Chirp design in a pulse compression procedure for the identification of non-linear systems

The Hammerstein model of a nonlinear systems can be efficiently identified by means of a technique based on pulse compression. The procedure relies on the properties of the exponential chirps, adopted as excitation signals. The present paper proposes to include the initial phase of the chirp, together with its time duration and frequency extremes, among the parameters to design the excitation signal. Considering this widened set of design parameters, we identify the constraints that the excitation signal must meet to carry out an accurate identification. The paper shows that introducing the initial phase as further degree of freedom, adds flexibility to the design process and allows for the use of much shorted chirp signals, making measurements faster and reliable. The experimental results reported demonstrate the validity of the constraints identified and show that, choosing appropriate combinations of the parameters, very short chirp accomplish the phase constraint needed for an accurate modelling of the non-linear system.