Identification of fractional-order transfer functions and nonzero initial conditions using exponentially modulated signals

A new methodology that uses exponentially modulated signals with arbitrary excitation waveforms for the identification of fractional order transfer functions is proposed. In contrast to previous approaches where initial conditions were not considered and the system was required to be at rest for the identification procedure, the current contribution extends the formulation to the case where the system has non-zero initial conditions, dispensing with the need to place it at a resting state. This generalization is important in feedback instrumentation and metrology applications where the measurement or control process may not be disrupted to perform identification. Moreover, the procedure has a broader scope of applications because it structurally contemplates the case when the model presents derivatives in the input. Full identification of the system parameters as well as the fractional exponents associated with the model dynamics are achieved through a grid search procedure with resolution adjustable by the user. Two simulation examples are presented to illustrate the effectiveness of the proposed approach. The first example is concerned with the effect of measurement noise at the observed system output, whereas the second involves the identification of the impedance of a three-dimensional RC network model. These types of RC networks have dynamics capturing complex phenomena with emergent responses and are ideal for emulating the complex dynamics encountered across physical sciences and in particular interdisciplinary subject areas such as biomedical engineering.