System modeling based on steady state frequency response measurements

The structure of the identification problem for linear systems from sinusoidal input, steady-state response measurements is treated from an interpolation point of view. Both the cases of amplitude plus phase, and amplitude only measurements are discussed. It is shown that if sufficient amplitude measurements are made, then fewer phase measurements are required for identification. These results are extended to the identification problem for a class of nonlinear systems. It is shown that measurement of the amplitude plus phase of each harmonic of the steady-state response for a number of sinusoidal inputs can yield complete identification of the system. For the case of amplitude measurements only, it is shown that the ambiguity in identification is similar in nature to the linear case, and is easily characterized.