Tracking control design for fractional order systems: A passivity-based port-Hamiltonian framework

Authors

Lalitesh Kumar, Sukhwinder Singh Dhillon

Abstract

This article focuses on the design of tracking control for chaotic fractional order systems subjected to perturbations in a port-Hamiltonian framework. The fractional order systems of general form are modeled into port-controlled Hamiltonian form. Then, the extended results on the dissipativity, energy balance, and passivity of the fractional order systems are proved and presented in this paper. The port-controlled Hamiltonian form of the fractional order systems are proved to be asymptotically stable via energy balancing concept. Furthermore, a tracking controller is designed for the fractional order port-controlled Hamiltonian form by utilizing the matching conditions of the port-Hamiltonian systems. Stability of the system is established and analyzed explicitly for the closed-loop system with the help of direct Lyapunov method. Finally, an application example is solved with simulation results and discussions to prove the effectiveness of the propounded control design approach.

Keywords

Port-controlled Hamiltonian systems; Fractional order systems; Tracking control; Energy balancing; Passivity

Citation

• Journal: ISA Transactions
• Year: 2023
• Volume: 138
• Issue:
• Pages: 1–9
• Publisher: Elsevier BV
• DOI: 10.1016/j.isatra.2023.03.024

BibTeX

@article{Kumar_2023,
  title={{Tracking control design for fractional order systems: A passivity-based port-Hamiltonian framework}},
  volume={138},
  ISSN={0019-0578},
  DOI={10.1016/j.isatra.2023.03.024},
  journal={ISA Transactions},
  publisher={Elsevier BV},
  author={Kumar, Lalitesh and Dhillon, Sukhwinder Singh},
  year={2023},
  pages={1--9}
}

Download the bib file

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