Fractional-Order Algebraic Parameter Estimation for Disturbed Differentially Flat Systems

Disturbances in dynamical systems pose a major challenge for parameter identification, particularly in the presence of unknown initial conditions and uncertain external influences. To address this issue, this paper proposes an algebraic parameter estimation methodology that incorporates fractional-order calculus in the Laplace domain for controlled linear engineering systems. The proposed approach eliminates the influence of unknown initial conditions and considers external disturbances that admit a local polynomial representation through Taylor series expansions over sufficiently small time intervals, while avoiding explicit numerical differentiation in the time domain. The manuscript includes analytical, numerical, and experimental validations to highlight the benefits of incorporating fractional-order differentiation in the derivation of algebraic estimators for online parameter estimation. The method is experimentally validated on two linear differentially flat electrical circuits, whose flat representations enable the proposed algebraic formulation under distinct disturbance signals. The results demonstrate that the fractional differentiation order acts as an additional tuning parameter, and that appropriately selected fractional orders can improve estimation accuracy, yielding parameter estimates consistently closer to their true values when compared with the conventional integer-order algebraic formulation.