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

Machines ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 129
Author(s):  
Phuc Thinh Doan ◽  
Phuc Duc Hong Bui ◽  
Mai The Vu ◽  
Ha Le Nhu Ngoc Thanh ◽  
Shakhawat Hossain
Keyword(s):  
Fractional Order ◽  
High Speed ◽  
Vehicle Speed ◽  
Bifurcation Diagrams ◽  
Order Model ◽  
New Model ◽  
Delay Term ◽  
Supercavitating Vehicle ◽  
Proposed Model ◽  
Mathematical Equations

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.

scholarly journals Modeling and Application of Fractional-Order Economic Growth Model with Time Delay

2021 ◽  
Vol 5 (3) ◽  
pp. 74
Author(s):  
Ziyi Lin ◽  
Hu Wang
Keyword(s):  
Economic Growth ◽  
Time Delay ◽  
Fractional Order ◽  
Growth Model ◽  
Capital Accumulation ◽  
High Speed ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Economic Growth Model ◽  
Proposed Model

This paper proposes a fractional-order economic growth model with time delay based on the Solow model to describe the economic growth path and explore the underlying growth factors. It effectively captures memory characteristics in economic operations by adding a time lag to the capital stock. The proposed model is presented in the form of a fractional differential equations system, and the sufficient conditions for the local stability are obtained. In the simulation, the theoretical results are verified and the sensitivity analysis is performed on individual parameters. Based on the proposed model, we predict China’s GDP in the next thirty years through optimization and find medium-to-high-speed growth in the short term. Furthermore, the application results indicate that China is facing the disappearance of demographic dividend and the deceleration of capital accumulation. Therefore, it is urgent for China to increase the total factor productivity (TFP) and transform its economic growth into a trajectory dependent on TFP growth.

scholarly journals Fractional Maxwell fluid with fractional derivative without singular kernel

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 871-877 ◽  
Author(s):  
Feng Gao ◽  
Xiao-Jun Yang
Keyword(s):  
Integral Operator ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Differential Form ◽  
Maxwell Fluid ◽  
Singular Kernel ◽  
Derivative Operator ◽  
New Model ◽  
Proposed Model ◽  
First Time

In this paper we propose a new model for the fractional Maxwell fluid within fractional Caputo-Fabrizio derivative operator. We present the fractional Maxwell fluid in the differential form for the first time. The analytical results for the proposed model with the fractional Losada-Nieto integral operator are given to illustrate the efficiency of the fractional order operators to the line viscoelasticity.

scholarly journals A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects

2020 ◽  
Author(s):  
Zhenzhen Lu ◽  
Yongguang Yu ◽  
YangQuan Chen ◽  
Guojian Ren ◽  
Conghui Xu ◽  
...  
Keyword(s):  
Fractional Order ◽  
Numerical Solutions ◽  
Least Squares Method ◽  
Real Data ◽  
Order System ◽  
Coupling Effects ◽  
Order Model ◽  
The Real ◽  
Proposed Model ◽  
City Network

AbstractA novel coronavirus, designated as COVID-19, emerged in Wuhan, China, at the end of 2019. In this paper, a mathematical model is proposed to analyze the dynamic behavior of COVID-19. Based on inter-city networked coupling effects, a fractional-order SEIHDR system with the real-data from 23 January to 18 March, 2020 of COVID19 is discussed. Meanwhile, hospitalized individuals and the mortality rates of three types of individuals (exposed, infected and hospitalized) are firstly taken into account in the proposed model. And infectivity of individuals during incubation is also considered in this paper. By applying least squares method and predictor-correctors scheme, the numerical solutions of the proposed system in the absence of the inter-city network and with the inter-city network are stimulated by using the real-data from 23 January to 18 − m March, 2020 where m is equal to the number of prediction days. Compared with integer-order system (α = 0), the fractional-order model without network is validated to have a better fitting of the data on Beijing, Shanghai, Wuhan, Huanggang and other cities. In contrast to the case without network, the results indicate that the inter-city network system may be not a significant case to virus spreading for China because of the lock down and quarantine measures, however, it may have an impact on cities that have not adopted city closure. Meanwhile, the proposed model better fits the data from 24 February to 31, March in Italy, and the peak number of confirmed people is also predicted by this fraction-order model. Furthermore, the existence and uniqueness of a bounded solution under the initial condition are considered in the proposed system. Afterwards, the basic reproduction number R0 is analyzed and it is found to hold a threshold: the disease-free equilibrium point is locally asymptotically stable when R0 ≤ 1, which provides a theoretical basis for whether COVID-19 will become a pandemic in the future.

