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.

ADRC FRACTIONAL ORDER PID CONTROLLER DESIGN OF HYPERSONIC FLIGHT VEHICLE

Active disturbance rejection controller（ADRC）uses tracking-differentiator（TD）to solve the contradiction between the overshoot and the rapid nature.Fractional order proportion integral derivative（PID）controller improves the control quality and expands the stable region of the system parameters.ADRC fractional order（ADRFO）PID controller is designed by combining ADRC with the fractional order PID and applied to reentry attitude control of hypersonic vehicle.Simulation results show that ADRFO PID controller has better control effect and greater stable region for the strong nonlinear model of hypersonic flight vehicle under the influence of external disturbance,and has stronger robustness against the perturbation in system parameters.

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.

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.

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.

Design and Robust Performance Evaluation of a Fractional Order PID Controller Applied to a DC Motor

This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 2~3 factorial experimental design for a fractional order proportional integral and derivative controller(FOPID), integer order proportional integral and derivative controller(IOPID)and the Skogestad internal model control controller(SIMC). The factors assumed in experiment are the presence of random noise,external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors.

基于粒子群算法的分数阶PID主动磁轴承控制

针对主动磁轴承(AMB)四自由度间强耦合、非线性导致控制器控制效果不佳的问题,将分数阶PID(FOPID)控制器引入AMB控制系统,提出了基于粒子群(PSO)算法的FOPID控制器以提高控制器的响应速度并抑制转轴位移超调量,提高控制精度。采用时间乘以误差绝对值积分(ITAE)作为性能指标,在限制电流模块不同幅值条件下,将FOPID控制器与PID控制器进行比较。仿真结果显示,PSO算法可以简化FOPID控制器参数的调节过程;随着限制电流的提升,FOPID控制器的控制效果明显优于PID控制器,在5 A输入电流的限制下其性能指标高出PID控制器约1.05%;随限制电流幅值增加,在60 A输入电流的限制下性能指标可高出PID控制器约26.25%。

SWISS整流器分数阶PID控制策略

针对SWISS整流器的传统整数阶PID控制策略动态响应速度较慢、鲁棒性较差的问题,提出一种基于分数阶PID的SWISS整流器控制策略。基于SWISS整流器的工作原理建立其小信号模型,得到SWISS整流器的等效传递函数,并设计基于分数阶PID电压控制的双闭环控制结构。为简化分数阶PID的阶次参数设计,采用整数阶PID参数预整定的方法得到参数初值,并利用粒子群算法对分数阶PID控制器参数进行进一步设计优化。仿真和实验结果表明,分数阶PID控制策略下的SWISS整流器发生参考电压突变时电压稳定时间小于7 ms、超调量小于2%,发生负载扰动时电压稳定时间小于4 ms、超调量小于3%,动态性能优于整数阶PID控制策略。

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.

Identification and PID Control for a Class of Delay Fractional-order Systems

In this paper, a new model identification method is developed for a class of delay fractional-order system based on the process step response. Four characteristic functions are defined to characterize the features of the normalized fractional-order model. Based on the time scaling technology, two identification schemes are proposed for parameters U+02BC estimation. The scheme one utilizes three exact points on the step response of the process to calculate model parameters directly. The other scheme employs optimal searching method to adjust the fractional order for the best model identification. The proposed two identification schemes are both applicable to any stable complex process, such as higher-order, under-damped U+002F over-damped, and minimum-phase U+002F nonminimum-phase processes. Furthermore, an optimal PID tuning method is proposed for the delay fractional-order systems. The requirements on the stability margins and the negative feedback are cast as real part constraints U+0028 RPC U+0029 and imaginary part constraints U+0028 IPC U+0029. The constraints are implemented by trigonometric inequalities on the phase variable, and the optimal PID controller is obtained by the minimization of the integral of time absolute error U+0028 ITAE U+0029 index. Identification and control of a Titanium billet heating process is given for the illustration. © 2014 Chinese Association of Automation.

Hydraulic cylinder control of injection molding machine based on differential evolution fractional order PID

Injection molding machine,hydraulic elevator,speed actuators belong to variable speed pump control cylinder system.Because variable speed pump control cylinder system is a nonlinear hydraulic system,it has some problems such as response lag and poor steady-state accuracy.To solve these problems,for the hydraulic cylinder of injection molding machine driven by the servo motor,a fractional order proportion-integration-diferentiation(FOPID)control strategy is proposed to realize the speed tracking control.Combined with the adaptive differential evolution algorithm,FOPID control strategy is used to determine the parameters of controller on line based on the test on the servo-motor-driven gear-pump-controlled hydraulic cylinder injection molding machine.Then the slef-adaptive differential evolution fractional order PID controller(SADE-FOPID)model of variable speed pump-controlled hydraulic cylinder is established in the test system with simulated loading.The simulation results show that compared with the classical PID control,the FOPID has better steady-state accuracy and fast response when the control parameters are optimized by the adaptive differential evolution algorithm.Experimental results show that SADE-FOPID control strategy is effective and feasible,and has good anti-load disturbance performance.

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.

