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.

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 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.

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.

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。

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.

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。

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.

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。

Control of a 3-RRR Planar Parallel Robot Using Fractional Order PID Controller

3-RRR planar parallel robots are utilized for solving precise material-handling problems in industrial automation applications.Thus,robust and stable control is required to deliver high accuracy in comparison to the state of the art.The operation of the mechanism is achieved based on three revolute(3-RRR)joints which are geometrically designed using an open-loop spatial robotic platform.The inverse kinematic model of the system is derived and analyzed by using the geometric structure with three revolute joints.The main variables in our design are the platform base positions,the geometry of the joint angles,and links of the 3-RRR planar parallel robot.These variables are calcula ted based on Cayley-Menger determinants and bilateration to det ermine the final position of the platform when moving and placing objects.Additionally,a proposed fractional order proportional integral derivative(FOPID)is optimized using the bat optimization algorithm to control the path tracking of the center of the 3-RRR planar parallel robot.The design is compared with the state of the art and simulated using the Matlab environment to validate the effectiveness of the proposed controller.Furthermore,real-time implementation has been tested to prove that the design performance is practical.

基于自适应布谷鸟搜索算法的分数阶PID控制器设计

针对分数阶PID(fractional order PID,FOPID)控制器的设计问题,提出一种基于自适应布谷鸟搜索算法的分数阶PID控制器参数整定算法。为改进经典布谷鸟算法的收敛速度与计算精度,并充分发挥全局搜索和局部挖掘两者各自的优势,采用了基于系统误差的自适应步长策略。为保证布谷鸟搜索算法初始化种群的均匀性,采用佳点集法初始化种群替代经典算法中的随机初始化种群。最后对2类系统进行仿真实验,并将实验结果与现有结果进行对比,验证了基于自适应布谷鸟搜索算法的分数阶PID控制器的设计和参数整定方法的有效性和优良性。

基于分数阶PID的连续变焦控制系统设计与实现

连续变焦系统是一种能够进行连续视场变换的光电成像装置,可对目标进行连续探测和识别,具有快速、稳定的特点。针对其高精度,高稳定控制需求,提出一种分数阶PID(proportion integration differentiation)控制器设计方法,该方法利用内模控制策略构造含有3个整定参数的分数阶PID控制器,且这3个参数通过给定系统穿越频率和相位裕度获得,大大简化了分数阶PID控制器的设计,同时提高了控制器的可实现性。在Matlab平台同传统整数阶PID进行了控制效果对比,仿真结果表明:分数阶PID控制器将稳态误差由0.1 mm提升至0 mm,具有抗干扰性强、鲁棒性强、数字实现后无超调、静差小的特点。最后将数字分数阶PID应用于实际的连续变焦系统,系统可获得清晰稳定的图像,验证了控制策略的有效性。

加热炉分数阶PID温度自适应控制系统设计

针对加热炉温度控制系统控制器参数不易选择的问题,提出一种分数阶自适应PID串级控制方法实现控制器参数自动调整。首先以分数阶PID控制器分别作为温度主控制器和燃气流量控制器,实现加热炉串级温度控制;其次应用自适应理论对控制器进行改进,设计了自适应分数阶PID控制器。最后通过数值仿真,验证了所设计控制系统对加热炉温度控制的有效性和可行性。

基于ENMSSFMPC-PID的原油稳定加热炉温度控制

为实现对非线性和时变系统的更精准建模和控制,适应系统动态变化和参数变化,应对系统变化和外部干扰,实现更可靠和安全的过程生产控制,提出一种新型模型预测控制策略。基于分数阶微积分运算的扩展非最小状态空间模型预测控制(ENMSSFMPC)算法,状态空间模型包含状态变量和输出跟踪误差,通过分数阶定义将系统模型离散化,利用ENMSSFMPC对比例—积分—微分(PID)控制器进行参数滚动优化,获得实时最优控制参数。原油稳定加热炉模型仿真结果表明,该控制策略优于传统的模型预测控制、非最小状态空间模型预测控制和分数阶模型预测控制。