scholarly journals MODELLING AND CONTROL OF H-SHAPED RACING QUADCOPTER WITH TILTING PROPELLERS

2017 ◽  
Vol 15 (2) ◽  
pp. 201 ◽  
Author(s):  
Ahmed Alkamachi ◽  
Ergun Ercelebi
Keyword(s):  
High Speed ◽  
Translational Motion ◽  
System Model ◽  
Reverse Direction ◽  
Vehicle Speed ◽  
Performance Simulation ◽  
Nonlinear Dynamical ◽  
Proposed Model ◽  
And Control ◽  
Moving Speed

Traditional quadcopter suffers terribly from its underactuation which implies the coupling between the rotational and the translational motion. In this paper, we present a quadcopter with dynamic rotor tilting capability in which the four propellers are allowed to tilt together around their arm axis. The proposed model provides leveled forward/backward horizontal motion and therefore, ensures a correct view of the onboard camera, and increases the vehicle speed by reducing the air drag. The rotor tilt mechanism also provides an instant high speed in the forward or reverse direction and offers a quick and solid air brake to restrain that fast moving speed.  The nonlinear dynamical model for the quadcopter under consideration is derived using Newton-Euler formalization. A control strategy is then proposed aimed to control the altitude, attitude, and the forward speed of the obtained model. Finally, a numerical simulation is used to integrate the system model with the controller and to test the system performance. Simulation results are reported to demonstrate the advantages of the proposed novel configuration.

Wave propagation and spiral wave formation in a Hindmarsh–Rose neuron model with fractional-order threshold memristor synaps

2020 ◽  
Vol 34 (17) ◽  
pp. 2050157 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Sajad Jafari ◽  
Fatemeh Parastesh ◽  
Christos Volos ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Fractional Order ◽  
Electromagnetic Induction ◽  
Neuron Model ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Bifurcation Diagrams ◽  
External Current ◽  
Proposed Model ◽  
External Stimuli

In this paper, a modified Hindmarsh–Rose neuron model is presented, which has a fractional-order threshold magnetic flux. The dynamics of the model is investigated by bifurcation diagrams and Lyapunov exponents in two cases of presence and absence of the external electromagnetic induction. Then the emergence of the spiral waves in the network of the proposed model is studied. To find the effects of different factors on the formation and destruction of spiral waves, the external current, the coupling strength and the external stimuli amplitude are varied. It is observed that all of these parameters have significant impacts on the spiral waves. Furthermore, the external electromagnetic induction influences the existence of spiral waves in specific external current values.

scholarly journals Influence of suspension parameter for derailment analysis of a full railway vehicle model cruising on a curved track

2021 ◽  
Author(s):  
Yamika Patel ◽  
◽  
Vikas Rastogi ◽  
Wolfgang Borutzky ◽  
◽  
...  
Keyword(s):  
High Speed ◽  
Research Work ◽  
Creep Model ◽  
Railway Vehicle ◽  
Vehicle Speed ◽  
Nonlinear Creep ◽  
Pitch Motion ◽  
Proposed Model ◽  
Curved Track ◽  
Creep Models

The main intention of this research work is to study the derailment response of high speed railway vehicle (HSRV) cruising on a curved track. In previous research work, lower degree of freedom (DOF) has been considered for the derailment analysis which may not give more accurate results. Hence, a 31 DOF bondgraph model of HSRV has been developed which consist of carbody, two truck frames and two selfsame wheelsets for each truck frame. Vertical, lateral, roll, yaw and pitch motion are considered for carbody and bogie and except pitch motion all the other motion are considered for wheelsets. Non-linearities in terms of heuristic nonlinear creep model and flange contact has been employed to simulate the derailment response at high speed. The effect of vehicle speed running on a curved track was investigated for derailment quotient. The main aim of present research work to evaluate derailment quotient at the speed range of 150 kmph to 600 kmph for hard and soft suspension parameter. Derailment quotient has been calculated for both linear and nonlinear creep models and it is seen that DQ for linear model has a lower value compare to non linear creep. The major advantages of the proposed model are that, the presented model can actively predict the derailment of a railway vehicle, and also precisely determine the nonlinear critical hunting speeds.