基于分数阶PID的宏微复合驱动器宏动控制策略

针对宏微复合驱动器控制系统中存在定位误差大和调节时间长的问题,提出了一种基于次最优分数阶PID的控制策略。简述了宏微复合驱动器结构及工作原理,并基于电磁驱动原理建立了宏动部分数学模型;设计了分数阶PID控制器,并采用遗传算法和次最优的方法对控制器进行参数整定;通过数值仿真和实验验证了分数阶PID控制器的有效性。结果显示,采用分数阶PID控制器相较于传统PID控制器在5 mm以及更大定位行程中位移超调量下降超过57%,调节时间减少超过24%,且行程越大驱动器采用分数阶PID控制器控制效果越明显。研究结果表明,分数阶PID控制器在宏微复合驱动器宏动系统中的控制效果明显优于传统PID控制器。

基于改进鲸鱼优化算法的分数阶PID参数整定

该文提出了一种自适应混合策略鲸鱼优化算法(adaptive mixed strategy whale optimization algorithm,AMSWOA)用于分数阶PID控制器的参数整定。该算法基于鲸鱼优化算法进行改进,引入Tent混沌序列用以提高WOA的种群多样性、全局搜索能力和收敛速度;同时,采用了收敛因子非线性变化策略,并引入自适应权重以克服算法陷入局部最优解的问题;高斯变异的加入则有助于提高算法的搜索精度和寻优性能。通过在MATLAB/Simulink环境下验证整数阶和分数阶系统的被控对象,并与鲸鱼算法、灰狼优化算法及粒子群优化算法进行比较,证实了该文的AMSWOA算法对求解分数阶PID控制器参数整定问题的有效性和实用性。

Heuristic-Based Optimal Load Frequency Control with Offsite Backup Controllers in Interconnected Microgrids

The primary factor contributing to frequency instability in microgrids is the inherent intermittency of renewable energy sources.This paper introduces novel dual-backup controllers utilizing advanced fractional order proportional integral derivative(FOPID)controllers to enhance frequency and tie-line power stability in microgrids amid increasing renewable energy integration.To improve load frequency control,the proposed controllers are applied to a two-area interconnectedmicrogrid system incorporating diverse energy sources,such as wind turbines,photovoltaic cells,diesel generators,and various storage technologies.A novelmeta-heuristic algorithm is adopted to select the optimal parameters of the proposed controllers.The efficacy of the advanced FOPID controllers is demonstrated through comparative analyses against traditional proportional integral derivative(PID)and FOPID controllers,showcasing superior performance inmanaging systemfluctuations.The optimization algorithm is also evaluated against other artificial intelligent methods for parameter optimization,affirming the proposed solution’s efficiency.The robustness of the intelligent controllers against system uncertainties is further validated under extensive power disturbances,proving their capability to maintain grid stability.The dual-controller configuration ensures redundancy,allowing them to operate as mutual backups,enhancing system reliability.This research underlines the importance of sophisticated control strategies for future-proofing microgrid operations against the backdrop of evolving energy landscapes.

FOPID-GPC算法在电厂过热蒸汽温度控制中的应用

为了克服在过热蒸汽温度控制中对象参数变化对控制效果的影响,将分数阶PID(FOPID)控制与广义预测控制(GPC)算法相结合,构成了分数阶PID型FOPID广义预测控制(FOPID-GPC)算法。该算法的参数设置与传统的整数阶PID广义预测控制算法的参数设置具有一定的相似性,并增加了积分阶数和微分阶数2个可调参数,该参数的取值对控制系统的性能具有很大的影响。仿真结果表明,FOPID-GPC算法使控制系统具有超调量小、调节时间短、能够快速跟踪系统变化的特点,提高了控制系统动态性能,能够较好地将蒸汽温度控制在设定值附近。

变论域模糊分数阶PID的矿用机车开关磁阻电机调速系统设计

开关磁阻电机被广泛应用于矿用基础中,其结构稳定可靠,能够有效降低煤矿开采成本。介绍了开关磁阻电机的基本原理,阐述了模糊控制以及变论域模糊控制的机理,使用MATLAB建立了分数阶PID仿真模型,和传统PID进行了比较,建立变论域模糊分数阶PID控制器仿真模型,提出了一种基于ARM的矿用机车调速系统,并阐述了从MATLAB模型到ARM嵌入式处理器的部署过程。仿真结果显示,建立的模型没有出现震荡的情况,具有较高的稳定性。

无刷直流电机的自适应分数阶PID控制优化仿真研究

为了提高无刷直流电机角速度信号跟踪精度,分析无刷直流电机数学模型,推导出电机运动方程式,引入人工蜂群算法对分数阶PID控制系统进行优化。在不同工况下,采用Matlab软件对电机角速度跟踪误差进行仿真实验,比较优化前后的电机角速度跟踪误差。结果显示,在外界负载干扰下,现有分数阶PID控制系统的自适应调节能力较弱,电机角速度跟踪误差较大;此次优化设计的分数阶PID控制系统的自适应调节能力较强,电机角速度跟踪误差较小。此外,此次优化设计的分数阶PID控制系统能够抑制外界负载的干扰,提高无刷直流电机角速度信号跟踪精度。

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.