Design and Implementation of Digital Fractional Order PID Controller Using Optimal Pole-Zero Approximation Method for Magnetic Levitation System

The aim of this paper is to employ fractional order proportional integral derivative(FO-PID)controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system(MLS),which is inherently nonlinear and unstable system.The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order controller.An approach of phase shaping by slope cancellation of asymptotic phase plots for zeros and poles within given bandwidth is explored.The controller parameters are tuned using dynamic particle swarm optimization(d PSO)technique.Effectiveness of the proposed control scheme is verified by simulation and experimental results.The performance of realized digital FO-PID controller has been compared with that of the integer order PID controllers.It is observed that effort required in fractional order control is smaller as compared with its integer counterpart for obtaining the same system performance.

Digital implementation of fractional order PID controller and its application

A new discretization scheme is proposed for the design of a fractional order PID controller. In the design of a fractional order controller the interest is mainly focused on the s-domain, but there exists a difficult problem in the s-domain that needs to be solved, i.e. how to calculate fractional derivatives and integrals efficiently and quickly. Our scheme adopts the time domain that is well suited for Z-transform analysis and digital implementation. The main idea of the scheme is based on the definition of Grünwald-Letnicov fractional calculus. In this case some limited terms of the definition are taken so that it is much easier and faster to calculate fractional derivatives and integrals in the time domain or z-domain without loss much of the precision. Its effectiveness is illustrated by discretization of half-order fractional differential and integral operators compared with that of the analytical scheme. An example of designing fractional order digital controllers is included for illustration, in which different fractional order PID controllers are designed for the control of a nonlinear dynamic system containing one of the four different kinds of nonlinear blocks: saturation, deadzone, hysteresis, and relay.

An Adaptive Neuro-Fuzzy Inference System to Improve Fractional Order Controller Performance

The design and analysis of a fractional order proportional integral deri-vate(FOPID)controller integrated with an adaptive neuro-fuzzy inference system(ANFIS)is proposed in this study.Afirst order plus delay time plant model has been used to validate the ANFIS combined FOPID control scheme.In the pro-posed adaptive control structure,the intelligent ANFIS was designed such that it will dynamically adjust the fractional order factors(λandµ)of the FOPID(also known as PIλDµ)controller to achieve better control performance.When the plant experiences uncertainties like external load disturbances or sudden changes in the input parameters,the stability and robustness of the system can be achieved effec-tively with the proposed control scheme.Also,a modified structure of the FOPID controller has been used in the present system to enhance the dynamic perfor-mance of the controller.An extensive MATLAB software simulation study was made to verify the usefulness of the proposed control scheme.The study has been carried out under different operating conditions such as external disturbances and sudden changes in input parameters.The results obtained using the ANFIS-FOPID control scheme are also compared to the classical fractional order PIλDµand conventional PID control schemes to validate the advantages of the control-lers.The simulation results confirm the effectiveness of the ANFIS combined FOPID controller for the chosen plant model.Also,the proposed control scheme outperformed traditional control methods in various performance metrics such as rise time,settling time and error criteria.

Fractional Order Proportional Integral Derivative Controller Design and Simulation for Bioengineering Systems

This paper deals with the study of fractional order system tuning method based on Factional Order Proportional Integral Derivative( FOPID) controller in allusion to the nonlinear characteristics and fractional order mathematical model of bioengineering systems. The main contents include the design of FOPID controller and the simulation for bioengineering systems. The simulation results show that the tuning method of fractional order system based on the FOPID controller outperforms the fractional order system based on Fractional Order Proportional Integral( FOPI) controller. As it can enhance control character and improve the robustness of the system.

A Novel ANFIS Based SMC with Fractional Order PID Controller

Interacting The highest storage capacity of a circular tank makes it pop-ular in process industries.Because of the varying surface area of the cross-sec-tions of the tank,this two-tank level system has nonlinear characteristics.Controlling theflow rate of liquid is one of the most difficult challenges in the production process.This proposed effort is critical in preventing time delays and errors by managing thefluid level.Several scholars have explored and explored ways to reduce the problem of nonlinearity,but their techniques have not yielded better results.Different types of controllers with various techniques are implemented by the proposed system.Sliding Mode Controller(SMC)with Fractional Order PID Controller based on Intelligent Adaptive Neuro-Fuzzy Infer-ence System(ANFIS)is a novel technique for liquid level regulation in an inter-connected spherical tank system to avoid interferences and achieve better performance in comparison of rise time,settling time,and overshoot decrease.Evaluating the simulated results acquired by the controller yields the efficiency of the proposed system.The simulated results were produced using MATLAB 2018 and the FOMCON toolbox.Finally,the performance of the conventional controller(FOPID,PID-SMC)and proposed ANFIS based SMC-FOPID control-lers are compared and analyzed the performance indices.

Variational Calculus With Conformable Fractional Derivatives

Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.

