Linear system identification from frequency-response data

When the input-output data of a system are given and the mathematical model of this system is desired, we have a system identification problem. In this thesis we identify the mathematical model of a system from frequency-response data. Previous developments of identification methods from frequency-response data are reviewed and criticized. Three methods are proposed in this thesis which are improvements over the past approaches. The proposed methods are described as follows: (1) The Slope Method is based on the principle that an irrational transfer function is constructed from the magnitude/frequency response curve which is approximated by piecewise linear segments with various slopes. Then a rational transfer function, that is a required mathematical model of a system, is obtained by approximating the irrational transfer function. (2) The Interpolation Method is proposed to fit the coefficients of a transfer function from real and imaginary parts of the selected frequency-response data of a system. (3) The Least Squares Method is suggested to determine the best estimate of the parameter matrices for the multi-input, multi-output state equations from the frequency-response data of all state variables. Several illustrative examples are included for each method. When using any of the proposed identification methods, the system is limited to only insignificant noise in the frequency-response data. The Interpolation and Least Squares Methods are applicable to minimum and non-minimum phase system identification. The particular advantage of these techniques is the ability to utilize a relatively limited amount of experimental data to obtain the system dynamic equations.Electrical and Computer Engineering, Department o