Novel Model of Proton Exchange Membrane Fuel Cell with Predictive Control Using Hildreth Algorithm Based on Fractional-order Dynamic Model

Considering the multivariable and fractional-order characteristics of proton exchange membrane fuel cells(PEMFCs),a fractional-order subspace identification method(FOSIM)is proposed in this paper to establish a fractionalorder state space(FOSS)model,which can be expressed as a multivariable configuration with two inputs,hydrogenflow rate and stack current,and two outputs,cell voltage and power.Based on this model,a novel constrained optimal control law named the Hildreth model predictive control(H-MPC)strategy is created,which employs a Hildreth quadratic programming algorithm to adjust the output power of fuel cells through adaptively regulating hydrogen flow and stack current.dSPACE semi-physical simulation results demonstrate that,compared with proportional-integral-derivative and quadratic programming MPC(QP-MPC),the proposed H-MPC exhibits better tracking ability and strong robustness against variations of PEMFC power.

True-temperature inversion algorithm for a multi-wavelength pyrometer based on fractional-order particle-swarm optimization

Herein,a method of true-temperature inversion for a multi-wavelength pyrometer based on fractional-order particle-swarm optimization is proposed for difficult inversion problems with unknown emissivity.Fractional-order calculus has the inherent advantage of easily jumping out of local extreme values;here,it is introduced into the particle-swarm algorithm to invert the true temperature.An improved adaptive-adjustment mechanism is applied to automatically adjust the current velocity order of the particles and update their velocity and position values,increasing the accuracy of the true temperature values.The results of simulations using the proposed algorithm were compared with three algorithms using typical emissivity models:the internal penalty function algorithm,the optimization function(fmincon)algorithm,and the conventional particle-swarm optimization algorithm.The results show that the proposed algorithm has good accuracy for true-temperature inversion.Actual experimental results from a rocket-motor plume were used to demonstrate that the true-temperature inversion results of this algorithm are in good agreement with the theoretical true-temperature values.

Intelligent Fractional-Order Controller for SMES Systems in Renewable Energy-Based Microgrid

An autonomous microgrid that runs on renewable energy sources is presented in this article.It has a supercon-ducting magnetic energy storage(SMES)device,wind energy-producing devices,and an energy storage battery.However,because such microgrids are nonlinear and the energy they create varies with time,controlling and managing the energy inside them is a difficult issue.Fractional-order proportional integral(FOPI)controller is recommended for the current research to enhance a standalone microgrid’s energy management and performance.The suggested dedicated control for the SMES comprises two loops:the outer loop,which uses the FOPI to regulate the DC-link voltage,and the inner loop,responsible for regulating the SMES current,is constructed using the intelligent FOPI(iFOPI).The FOPI+iFOPI parameters are best developed using the dandelion optimizer(DO)approach to achieve the optimum performance.The suggested FOPI+iFOPI controller’s performance is contrasted with a conventional PI controller for variations in wind speed and microgrid load.The optimal FOPI+iFOPI controller manages the voltage and frequency of the load.The behavior of the microgrid as a reaction to step changes in load and wind speed was measured using the proposed controller.MATLAB simulations were used to evaluate the recommended system’s performance.The results of the simulations showed that throughout all interruptions,the recommended microgrid provided the load with AC power with a constant amplitude and frequency.In addition,the required load demand was accurately reduced.Furthermore,the microgrid functioned incredibly well despite SMES and varying wind speeds.Results obtained under identical conditions were compared with and without the best FOPI+iFOPI controller.When utilizing the optimal FOPI+iFOPI controller with SMES,it was found that the microgrid performed better than the microgrid without SMES.

Dynamics analysis and cryptographic implementation of a fractional-order memristive cellular neural network model

Due to the fact that a memristor with memory properties is an ideal electronic component for implementation of the artificial neural synaptic function,a brand-new tristable locally active memristor model is first proposed in this paper.Here,a novel four-dimensional fractional-order memristive cellular neural network(FO-MCNN)model with hidden attractors is constructed to enhance the engineering feasibility of the original CNN model and its performance.Then,its hardware circuit implementation and complicated dynamic properties are investigated on multi-simulation platforms.Subsequently,it is used toward secure communication application scenarios.Taking it as the pseudo-random number generator(PRNG),a new privacy image security scheme is designed based on the adaptive sampling rate compressive sensing(ASR-CS)model.Eventually,the simulation analysis and comparative experiments manifest that the proposed data encryption scheme possesses strong immunity against various security attack models and satisfactory compression performance.