Chaos in a fractional-order micro-electro-mechanical resonator and its suppression

The present paper investigates the existence of chaos in a non-autonomous fractional-order micro-electromechanical resonator system（FOMEMRS）.Using the maximal Lyapunov exponent criterion,we show that the FOMEMRS exhibits chaos.Strange attractors of the system are plotted to validate its chaotic behavior.Afterward,a novel fractional finite-time controller is introduced to suppress the chaos of the FOMEMRS with model uncertainties and external disturbances in a given finite time.Using the latest version of the fractional Lyapunov theory,the finite time stability and robustness of the proposed scheme are proved.Finally,we present some computer simulations to illustrate the usefulness and applicability of the proposed method.

Fractional order PID control for steer-by-wire system of emergency rescue vehicle based on genetic algorithm

Aiming at dealing with the difficulty for traditional emergency rescue vehicle(ECV)to enter into limited rescue scenes,the electro-hydraulic steer-by-wire(SBW)system is introduced to achieve the multi-mode steering of the ECV.The overall structure and mathematical model of the SBW system are described at length.The fractional order proportional-integral-derivative(FOPID)controller based on fractional calculus theory is designed to control the steering cylinder’s movement in SBW system.The anti-windup problem is considered in the FOPID controller design to reduce the bad influence of saturation.Five parameters of the FOPID controller are optimized using the genetic algorithm by maximizing the fitness function which involves integral of time by absolute value error(ITAE),peak overshoot,as well as settling time.The time-domain simulations are implemented to identify the performance of the raised FOPID controller.The simulation results indicate the presented FOPID controller possesses more effective control properties than classical proportional-integral-derivative(PID)controller on the part of transient response,tracking capability and robustness.

Fractional-Order Control of a Wind Turbine Using Manta Ray Foraging Optimization

In this research paper,an improved strategy to enhance the performance of the DC-link voltage loop regulation in a Doubly Fed Induction Generator(DFIG)based wind energy system has been proposed.The proposed strategy used the robust Fractional-Order(FO)Proportional-Integral(PI)control technique.The FOPI control contains a non-integer order which is preferred over the integer-order control owing to its benefits.It offers extra flexibility in design and demonstrates superior outcomes such as high robustness and effectiveness.The optimal gains of the FOPI controller have been determined using a recent Manta Ray Foraging Optimization(MRFO)algorithm.During the optimization process,the FOPI controller’s parameters are assigned to be the decision variables whereas the objective function is the error racking that to be minimized.To prove the superiority of the MRFO algorithm,an empirical comparison study with the homologous particle swarm optimization and genetic algorithm is achieved.The obtained results proved the superiority of the introduced strategy in tracking and control performances against various conditions such as voltage dips and wind speed variation.

Optimal FOPID Controllers for LFC Including Renewables by Bald Eagle Optimizer

In this study,a bald eagle optimizer(BEO)is used to get optimal parameters of the fractional-order proportional-integral-derivative(FOPID)controller for load frequency control(LFC).SinceBEOtakes only a very short time in finding the optimal solution,it is selected for designing the FOPID controller that improves the system stability and maintains the frequency within a satisfactory range at different loads.Simulations and demonstrations are carried out using MATLAB-R2020b.The performance of the BEOFOPID controller is evaluated using a two-zone interlinked power system at different loads and under uncertainty of wind and solar energies.The robustness of the BEO-FOPID controller is examined by testing its performance under varying system time constants.The results obtained by the BEOFOPID controller are compared with those obtained by BEO-PID and PID controllers based on recent metaheuristics optimization algorithms,namely the sine-cosine approach,Jaya approach,grey wolf optimizer,genetic algorithm,bacteria foraging optimizer,and equilibrium optimization algorithm.The results confirm that the BEO-FOPID controller obtains the finest result,with the lowest frequency deviation.The results also confirm that the BEOFOPID controller is stable and robust at different loads,under varying system time constants,and under uncertainty of wind and solar energies.

Damping controller design based on FO-PID-EMA in VSC HVDC system to improve stability of hybrid power system

Wind energy sources have different structures and functions from conventional power plants in the power system.These resources can affect the exchange of active and reactive power of the network.Therefore,power system stability will be affected by the performance of wind power plants,especially in the event of a fault.In this paper,the improvement of the dynamic stability in power system equipped by wind farm is examined through the supplementary controller design in the high voltage direct current(HVDC)based on voltage source converter(VSC)transmission system.In this regard,impacts of the VSC HVDC system and wind farm on the improvement of system stability are considered.Also,an algorithm based on controllability(observability)concept is proposed to select most appropriate and effective coupling between inputs-outputs(IO)signals of system in different work conditions.The selected coupling is used to apply damping controller signal.Finally,a fractional order PID controller(FO-PID)based on exchange market algorithm(EMA)is designed as damping controller.The analysis of the results shows that the wind farm does not directly contribute to the improvement of the dynamic stability of power system.However,it can increase the controllability of the oscillatory mode and improve the performance of the supplementary controller.

Convergence and Superconvergence of Fully Discrete Finite Element for Time Fractional Optimal Control Problems

In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and L1 scheme in time. The control is obtained by the variational discretization technique. The main purpose of this work is to derive the convergence and superconvergence. A numerical example is presented to validate our theoretical results.

