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An Event-Driven Method to Simulate Filippov Systems with Accurate Computing of Sliding Motions

机译:精确计算滑动运动的Filippov系统的事件驱动方法

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This article describes how to use smooth solvers for simulation of a class of piecewise smooth systems of ordinary differential equations, called Filippov systems, with discontinuous vector fields. In these systems constrained motion along a discontinuity surface (so-called sliding) is possible and requires special treatment numerically. The introduced algorithms are based on an extension to Filippov's method to stabilise the sliding flow together with accurate detection of the entrance and exit of sliding regions. The methods are implemented in a general way in MATLAB and sufficient details are given to enable users to modify the code to run on arbitrary examples. Here, the method is used to compute the dynamics of three example systems, a dry-friction oscillator, a relay feedback system and a model of an oil well drill-string.
机译:本文介绍如何使用平滑求解器来模拟一类具有不连续矢量场的常微分方程的分段光滑系统,称为Filippov系统。在这些系统中,沿着不连续表面的约束运动(所谓的滑动)是可能的,并且需要在数值上进行特殊处理。引入的算法基于对Filippov方法的扩展,以稳定滑动流并精确检测滑动区域的入口和出口。这些方法以通用方式在MATLAB中实现,并且给出了足够的详细信息,使用户可以修改代码以在任意示例上运行。这里,该方法用于计算三个示例系统,干摩擦振荡器,继电反馈系统和油井钻柱模型的动力学。

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