Parameter Identification of Fractional-Order LTI Systems using Modulating Functions with Memory Reduction
- Resource Type
- Conference
- Authors
- Weise, Christoph; Pfeffer, Philipp; Reger, Johann; Ruderman, Michael
- Source
- 2021 60th IEEE Conference on Decision and Control (CDC) Decision and Control (CDC), 2021 60th IEEE Conference on. :5156-5162 Dec, 2021
- Subject
- Aerospace
Bioengineering
Communication, Networking and Broadcast Technologies
Components, Circuits, Devices and Systems
Power, Energy and Industry Applications
Robotics and Control Systems
Signal Processing and Analysis
Transportation
Linear systems
Parameter estimation
Sensitivity
Estimation
Mathematical models
Robustness
Noise measurement
- Language
- ISSN
- 2576-2370
The parameter estimation problem of a linear time-invariant fractional-order system is investigated by means of the modulating function method. Based on the assumption of known model structure and derivative orders, the modulating function method can be generalized to the fractional-order case in three different ways. We show that two approaches are identical for linear systems. This facilitates the computation of the fractional-order derivatives of modulating functions. In comparison to integer-order systems we have to include the initialization of the fractional-order system. We show that the spline type modulating function is capable of reducing the effect of the memory on the parameter estimation. However, it is not possible to compensate the memory initialization completely. In contrast to these tuning principles also the robustness against measurement noise must be considered. For this purpose we decouple the memory and noise compensation. The adjusted spline-type modulating functions reduce the initialization effect and the recursive least squares estimation provides the possibility to increase the numbers of equations such that the effect of the noise is reduced.