Guest Editorial for Special Issue on Fractional Order Systems and Controls

I.INTRODUCTION FRACTIONAL calculus has been applied in all MAD(modeling,analysis and design)aspects of control systems engineering since Shunji Manabe’s pioneering work in early 1960s.The 2016 International Conference on Fractional Differentiation and Its Applications(ICFDA)was held in Novi Sad,Serbia,July 18-20.Quoting from the

Reduced differential transform and Sumudu transform methods for solving fractional financial models of awareness

In that paper,we new study has been carried out on previous studies of one of the most important mathematical models that describe the global economic movement,and that is described as a non-linear fractional financial model of awareness,where the studies are represented at the steps following:One:The schematic of the model is suggested.Two:The disease-free equilibrium point(DFE)and the stability of the equilibrium point are discussed.Three:The stability of the model is fulfilled by drawing the Lyapunov exponents and Poincare map.Fourth:The existence of uniformly stable solutions have discussed.Five:The Caputo is described as the fractional derivative.Six:Fractional optimal control for NFFMA is discussed by clarifying the fractional optimal control through drawing before and after control.Seven:Reduced differential transform method(RDTM)and Sumudu Decomposition Method(SDM)are used to take the resolution of an NFFMA.Finally,we display that SDM and RDTM are highly identical.

Set-point Filter Design for a Two-degree-of-freedom Fractional Control System

This paper focuses on a new approach to design(possibly fractional) set-point filters for fractional control systems.After designing a smooth and monotonic desired output signal,the necessary command signal is obtained via fractional input-output inversion.Then,a set-point filter is determined based on the synthesized command signal.The filter is computed by minimizing the 2-norm of the difference between the command signal and the filter step response.The proposed methodology allows the designer to synthesize both integer and fractional setpoint filters.The pros and cons of both solutions are discussed in details.This approach is suitable for the design of two degreeof-freedom controllers capable to make the set-point tracking performance almost independent from the feedback part of the controller.Simulation results show the effectiveness of the proposed methodology.

Guest Editorial for Special Issue on Fractional Order Systems and Controls

I.INTRODUCTION FRACTIONAL calculus is about differentiation and integration of non-integer orders.Using integer-order models and controllers for complex natural or man-made systems is simply for our own convenience while the nature runs in a fractional order dynamical way.Using integer order traditiona tools for modelling and control of dynamic systems may resul in suboptimum performance,that is,using fractional order calculus tools,we could be'more optimal'as already doc-

Fractional synergetic tracking control for robot manipulator

This work takes advantage of synergetic control theory and fractional calculus to develop and propose fractional synergetic control(FSC)strategy for Four Degrees of Freedom(4-DOF)robot manipulator.The proposed fractional synergetic control is designed to track a joint space as well as workspace desired trajectories.Fractional calculus gives more flexibility in the design since it has a wider stability region.Added to that,as stated in the literature,compared to a similar approach such as sliding mode control,the synergetic control approach converges faster to the equilibrium point,without chattering with a fast response.This paper proposes a new control strategy that takes advantage of fractional calculus and synergetic control theory.This proposed control strategy is tested experimentally on a 4-DOF manipulator to study the performance of the proposed control scheme.The stability of the closed-loop system is proved using the Lyapunov approach.The experimental results have shown that the proposed FSC design has achieved a good tracking performance.

Design of internal model control based fractional order PID controller

This article presents a design of the internal model control （IMC） based single degree of freedom （SDF） fractional order （FO） PID controller with a desired bandwidth specification for a class of fractional order system （FOS）. The drawbacks of the SDF FO-IMC are eliminated with the help of the two-degree of freedom （TDF） FO PID controller. The robust stability and robust performance of the designed controller are analyzed using an example.

Conical tank level control using fractional order PID controllers： a simulated and experimental study

In this paper, simulated and experimental results on the conical tank level control are presented. PI/PID controllers of integer order （IO） as well as of fractional order （FO） are studied and compared. The tuning parameters are obtained first by using root locus （RL） and Ziegler and Nichols methods, for comparison purposes. Next, particle swarm optimization （PSO） is employed to determine the optimal controllers＇ parameters using as fitness function the integral of the absolute value of tracking error （IAE）. From the experimental results it is concluded that PI/FOPI are the controllers presenting the lowest IAE indexes, whereas PID/FOPID controllers present the lowest energy consumption by the control signal.

Design of a fractional PI~λD~μ controller using the cohort intelligence method

The cohort intelligence （CI） method has recently evolved as an optimization method based on artificial intelligence. We use the CI method for the first time to optimize the parameters of the fractional proportional- integral-derivative （PID） controller. The performance of the CI method in designing the fractional PID controller was validated and compared with those of some other popular algorithms such as particle swarm optimization, the genetic algorithm, and the improved electromagnetic algorithm. The CI method yielded improved solutions in terms of the cost function, computing time, and function evaluations in comparison with the other three algorithms. In addition, the standard deviations of the CI method demonstrated the robustness of the proposed algorithm in solving control problems.