# Design of an Optimal Input Signal for Parameter Estimation of Linear Fractional-Order Systems

• Wiktor Jakowluk
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 559)

## Abstract

The optimal input signal design is a procedure of generating an informative excitation signal to extract the model parameters with maximum accuracy during the estimation process. Non-integer order calculus is a very useful tool, which is often utilized for modeling and control purposes. In the paper, we present a novel optimal input formulation and a numerical scheme for fractional order LTI system identification. The Oustaloup recursive approximation (ORA) method is used to determine the fractional order differentiation in an integer order state-space form. Then, the presented methodology is adopted to obtain an optimal input signal for fractional order system identification from the order interval $$0.5 \le \alpha \le 2.0$$. The fundamental step in the presented method was to reformulate the problem into a similar fractional optimal input design problem described by Lagrange formula with the set of constraints. The methodology presented in the paper was verified using a numerical example, and the computational results were discussed.

## Keywords

Fractional calculus Optimal inputs Oustaloup filter Parameter identification

## Notes

### Acknowledgement

The present study was supported by a grant S/WI/3/18 from the Bialystok University of Technology and funded from the resources for research by the Ministry of Science and Higher Education.

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## Authors and Affiliations

• Wiktor Jakowluk
• 1
1. 1.Faculty of Computer ScienceBialystok University of TechnologyBialystokPoland