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.

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.

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.

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.

External stability of fractional-order control systems

The external stability of fractional-order continuous linear control systems described by both fractional-order state space representation and fractional-order transfer function is mainly investigated in this paper. In terms of Lyapunov’s stability theory and the stability analysis of the integer-order linear control systems, the definitions of external stability for fractional-order control systems are presented. By using the theorems of the Mittag-Leffler function in two parameters, the necessary and sufficient conditions of external stability are directly derived. The illustrative examples and simulation results are also given.

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.

Function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems

This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.

Adaptive fuzzy synchronization for a class of fractional-order neural networks

In this paper, synchronization for a class of uncertain fractional-order neural networks with external disturbances is discussed by means of adaptive fuzzy control. Fuzzy logic systems, whose inputs are chosen as synchronization errors, are employed to approximate the unknown nonlinear functions. Based on the fractional Lyapunov stability criterion, an adaptive fuzzy synchronization controller is designed, and the stability of the closed-loop system, the convergence of the synchronization error, as well as the boundedness of all signals involved can be guaranteed. To update the fuzzy parameters, fractional-order adaptations laws are proposed. Just like the stability analysis in integer-order systems, a quadratic Lyapunov function is used in this paper. Finally, simulation examples are given to show the effectiveness of the proposed method.

Dynamic analysis and fractional-order adaptive sliding mode control for a novel fractional-order ferroresonance system

Ferroresonance is a complex nonlinear electrotechnical phenomenon, which can result in thermal and electrical stresses on the electric power system equipments due to the over voltages and over currents it generates. The prediction or determination of ferroresonance depends mainly on the accuracy of the model used. Fractional-order models are more accurate than the integer-order models. In this paper, a fractional-order ferroresonance model is proposed. The influence of the order on the dynamic behaviors of this fractional-order system under different parameters n and F is investigated. Compared with the integral-order ferroresonance system, small change of the order not only affects the dynamic behavior of the system, but also significantly affects the harmonic components of the system. Then the fractional-order ferroresonance system is implemented by nonlinear circuit emulator. Finally, a fractional-order adaptive sliding mode control （FASMC） method is used to eliminate the abnormal operation state of power system. Since the introduction of the fractional-order sliding mode surface and the adaptive factor, the robustness and disturbance rejection of the controlled system are en- hanced. Numerical simulation results demonstrate that the proposed FASMC controller works well for suppression of ferroresonance over voltage.

Analysis of the effect on control systems of order variation for fractional-orderPI~λD~μcontrollers

This paper is concerned with fractional-order PI~λD~μcontrollers. The definitions and properties of fractional calculus are introduced. The mathematical descriptions of a fractional-order controller and fractional-order control systems are outlined. The effects on control systems of order variation for fractional-order PI~λD~μ controllers are investigated by qualitative analysis and simulation. The conclusions and simulation examples are given. The results show the fractional-order PI~λD~μ controller is not sensitive to variation of its order.

A modified fractional-order thermo-viscoelastic model and its application to a polymer micro-rod heated by a moving heat source

Classical thermo-viscoelastic models may be challenged to predict the precise thermo-mechanical behavior of viscoelastic materials without considering the memorydependent effect.Meanwhile,with the miniaturization of devices,the size-dependent effect on elastic deformation is becoming more and more important.To capture the memory-dependent effect and the size-dependent effect,the present study aims at developing a modified fractional-order thermo-viscoelastic coupling model at the microscale to account for two fundamentally distinct fractional-order models which govern the memory-dependent features of thermal conduction and stress-strain relation,respectively.Then,the modified theory is used to study the dynamic response of a polymer micro-rod heated by a moving heat source.The governing equations are obtained and solved by the Laplace transform method.In calculation,the effects of the fractional-order parameter,the fractional-order strain parameter,the mechanical relaxation parameter,and the nonlocal parameter on the variations of the considered variables are analyzed and discussed in detail.

Chaotic dynamics of the fractional-order Ikeda delay system and its synchronization

In this paper we numerically investigate the chaotic behaviours of the fractional-order Ikeda delay system. The results show that chaos exists in the fractional-order Ikeda delay system with order less than 1. The lowest order for chaos to be a, ble to appear in this system is found to be 0.1. Master-slave synchronization of chaotic fractional-order Ikeda delay systems with linear coupling is also studied.

Chaotic synchronization for a class of fractional-order chaotic systems

In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-order systems, is simple and theoretically rigorous.

Fractional-order permanent magnet synchronous motor and its adaptive chaotic control

In this paper we investigate the chaotic behaviors of the fractional-order permanent magnet synchronous motor（PMSM）.The necessary condition for the existence of chaos in the fractional-order PMSM is deduced.And an adaptivefeedback controller is developed based on the stability theory for fractional systems.The presented control scheme,which contains only one single state variable,is simple and flexible,and it is suitable both for design and for implementation in practice.Simulation is carried out to verify that the obtained scheme is efficient and robust against external interference for controlling the fractional-order PMSM system.

Improved quantum bacterial foraging algorithm for tuning parameters of fractional-order PID controller

The quantum bacterial foraging optimization(QBFO)algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is discrete and constant,which cannot affect the situation of the solution space and limit the diversity of bacterial population. In this paper, an improved QBFO(IQBFO) algorithm is proposed, which can adaptively make the quantum rotation angle continuously updated and enhance the global search ability. In the initialization process, the modified probability of the optimal rotation angle is introduced to avoid the existence of invariant solutions. The modified operator of probability amplitude is adopted to further increase the population diversity.The tests based on benchmark functions verify the effectiveness of the proposed algorithm. Moreover, compared with the integerorder PID controller, the fractional-order proportion integration differentiation(PID) controller increases the complexity of the system with better flexibility and robustness. Thus the fractional-order PID controller is applied to the servo system. The tuning results of PID parameters of the fractional-order servo system show that the proposed algorithm has a good performance in tuning the PID parameters of the fractional-order servo system.

Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

Robust Admissibility and Stabilization of Uncertain Singular Fractional-Order Linear Time-Invariant Systems

This paper addresses the robust admissibility problem in singular fractional-order continuous time systems. It is based on new admissibility conditions of singular fractional-order systems expressed in a set of strict linear matrix inequalities(LMIs). Then, a static output feedback controller is designed for the uncertain closed-loop system to be admissible. Numerical examples are given to illustrate the proposed methods.

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method.

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.

Distributed Adaptive Cooperative Tracking of Uncertain Nonlinear Fractional-order Multi-agent Systems

In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws,we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result.