Parameter estimation of linear fractional-order system from laplace domain data

A novel parameter estimation method based on the Laplace transform and the response sensitivity method has been presented to recognize the parameters of linear fractional -order systems (FOS) rapidly . The proposed method consumes two orders of magnitude computational resources lower than the traditional time-domain method. Fractional-order operators are increasingly widely used in control and synchronization, epidemiology, vis-coelastic material modelling and other emerging disciplines. It is difficult to measure the fractional-order alpha and system parameters directly in real engineering applications. This paper's main work include: Firstly, a general linear fractional differential equation is trans-formed into an algebraic equation by the Laplace transform, and the parameter sensitivity analysis concerning the unknown parameters is also deduced. Then, the parameter esti-mation problem of the linear FOS is established as a nonlinear least-squares optimization in the Laplace domain, and the enhanced response sensitivity method is adopted to re-solve this nonlinear minimum optimization equation iteratively. In addition, the Tikhonov regularization is employed to cope with the potential ill-posed situations, and the trust -region restriction is also introduced to improve the convergence. Finally, taking a differen-tial system with two types of fractional-order operators, a multi-degree-of-freedom FOS with external excitation and an actual piezoelectric actuator model as examples, the spe-cific implementation process is demonstrated in detail to test the robustness and validity of the proposed approach.(c) 2022 Elsevier Inc. All rights reserved.