Solution of matrix differential Riccati equations in the medium of modeling system of MVTU 3.7

Abstract

Purpose. For the design of systems under the action of random perturbations, a method of stochastic dynamic programming has been developed. The method is very effective because it allows one to find the optimal control of the parameters of elastic-dissipative connections of the crew suspension as a function of estimating the phase coordinates. The main reason that hinders the widespread use of this method for linear dynamic systems with many degrees of freedom is related to the lack of software for solving the matrix non-linear differential equation of Riccati type, which is included in the algorithm of the method. The aim of the work is to develop modeling schemes for solving differential equations of Riccati type in the system of modeling MVTU 3.7 (modeling in technical devices). The technique. The simulation system of MVTU 3.7 allows studying transient processes in complex dynamic systems and analyzing the stability and stability of oscillatory processes along a phase trajectory. A mathematical model of a dynamic system is created - differential equations, after - a structural diagram of the model and in the environment of MVTU 3.7 a modeling scheme is constructed. MVTU 3.7 has a graphics editor, so the modeling scheme is assembled from library blocks, which is located on the working field. The block parameters, initial conditions, integration method, simulation time, solution accuracy, etc. are set. The simulation results are given in the form of graphs. In addition, there is a text editor that records the numerical data of the simulation results. To solve differential equations like Riccati, a structural scheme is not needed. Results. A simulation scheme was created for solving differential equations of Riccati type and correlation functions of the matrix of parameters of the optimal filter were obtained. The simulation of the oscillation process of the body of the 2TE10L locomotive and the filter was performed. It has been established that for the 2TE10L locomotive it is not required to create devices for actively controlling the parameters of elastic-dissipative links. Naukova novelty. A method for solving differential equations in the simulation system of MVTU 3.7 Practical value. The main reason that prevented the widespread use of the method of stochastic dynamic programming has been eliminated and has hampered the development of the theory of creating active suspensions of transport crews.