Fractional-order sliding mode control synthesis of supercavitating underwater vehicles

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1909-1919
Author(s):  
Bui Duc Hong Phuc ◽  
Viet-Duc Phung ◽  
Sam-Sang You ◽  
Ton Duc Do
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
High Speed ◽  
Sliding Mode ◽  
Underwater Vehicle ◽  
Sliding Mode Controller ◽  
Integer Order ◽  
Mode Control ◽  
Supercavitating Vehicle ◽  
Control Actions

A high-speed supercavitating vehicle is a future underwater vehicle which exploits the supercavitating propulsion technology providing a promising way to increase the vehicle speed. Robust control challenges include complex vehicle maneuvering dynamics caused by factors such as undesired switching, delayed state dependency, and nonlinearities. As effective and applicable controllers, a novel fractional-order sliding mode controller is proposed to robustly control the uncertain high-speed supercavitating vehicle system against external disturbances. The control scheme uses sliding mode control and can produce better control actions than conventional the integer-order counterpart. In this algorithm, the fractional calculus is applied to calculate the noninteger integral or derivative in the sliding mode control algorithm, providing new capabilities for uncertain high-speed supercavitating vehicle control in seeking to operate the underwater vehicle better. The performance of the proposed fractional-order sliding mode controller has been proven through analytic simulation results, which show fast responses with smooth control actions and the ability to deal with nonlinear planing force and external disturbance. One of the interesting features of the fractional-order control system is the time convergence rate of the sliding variable vector, which is greatly improved compared with the integer-order sliding mode control. Finally, the robust control system with a novel fractional-order sliding mode controller algorithm, using high flexibility of controlling undersea vehicles, can provide superior dynamical performance with stability compared with its integer-order counterpart against system uncertainties and disturbances.

scholarly journals Signal Smoothing with Time-Space Fractional Order Model

2021 ◽  
Vol 21 (1) ◽  
pp. 25-32
Author(s):  
Yuanlu Li
Keyword(s):  
Diffusion Model ◽  
Fractional Order ◽  
Order Model ◽  
Comparison Result ◽  
Smoothing Methods ◽  
Fractional Order Model ◽  
Time Space ◽  
Proposed Model ◽  
Noisy Signals ◽  
And Performance

Abstract The time-space fractional-order model (TSFOM) is a generation of the classical diffusion model which is an excellent smoothing method. In this paper, the fractional-order derivative in the model is found to have good performance for peak-preserving. To check the validity and performance of the model, some noisy signals are smoothed by some commonly used smoothing methods and results are compared with those of the proposed model. The comparison result shows that the proposed method outperforms the classical nonlinear diffusion model and some commonly used smoothing methods.

scholarly journals Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mansoor H. Alshehri ◽  
Sayed Saber ◽  
Faisal Z. Duraihem
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Euler Method ◽  
Dynamical Analysis ◽  
Order Model ◽  
Insulin Metabolism ◽  
Fractional Order Model ◽  
Proposed Model ◽  
Predictor Corrector ◽  
Tolerance Testing

Abstract This paper proposes a fractional-order model of glucose–insulin interaction. In Caputo’s meaning, the fractional derivative is defined. This model arises in Bergman’s minimal model, used to describe blood glucose and insulin metabolism, after intravenous tolerance testing. We showed that the established model has existence, uniqueness, non-negativity, and boundedness of fractional-order model solutions. The model’s local and global stability was investigated. The parametric conditions under which a Hopf bifurcation occurs in the positive steady state for a proposed model are studied. Moreover, we present a numerical treatment for solving the proposed fractional model using the generalized Euler method (GEM). The model’s local stability and Hopf bifurcation of the proposed model in sense of the GEM are presented. Finally, numerical simulations of the model using the Adam–Bashforth–Moulton predictor corrector scheme and the GEM have been presented to support our analytical results.

scholarly journals Fractional Order Model of the Two Dimensional Heat Transfer Process

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6371
Author(s):  
Krzysztof Oprzędkiewicz ◽  
Wojciech Mitkowski ◽  
Maciej Rosół
Keyword(s):  
Heat Transfer ◽  
Fractional Order ◽  
Heat Transfer Process ◽  
Two Dimensional ◽  
Thermal Camera ◽  
Order Model ◽  
Fractional Order Model ◽  
Proposed Model ◽  
Spectrum Decomposition ◽  
Theoretical Results

In this paper, a new, state space, fractional order model of a heat transfer in two dimensional plate is addressed. The proposed model derives directly from a two dimensional heat transfer equation. It employes the Caputo operator to express the fractional order differences along time. The spectrum decomposition and stability of the model are analysed. The formulae of impluse and step responses of the model are proved. Theoretical results are verified using experimental data from thermal camera. Comparison model vs experiment shows that the proposed fractional model is more accurate in the sense of MSE cost function than integer order model.

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