On One Approach to Simulation of Stiff Dynamic Systems

Abstract

The article describes the features of modeling dynamic systems adapted to real production processes. An approach to solving problems using the numerical and analytical method of modeling rigid dynamic systems is described. The algorithm of this approach is based on the following procedures: recording the original system of differential equations in the form of state variables, determining the characteristic polynomial of the system, finding its roots, and determining the solution of the original system of differential equations in the analytical form under typical input effects. The analytical view of the solution allows you: to keep track of all components (both fast and slow), which is especially important when modeling hard systems; the ability to obtain a solution with the accuracy of a computer bit grid for any time, as well as complete algorithmic independence from the solution at the previous point; the lack of iteration, the ability to pre-evaluate the nature of the transition process by the type of roots. The solutions for all possible types of roots are considered (Simple roots, Multiple roots, Complex-conjugate roots). For typical input effects, analytical expressions are given and the areas of application of the proposed approach in modeling complex technical systems in specific engineering tasks are considered. The method is implemented as a software package written in the Pascal algorithmic language for a personal computer of the IBM PC type. At the user’s request, solutions are issued in the analytical, digital or graphical form.