提高隐式非线性微分方程的数值解算速度

How to Accelerate Numeric Algorithm of Implicit Nonlinear Differential Equation

非线性反馈控制系统的数学模式常常表现为隐式非线性微分方程,用通用数值积分法求解该系统的动态响应时,每步都要进行费时的矩阵求逆运算,使得解算速度大大下降。文中第一部分提出先求出隐式微分方程中时变矩阵A(x)逆的符号表达式,再用通用数值积分法求解该类系统时,每步积分不再求矩阵逆运算,从而可以大大提高解算速度。第二部分讨论了在MATLAB/Simulink新版本的各种环境下加速仿真速度的真实有效性。

Mathematical model of nonlinear feedback control system is expressed implicit nonlinear differential equation. When using general numerical integral approach solve dynamic response of the system, to carry on time-consuming matrix inversion calculation, make the speed of solution to descend consumedly.In the paper,the symbol expression of implicit differential equation's time-variable matrix inversion are yiclded, then solve that type of system with numerical integral approach, no longer need to be each the step matrix inversion calculate, thus can raise solution consumedly on the whole speed.In the second part of the paper, the authenticity and validity of acceleration simulation under various environments basing on the new edition of MATLAB/Simulink are discussed.