Stability Analysis of a Fractional-Order High-Speed Supercavitating Vehicle Model with Delay

• Published in: Machines (Basel) Vol. 9; no. 7; p. 129
• Main Authors: Doan, Phuc Thinh, Bui, Phuc Duc Hong, Vu, Mai The, Thanh, Ha Le Nhu Ngoc, Hossain, Shakhawat
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-07-2021
• Subjects: Advection; advection delay; Behavior; bifurcation; Bifurcations; Calculus; Cavitation; dynamical analysis; fractional calculus; fractional-order model (FOM); Gravity; High speed supercavitating vehicles; high-speed super-cavitating vehicle (HSSV); Mathematical analysis; Mathematical models; Nonlinear equations; Nonlinearity; Stability analysis; Time lag; Traffic speed; Transient response
• ISSN: 2075-1702; 2075-1702
• DOI: 10.3390/machines9070129

A novel fractional-order model (FOM) of a high-speed super-cavitating vehicle (HSSV) with the nature of memory is proposed and investigated in this paper. This FOM can describe the behavior of the HSSV superior to the integer-order model by the memory effects of fractional-order derivatives. The fractional order plays the role of the advection delay, which is ignored in most of the prior studies. This new model takes into account the effect of advection delay while preserving the nonlinearity of the mathematical equations. It allows the analysis of nonlinear equations describing the vehicle with ease when eliminating the delay term in its equations. By using the fractional order to avoid the approximation of the delay term, the proposed FOM can also preserve the nature of the time delay. The numerical simulations have been carried out to study the behavior of the proposed model through the transient responses and bifurcation diagrams concerning the fractional-order and vehicle speed. The bifurcation diagrams provide useful information for a better control and design of new supper super-cavitating vehicles. The similar behaviors between the proposed model and prior ones validate the FOM while some discrepancies suggest that more appropriate controllers should be designed based on this new model.