Invariance of reachability and observability for fractional positive linear electrical circuit with delays

• Autorzy: Yuan Tong , Yang Hongli

Identyfikatory

DOI

10.24425/aee.2021.137571

• Języki publikacji: EN

Abstrakty

EN

This paper focuses on the invariance of the reachability and observability for fractional order positive linear electrical circuits with delays and their checking methods. By derivation and comparison, it shows that conditions and checking methods of reachability and observability for integer and fractional order positive linear electrical circuits with delays are invariant. An illustrative example is presented at the end of the paper.

Słowa kluczowe

EN

invariance; observability; positive linear electrical circuits with delays; reachability

PL

niezmienność; obserwowalność; obwody elektryczne; osiągalność

• Wydawca: Polish Academy of Sciences, Committee on Electrical Engineering
• Czasopismo: Archives of Electrical Engineering
• Rocznik: 2021
• Tom: Vol. 70, nr 3
• Strony: 513--530
• Opis fizyczny: Bibliogr. 25 poz., rys., wz.

Twórcy

autor

Yuan Tong

• Shandong University of Science and Technology, China

• https://orcid.org/0000-0003-0984-2581

autor

Yang Hongli

• Shandong University of Science and Technology, China

Bibliografia

• [1] Dorf C.R., Svoboda A.J., Introduction to electric circuits, John Wiley & Sons (2010).
• [2] Kaczorek T., Rogowski K., Fractional linear systems and electrical circuit, Springer (2015).
• [3] Federico M., Power system modelling and scripting, Springer (2010).
• [4] Kaczorek T., Selected problems of fractional systems theory, Springer (2011).
• [5] Xin Z., Wenru L. et al., Application of fractional calculus in iterative sliding mode synchronization control, Archives of Electrical Engineering, vol. 69, no. 3, pp. 499–519 (2020).
• [6] Piotrowska E., Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo, Archives of Electrical Engineering, vol. 67, no. 3, pp. 629–639 (2018).
• [7] Francisco G.A.J., Juan R.G., Fractional RC and LC electrical circuits, Ingeniera, Investigacin y Tecnologa, vol. 15, no. 2, pp. 311–319 (2014).
• [8] Sikora R., Fractional derivatives in electrical circuit theory-critical remarks, Archives of Electrical Engineering, vol. 66, no. 1, pp. 155–163 (2017).
• [9] Sikora R., Pawłowski S., Problematic Applications of Fractional Derivatives in Electrotechnics and Electrodynamics, Conference on Selected Issues of Electrical Engineering and Electronics, Szczecin, Poland, pp. 1–5 (2018).
• [10] Sikora R., Pawłowski S., Fractional derivatives and the laws of electrical engineering, COMPEL-The international journal for computation and mathematics in electrical and electronic engineering, vol. 37, no. 4, pp. 1384–1391 (2018).
• [11] Muthana T.A., Mohamed Z., On the control of time delay power systems, International Journal of Innovative Computing, Information and Control, vol. 9, no. 2, pp. 769–792 (2013).
• [12] Zhaoyan L., Jun Q., A simple method to compute delay margin of power system with single delay, Automation of Electric Power System, vol. 32, no. 18, pp. 8–13 (2008).
• [13] Jianjun Z., Yonggao Z., Research on optimal configuration of fault current limiter based on reliability in large power network, Archives of Electrical Engineering, vol. 69, no. 3, pp. 661–677 (2020).
• [14] Kaczorek T., Stability of positive continuous-time linear systems with delays, Bulletin of The Polish Academy of Sciences-technical Sciences, vol. 57, no. 4, pp. 395–398 (2009).
• [15] Kaczorek T., Stability tests of positive fractional continuous-time linear systems with delays, TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation, vol. 7, no. 2, pp. 211–215 (2013).
• [16] Xianming Z., Min W., On delay-dependent stability for linear systems with delay, Journal of Circuit and Systems, vol. 8, no. 3, pp. 118–120 (2003).
• [17] Hai Z., Daiyong W., Stability analysis for fractional-order linear singular delay differential systems, Discrete Dynamics in Nature and Society, vol. 2014, no. 2014, pp. 1–8 (2014).
• [18] Xianggeng Z., Yuxia L. et al., Stability analysis of fractional-order Langford systems, Journal of Shandong University of Science and Technology (Natural Science), vol. 38, no. 3, pp. 65–71(2019).
• [19] Wei J., Zhicheng W., Controllability of singular control systems with delay, Journal of Hunan University, vol. 26, no. 4, pp. 6–9 (1999).
• [20] Qiong W., Wei J., The complete controllability, after all controllability, ultimate controllability and quasi controllability of delay control system, College Mathematic, vol. 19, no. 3, pp. 63–66 (2003).
• [21] Wei J., The controllability of delay degenerate control systems with independent subsystems, Applied Mathematics and Mechanics, vol. 24, no. 6, pp. 706–713 (2003).
• [22] Peng L., Wenlong W. et al., Alternate Charging and Discharging of Capacitor to Enhance the Electron Production of Bioelectrochemical Systems, Environmental Science and Technology, vol. 45, no. 15, pp. 6647–6653 (2011).
• [23] Kaczorek T., Reachability and controllability to zero of positive fractional discrete-time systems, European Control Conference, Kos, Greece, pp. 1708–1712 (2007).
• [24] Xindong S., Hongli Y., A new method for judgement computation of stability and stabilization of fractional order positive systems with constraints, Journal of Shandong University of Science and Technology (Natural Science), vol. 40, no. 1, pp. 12–20 (2021).
• [25] Kaczorek T., Invariant properties of positive linear electrical circuit, Archives of Electrical Engineering, vol. 68, no. 4, pp. 875–890 (2019).

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).