool feed system modeling method based on an improved SVD-Krylov algorithm. Background technique [0002] Dynamic modeling and simulation of the CNC machine tool feed system is an intuitive and effective analysis method to master its internal characteristics. However, the electromechanical system involves many fields such as mechanics, electrical, and control, which makes the system very complicated, with many state variables and very high order. high. It is relatively difficult to directly model and simulate using the initial system model of the CNC machine tool feed system, or the numerical simulation is very time-consuming, inefficient, and sometimes unsustainable. In this context, in order to reduce the difficulty of theoretical analysis of large complex systems, improve modeling ...

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Problems solved by technology

The model reduction algorithm based on SVD has good theoretical properties. The reduced-order system can maintain the structural characteristics of the initial system, and it is easy to obtain the error relationship between the reduced-order system and the initial system. However, two Lyapunov equations need to be solved, and the calculation cost is as high as k 1 no 3 , the required storage capacity is up to k 2 no 2 (where k 1 、k 2 is the characteristic coefficient related to the Lyapunov equation), so it cannot adapt to large-scale system reduction (n1 no 2 q, storage reduced to p 2 nq (where p 1 ,p 2 is the calculation coefficient related to the Krylov subspace, and q is the order of the reduced-order system), so it is suitable for large-scale system reduction (n>1000), but the reduced-order system obtained by this algorithm cannot guarantee system stability, and it is difficult Calculate the reduced-order error bound; based on the SVD-Krylov algorithm, it combines the advantages of the first two algorithms. On the one hand, it uses the good theoretical characteristics of SVD such as stability and global error bounds, and on the other hand, it uses the efficient numerical calculation capabilities of the Krylov subspace method. , so that the numerical calculation process is stable and efficient, the theoretical characteristics are good, and the approximation error is small enough. However, further research shows that it still has the following defects: 1) In terms of accuracy of order reduction: it adopts the single-point moment matching principle, and the moment The number of matches is limited, and only moments equivalent to the number of order reductions can be matched, and the order reduction accuracy is poor; 2) In terms of computational efficiency: the SVD-Krylov algorithm needs to solve the Lyapunov equation, although compared with the SVD order reduction algorithm, the calculation amount is greatly reduced. But still not the best result; 3) In terms of algorithm performance: the selection of interpolation points in the SVD-Krylov algorithm is a random process, and the convergence speed of the algorithm depends too much on the selection of initial interpolation points, which will cause the instability of the algorithm

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