Numerical Simulation and Parameter Estimation of Fractional-Order Dynamic Epidemic Model for COVID-19

The outbreak of COVID-19 in 2019 resulted in numerous infections and deaths. In order to better study the transmission of COVID-19, this article adopts an improved fractional-order SIR model. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system and combined with the improved MH-NMSS-PSO parameter estimation method to fit the real data of Delhi, India from April 1, 2020 to June 30, 2020. The results show that the fitting effect is quite ideal. Finally, long-term predictions were made on the number of infections. We accurately estimate that the peak number of infections in Delhi, India, can reach around 2.1 million. This paper also compares the fitting performance of the integer-order COVID-19 model and the fractional-order COVID-19 model using the real data from Delhi. The results indicate that the fractional-order model with different orders, as we proposed, performs the best.

Circuit implementation of a new hyperchaos in fractional-order system

This paper introduces a new four-dimensional （4D） hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then investigated in detail by using bifurcations, Poincare mapping, LE spectra. Furthermore, a simple fourth-order electronic circuit is designed for hardware implementation of the 4D hyperchaotic attractors. In particular, a remarkable fractional-order circuit diagram is designed for physically verifying the hyperchaotic attractors existing not only in the integer-order system but also in the fractional-order system with an order as low as 3.6.

Fractional-order L_βC_a filter circuit network

In this paper we introduce the new fundamentals of the conventional LC filter circuit network in the fractional domain.First, we derive the general formulae of the impedances for the conventional and fractional-order filter circuit network.Based on this, the impedance characteristics and phase characteristics with respect to the system variables of the filter circuit network are studied in detail, which shows the greater flexibility of the fractional-order filter circuit network in design.Moreover, from the point of view of the filtering property, we systematically study the effects of the filter units and fractional orders on the amplitude–frequency characteristics and phase–frequency characteristics. In addition, numerical tables of the cut-off frequency are presented. Finally, two typical examples are presented to promote the industrial applications of the fractional-order filter circuit network. Numerical simulations are presented to verify the theoretical results introduced in this paper.

Realization of fractional-order Liu chaotic system by circuit

In this paper, chaotic behaviours in the fractional-order Liu system are studied. Based on the approximation theory of fractional-order operator, circuits are designed to simulate the fractional- order Liu system with q=0.1 - 0.9 in a step of 0.1, and an experiment has demonstrated the 2.7-order Liu system. The simulation results prove that the chaos exists indeed in the fractional-order Liu system with an order as low as 0.3. The experimental results prove that the fractional-order chaotic system can be realized by using hardware devices, which lays the foundation for its practical applications.

Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation

The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to the circuit unit, an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system. Furthermore, synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method. Circuit experiment simulation results verify the effectiveness of the proposed scheme.

Realization of fractional-order Liu chaotic system by a new circuit unit

A new circuit unit for the analysis and the synthesis of the chaotic behaviours in a fractional-order Liu system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to describe the dynamic behaviours of the fractional-order Liu system with α = 0.9. The results between simulation and experiment are in good agreement with each other, thereby proving that the chaos exists indeed in the fractional-order Liu system.

Synchronization of the fractional-order generalized augmented L u¨system and its circuit implementation

In this paper, the synchronization of the fractional-order generalized augmented Lti system is investigated. Based on the predictor--corrector method, we obtain phase portraits, bifurcation diagrams, Lyapunov exponent spectra, and Poincar6 maps of the fractional-order system and find that a four-wing chaotic attractor exists in the system when the system pa- rameters change within certain ranges. Further, by varying the system parameters, rich dynamical behaviors occur in the 2.7-order system. According to the stability theory of a fractional-order linear system, and adopting the linearization by feedback method, we have designed a nonlinear feedback controller in our theoretical analysis to implement the synchro- nization of the drive system with the response system. In addition, the synchronization is also shown by an electronic circuit implementation for the 2.7-order system. The obtained experiment results accord with the theoretical analyses, which further demonstrate the feasibility and effectiveness of the proposed synchronization scheme.

