Inversion of Dynamic Systems for Certain Classes of Signals

Abstract

Methods of inversion of dynamic systems are widely used for solving problems of control of mechanical and electrical systems. Solving the inversion problems raises a number of difficulties related to the high sensitivity of the results with respect to the accuracy of setting the parameters of a mathematical model of object parameters, instability in controlling non-minimum phase objects, and violation of the conditions of physical realizability. In this paper, an approximate method of solving the inversion problem for linear stationary dynamic systems is proposed which is largely free from those disadvantages. The method is based on the representation of the input and output signals by their approximations in the linear space of specially selected D-functions of time. The feature of the proposed method of inversion of dynamic systems is the representation of multidimensional polynomials approximating the input and output signals as a product of rectangular matrices and a vector of powers of time. Mathematical models of linear dynamic systems in the form of differential equations in the state space and in the equivalent input-output form, as well as SISO and MIMO dynamical systems are considered in the paper.