Stability Analysis of a Fractional-Order High-Speed Supercavitating Vehicle Model with Delay
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 fra...
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MDPI AG
2021-06-01
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| Series: | Machines |
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| Online Access: | https://www.mdpi.com/2075-1702/9/7/129 |
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| author | Phuc Thinh Doan Phuc Duc Hong Bui Mai The Vu Ha Le Nhu Ngoc Thanh Shakhawat Hossain |
| author_facet | Phuc Thinh Doan Phuc Duc Hong Bui Mai The Vu Ha Le Nhu Ngoc Thanh Shakhawat Hossain |
| author_sort | Phuc Thinh Doan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T04:54:41Z |
| format | Article |
| id | doaj.art-f830c642d75840c88163f44deb87489c |
| institution | Directory Open Access Journal |
| issn | 2075-1702 |
| language | English |
| last_indexed | 2024-03-09T04:54:41Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Machines |
| spelling | doaj.art-f830c642d75840c88163f44deb87489c2023-12-03T13:07:25ZengMDPI AGMachines2075-17022021-06-019712910.3390/machines9070129Stability Analysis of a Fractional-Order High-Speed Supercavitating Vehicle Model with DelayPhuc Thinh Doan0Phuc Duc Hong Bui1Mai The Vu2Ha Le Nhu Ngoc Thanh3Shakhawat Hossain4Nguyen Tat Thanh Hi-Tech Institute, Nguyen Tat Thanh University, Ho Chi Minh City 754000, VietnamDepartment of Mechanical Engineering, The University of Tulsa, 800 S. Tucker Drive, Tulsa, OK 74104, USASchool of Intelligent Mechatronics Engineering, Sejong University, 98 Gunja-dong, Gwangjin-gu, Seoul 143-747, KoreaDepartment of Mechatronics Engineering, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City 700000, VietnamDepartment of Industrial and Production Engineering, Jashore University of Science and Technology, Jashore 7408, BangladeshA 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.https://www.mdpi.com/2075-1702/9/7/129high-speed super-cavitating vehicle (HSSV)fractional-order model (FOM)fractional calculusadvection delaybifurcationdynamical analysis |
| spellingShingle | Phuc Thinh Doan Phuc Duc Hong Bui Mai The Vu Ha Le Nhu Ngoc Thanh Shakhawat Hossain Stability Analysis of a Fractional-Order High-Speed Supercavitating Vehicle Model with Delay Machines high-speed super-cavitating vehicle (HSSV) fractional-order model (FOM) fractional calculus advection delay bifurcation dynamical analysis |
| title | Stability Analysis of a Fractional-Order High-Speed Supercavitating Vehicle Model with Delay |
| title_full | Stability Analysis of a Fractional-Order High-Speed Supercavitating Vehicle Model with Delay |
| title_fullStr | Stability Analysis of a Fractional-Order High-Speed Supercavitating Vehicle Model with Delay |
| title_full_unstemmed | Stability Analysis of a Fractional-Order High-Speed Supercavitating Vehicle Model with Delay |
| title_short | Stability Analysis of a Fractional-Order High-Speed Supercavitating Vehicle Model with Delay |
| title_sort | stability analysis of a fractional order high speed supercavitating vehicle model with delay |
| topic | high-speed super-cavitating vehicle (HSSV) fractional-order model (FOM) fractional calculus advection delay bifurcation dynamical analysis |
| url | https://www.mdpi.com/2075-1702/9/7/129 |
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