Circuit realization of the fractional-order unified chaotic system

This paper studies the chaotic behaviours of the fractional-order unified chaotic system. Based on the approximation method in frequency domain, it proposes an electronic circuit model of tree shape to realize the fractional-order operator. According to the tree shape model, an electronic circuit is designed to realize the 2.7-order unified chaotic system. Numerical simulations and circuit experiments have verified the existence of chaos in the fraction-order unified system.

Circuit Implementations,Bifurcations and Chaos of a Novel Fractional-Order Dynamical System

Linear transfer function approximations of the fractional integrators 1Is~ with m ^- 0.80-0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency-domain approximation method. To illustrate the effectiveness for fractional functions, the magnitude Bode diagrams of the actual and approximate transfer functions 1Ism with a slope of -20m dB//decade are depicted. By using the transfer function approxima- tions of the fractional integrators, a new fractional-order nonlinear system is investigated through the bifurcation diagram and Lyapunov exponent. The corresponding circuit of the fractional-order system is designed and the experimental results match perfectly with the numerical simulations.

Firing activities in a fractional-order Hindmarsh–Rose neuron with multistable memristor as autapse

Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh–Rose(HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval(ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic(A-periodic)bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.

Reliability analysis of torpedo loading based on fractional-order optimization model

A fractional-order cumulative optimization GM(1,2)model based on grey theory is proposed to study the relationship between torpedo loading and working reliabilities.In this model,the average relative error function related to order and background value is established.Taking the average relative error function as the objective function,the optimal value of the two parameters is obtained through the optimization method,and the minimum value of the average relative error is determined.The calculation example shows that this method can greatly improve the accuracy of the model and more accurately reflect the relationship between torpedo loading and working reliabilities compared with the traditional GM(1,2)model.

BIFURCATION CONTROL FOR A FRACTIONAL-ORDER DELAYED SEIR RUMOR SPREADING MODEL WITH INCOMMENSURATE ORDERS

A fractional-order delayed SEIR rumor spreading model with a nonlinear incidence function is established in this paper,and a novel strategy to control the bifurcation of this model is proposed.First,Hopf bifurcation is investigated by considering time delay as bifurcation parameter for the system without a feedback controller.Then,a state feedback controller is designed to control the occurrence of bifurcation in advance or to delay it by changing the parameters of the controller.Finally,in order to verify the theoretical results,some numerical simulations are given.

Quasi-synchronization of fractional-order complex networks with random coupling via quantized control

We investigate the quasi-synchronization of fractional-order complex networks(FCNs) with random coupling via quantized control. Firstly, based on the logarithmic quantizer theory and the Lyapunov stability theory, a new quantized feedback controller, which can make all nodes of complex networks quasi-synchronization and eliminate the disturbance of random coupling in the system state, is designed under non-delay conditions. Secondly, we extend the theoretical results under non-delay conditions to time-varying delay conditions and design another form of quantization feedback controller to ensure that the network achieves quasi-synchronization. Furthermore, the error bound of quasi-synchronization is obtained.Finally, we verify the accuracy of our results using two numerical simulation examples.

Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems:A Case Study in Level Control Process

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time

A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length.The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic time.Numerical calculations are performed to analyze the effects of the nonlocal strain gradient parameters,the spatiotemporal fractional order,the nonlocal characteristic length,and the memory characteristic time on the natural frequencies,the vibration attenuation,and the phase shift between the temperature field and the displacement field.The numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.

Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with Caputo Fractional Derivative

Although some numerical methods of the fractional-order chaotic systems have been announced,high-precision numerical methods have always been the direction that researchers strive to pursue.Based on this problem,this paper introduces a high-precision numerical approach.Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method.We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies.We investigate the influence of α_(1),α_(2),α_(3) on the numerical solution of fractional-order Lorenz chaotic systems.The simulation results of integer order are in good agreement with those of othermethods.The simulation results of numerical experiments demonstrate the effectiveness of the present method.