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

Abstract

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, viscoelastic material modelling and other emerging disciplines. It is difficult to measure the fractional-order α and system parameters directly in real engineering applications. This paper’s main work include: Firstly, a general linear fractional differential equation is transformed into an algebraic equation by the Laplace transform, and the parameter sensitivity analysis concerning the unknown parameters is also deduced. Then, the parameter estimation 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 resolve 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 differential 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 specific implementation process is demonstrated in detail to test the robustness and validity of the proposed approach.