Bias-free Parameter Identification for Non-Commensurable Fractional Systems

Parameter and Order Identification of Fractional Systems with Application to a Lithium-Ion Battery

“…The optimization-based approach ensured the order identification to be robust against measurement noise. The parameter identification was based on the instrumental variable approach from [19]. In contrast to the methods from the literature, our method did not require the system to be at rest at the beginning of the identification process.…”

“…To simulate a fractional model (4), a closed-form solution with zero initial conditions is given in [18] (p. 113). In general, if the system is not at rest and, hence, no zero initial conditions are present, an error between the simulated output signal with and without zero initial conditions occurs [19]. To reduce this error, an extension based on a closed form solution that considers the latest past of the system in sense of the short-memory principle [20] is proposed in [19].…”

“…This procedure is shown in Figure 1. For a consistent parameter estimation under noisy measurements, we apply the approach from [19]. This approach is outlined in Section 3.1.…”

“…The method introduced in [19] is an extension of the instrumental variable method for integer order models to fractional order models. To apply the instrumental variable method, we require N p ≥ N identification equations, where N = n + m + 1 is the number of model parameters.…”

“…The fulfillment of requirement (b) can be ensured by the choice of the modulating function without any restriction by the properties (P1) and (P2). The boundedness of the input signal, output signal, parameters, and the derivatives of the parameters regardless of the chosen method is guaranteed by the practical Assumption 2, which fulfills requirement (c) [19]. However, the Gauß-Newton method generally does not ensure that the global minimum is reached.…”