Maximum Power Extraction Control Algorithm for Hybrid Renewable Energy System

In this research,a modified fractional order proportional integral derivate(FOPID)control method is proposed for the photovoltaic(PV)and thermoelectric generator(TEG)combined hybrid renewable energy system.The faster tracking and steady-state output are aimed at the suggested maximum power point tracking(MPPT)control technique.The derivative order number(μ)value in the improved FOPID(also known as PIλDμ)control structure will be dynamically updated utilizing the value of change in PV array voltage output.During the transient,the value ofμis changeable;it’s one at the start and after reaching the maximum power point(MPP),allowing for strong tracking characteristics.TEG will use the freely available waste thermal energy created surrounding the PVarray for additional power generation,increasing the system’s energy conversion efficiency.A high-gain DC-DC converter circuit is included in the system to maintain a high amplitude DC input voltage to the inverter circuit.The proposed approach’s performance was investigated using an extensive MATLAB software simulation and validated by comparing findings with the perturbation and observation(P&O)type MPPT control method.The study results demonstrate that the FOPID controller-based MPPT control outperforms the P&O method in harvesting the maximum power achievable from the PV-TEG hybrid source.There is also a better control action and a faster response.

基于模糊自适应分数阶PID的PMSM控制研究

设计一种模糊自适应分数阶PID(Fuzzy Adaptive Fractional Order PID,FAFOPID)控制器,应用于永磁同步电机(Permanent Magnet Synchronous Motor,PMSM)的跟踪控制,应用模糊逻辑实现控制器参数的在线调整,对其进行控制器参数优化,提高系统的稳态精度和控制性能。此外,通过改变系统参数验证了PMSM系统的鲁棒性,结果表明设计的FAFOPID控制系统具有超调量更小、响应速度更快、系统更稳定的优点。

基于模糊分数阶PID控制的轮式移动机器人轨迹跟踪研究

轮式移动机器人的轨迹跟踪是目前学者研究的热点问题之一。为了使其能够按照预定设置目标轨迹进行移动,文章作者绘制了轮式移动机器人平面简图,建立其动力学模型;利用模糊规则对传统PID控制器加以改进,并根据模糊理论在线调整PID控制器参数,最终得到轮式移动机器人的最优控制参数;采取不同环境对轮式移动机器人跟踪误差进行仿真分析,检验模糊分数阶PID控制器的优势。研究结果显示:在无干扰波形中设置轮式移动机器人移动目标,两种控制效果差别不大。在有干扰波形中设置轮式移动机器人移动目标,PID控制器输出误差明显增大,而模糊分数阶PID控制器输出误差保持不变,可以看出模糊分数阶PID控制器能够更好地服务轮式移动机器人,使其具有强大的抗干扰能力,效果较好。

Auto-Tuning Parameters of Fractional PID Controller Design for Air-Conditioning Fan Coil Unit

The traditional integer order PID controller manipulates the air-conditioning fan coil unit(FCU)that offers cooliug and heatins loads to each air-conditioning room in summer and winter,respectivelv.In order to maintain a steady indoor temperature in summer and winter,the control quality cannot meet the related requirements of air-conditioning automation,such as large overshoot,large steady state error.long regulating time,etc.In view of these factors,this paper develops a fractional order PID controller to deal with such problem associated with FCU.Then,by varving mutation factor and crossover rate of basic differential evolution algorithmadaptivelv,a modified differential evolution algorithm(MDEA)is designed to tune the satisfactory values of five parameters of indoor temperature fractional order PID controller.This fractional order PID coutrol system is configured and the corresponding mumerical simulation is conducted by means of MATLAB software.The results indicate that the proposed fractional order PID control svstem and MDEA are reliable and the related control performance indexes meet with the related requirements of comfortable air-conditioning design and control criteria.

基于时域的分数阶PID预测函数励磁控制器

为了提高电力系统的稳定性,将分数阶PID算法与预测函数算法相结合,提出了一种新型的基于时域的分数阶PID预测函数励磁控制器的设计方法。该算法不仅具有分数阶PID静态误差小、上升速度快以及预测函数算法超调小、调节时间短的优点,还克服了分数阶PID调节时间长和预测函数算法静态误差大的缺点,同时还比预测函数算法多出了5个可调参数,设计更加灵活。研究结果表明该算法不仅能有效地解决机端电压偏移问题,还能有效地抑制电网低频振荡,为电力系统稳定性控制提供了一种新型有效的方法。