Rational interpolation of transfer functions of linear dynamic systems with distributed parameters
A method of rational interpolation of the transfer function of linear dynamic systems with distributed parameters is presented, the values of which can be found by numerical methods or by calculating the transcendental functions of the Laplace integral transform variable. The method allows one to define explicitly the transfer function and, in particular, the characteristic equation of such a degree that is sufficient to meet the accuracy requirements when calculating the root quality criteria for the dynamics of automatic control systems. According to the proposed method, rational interpolation is reduced to solving a system of linear equations, the order of which is much lower (more than twice) the order of similar systems used for rational interpolation of functions by known methods. The properties of this system are such that its solution can be obtained by special fast methods of the quadratic order of complexity. An example of the practical use of an iterative algorithm for rational interpolation and calculation with a given accuracy of the root quality criteria for the dynamics of a support with gas lubrication is considered.