Research of the stable equilibrium position of a dissipative system

The article deals with the issue of checking the stability of a trivial solution of a fourth-order differential equation describing a dissipative feedback system. Systems with feedback have found wide use in automatic control devices and robotic complexes. The article presents an algorithm for quickly calculating the stability of the system according to the Lienard-Chipart criterion, supplemented by solving the inequality that determines the permissible values of the controlled parameters and constructing a curve of a D-partitions. Comparative analysis of Routh-Hurwitz’s and Lienard-Chipart’s stability criterions is given. The nature of the change in the kinematic characteristics of the control object under different positioning modes is investigated. The balancing simulation of studied object’s control surfaces is carried out in the Wolfram Mathematica computer environment. The program codes for evaluating the stability of the feedback system are written in C++.