How to Identify from a Step Response a Non-Commensurate Second-Species Transfer Function

This paper proposes a time-domain identification method for second-species non-commensurate fractional-order transfer functions with exponents ν∈(0,2) and ν+1. To successfully identify the system’s parameters, the method requires knowing the system’s step response, from which a limited number of points is needed. The rules developed are different depending on whether there is an overshoot or not. Performance is assessed in the presence of additive Gaussian white noise. While parameter estimation exhibits some numerical sensitivity to noisy data, the computation of the model’s natural frequency ωn acts as a crucial compensator by scaling the system’s time constant, thereby arriving at useful models in most circumstances.