Method of simplification of mathematical models of objects of management with the distributed parameters

This paper develops a method of simplifying the mathematical models of objects control with distributed parameters based on the method of separation of variables. It analyzes a number of methods available, which can be divided into two groups according to the "object approximation." The first group is formed in different ways simplified representation of the same object output differential equations, solution of which the following known methods provides a satisfactory accuracy in certain specific circumstances describe properties of systems with distributed parameters in a relatively simple way. The methods of the second group are based on approximate representation (usually in a typical system with lumped parameters form the corresponding transfer functions) exact solutions of partial differential equations that model the behavior of systems with distributed parameters. To calculate the optimal basis vectors used two algorithms. The algorithm, which by maximizing limited Fourier coefficients vector minimizes the norm of the vector error and iterative algorithm. Separation of variables - definition of basis vectors and the Fourier coefficients - by using orthogonal decomposition (basis vectors) and original method of system identification based on a mathematical model in state space (Fourier coefficients). This was considered Galerkin method and system identification method in which the object of study is represented as a "black box". The result is a streamlined mathematical model, which allows you to build on the basis of real-time control system that cannot be done on the basis of the initial complex mathematical models due to the fact that the last calculation requires considerable time. For future research is to study the quality of the proposed method models simplify systems with distributed parameters for real industrial projects.