A novel interval type-2 fractional order fuzzy PID controller: Design,performance evaluation,and its optimal time domain tuning

In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases.     

Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms

The most studied controller for pitch control of wind turbines is proportional-integral-derivative (PID) controller. However, due to uncertainties in wind turbine modeling and wind speed profiles, the need for more effective controllers is inevitable. On the other hand, the parameters of PID controller usually are unknown and should be selected by the designer which is neither a straightforward task nor optimal. To cope with these drawbacks, in this paper, two advanced controllers called fuzzy PID (FPID) and fractional-order fuzzy PID (FOFPID) are proposed to improve the pitch control performance. Meanwhile, to find the parameters of the controllers the chaotic evolutionary optimization methods are used. Using evolutionary optimization methods not only gives us the unknown parameters of the controllers but also guarantees the optimality based on the chosen objective function. To improve the performance of the evolutionary algorithms chaotic maps are used. All the optimization procedures are applied to the 2-mass model of 5-MW wind turbine model. The proposed optimal controllers are validated using simulator FAST developed by NREL. Simulation results demonstrate that the FOFPID controller can reach to better performance and robustness while guaranteeing fewer fatigue damages in different wind speeds in comparison to FPID, fractional-order PID (FOPID) and gain-scheduling PID (GSPID) controllers.     

Position control of an electro-pneumatic system based on PWM technique and FLC

In this paper, modeling and PWM based control of an electro-pneumatic system, including the four 2–2 valves and a double acting cylinder are studied. Dynamic nonlinear behavior of the system, containing fast switching solenoid valves and a pneumatic cylinder, as well as electrical, magnetic, mechanical, and fluid subsystems are modeled. A DC–DC power converter is employed to improve solenoid valve performance and suppress system delay. Among different position control methods, a proportional integrator derivative (PID) controller and fuzzy logic controller (FLC) are evaluated. An experimental setup, using an AVR microcontroller is implemented. Simulation and experimental results verify the effectiveness of the proposed control strategies.     

基于新型模糊PID控制的DC-DC变换器仿真研究

DC-DC功率变换器是一种强非线性系统,传统的PID控制是建立在其线性化小信号模型的基础上进行设计的,虽然算法简单,设计容易,但PID控制器在功率变换器的参数发生变化时并不能相应地改变参数。针对传统PID控制的特点,结合模糊控制不需要建立被控对象精确数学模型的特点,本文提出了一种新型的模糊PID控制器—指数形式模糊PID控制器,并设计了Buck变换器的新型模糊PID控制系统,该控制系统能够根据系统的变化实时地改变控制系统的参数。运用MATLAB/Simulink软件对该变换器系统进行了仿真,仿真结果表明,新型模糊PID控制器有着响应速度快,超调量小,鲁棒性强等特点。     

Intelligent fractional-order backstepping control for an ironless linear synchronous motor with uncertain nonlinear dynamics

This study aims to develop an intelligent fractional-order backstepping controller to control the mover position of an ironless permanent magnet linear synchronous motor. First, we investigated the operating principle and dynamic modeling of the linear synchronous motor based on the field-oriented control method. Next, to improve the convergence speed and control accuracy of the conventional backstepping controller, we designed a fractional-order backstepping controller that has more degrees of freedom in the control parameters. However, designing the switching control gain is difficult owing to the unknown degree of uncertainty. To address this problem, we proposed an intelligent fractional-order backstepping controller to further enhance the adaptiveness and robustness of the fractional-order backstepping controller. In this intelligent controller, we proposed a Hermite-polynomial-based functional-link fuzzy neural network as an uncertainty estimator that can directly estimate system uncertainty, thereby improving the disturbance rejection ability and requiring no uncertainty bound information. Additionally, to compensate for the estimation error introduced by the estimator, we designed an exponential compensator that employs a smooth exponential self-regulation mechanism. We utilized the Lyapunov theorem to derive estimation laws for the online tuning of the control parameters. Experimental results demonstrate the effectiveness and high positioning performance of the proposed intelligent fractional-order backstepping controller in comparison with the backstepping controller and fractional-order backstepping controller in the linear synchronous motor control system.     

Fractional order phase shaper design with Bode’s integral for iso-damped control system

The phase curve of an open loop system is flat in nature if the derivative of its phase with respect to frequency is zero. With a flat-phase curve, the corresponding closed loop system exhibits an iso-damped property i.e. maintains constant overshoot with the change of gain. This implies enhanced parametric robustness e.g. to variation in system gain. In the recent past, fractional order (FO) phase shapers have been proposed by contemporary researchers to achieve enhanced parametric robustness. In this paper, a simple methodology is proposed to design an appropriate FO phase shaper to achieve phase flattening in a control loop, comprising a plant controlled by a classical Proportional Integral Derivative (PID) controller. The methodology is demonstrated with MATLAB simulation of representative plants and accompanying PID controllers.     

基于遗传算法的数控机床进给伺服系统模糊PID位置控制研究

文章针对电机引入的非线性、参数不确定性及对位置伺服系统快速定位和无超调的要求问题,提出了一种新的位置控制方法,即基于遗传算法的模糊PID位置控制。该方法结合遗传算法和模糊PID控制的优点,利用遗传算法优化模糊PID控制系统的模糊控制规则,通过模糊控制规则对PID参数进行实时修改。仿真结果表明,这种位置控制器具有良好的稳态精度和动态响应,与传统比例位置控制的伺服系统相比,具有良好的动态、稳态性能以及较强的鲁棒性。     

PID参数模糊自整定非线性系统仿真研究

针对常规PID控制器不能在线进行参数自整定的问题,构造了一个自适应模糊PID。通过模糊控制规则在线调整PID控制器的参数,并利用MATLAB语言对该控制器进行了计算机仿真。仿真研究表明,该控制器能迅速消除系统余差,改善普通模糊控制器的性能;既具有PID控制器高精度的优点,又具有模糊控制器快速、适应性能的特点,保证了调节系统具有良好的动、稳态特性。     

Machining force control with intelligent compensation

Force control is an effective means of improving the quality and efficiency of machining operations, so various approaches for force control have been proposed. However, due to the nonlinear, time-varying and uncertain characteristics of machining processes, it is difficult to develop force control systems that are stable and robust over the full range of operating conditions. This study proposed two control schemes to address such difficulties in the field of nonlinear force control by using a linear feedback proportional-derivate (PD) controller respectively with two different nonlinear intelligent compensators: fuzzy logic compensator (FLC) and neural network compensator (NNC). The PD controller is used to improve the transient response while maintaining the stability of the process system, and the FLC or NNC is employed to eliminate the steady-state error and compensate for the system nonlinearity (or uncertainty). The applications of the proposed schemes in machining processes show that the controllers adapt well to nonlinearity under time-varying cutting conditions in comparison to PID, PD, and FLC. The online updating of the NNC parameters through the Feedback-Error Learning can further improve the system performance.     

Modeling and control of the magnetic suspension system

A fuzzy logic based controller applied to a simple magnetic suspension is presented in this paper. The simple electromagnet-ball system and the contactless optical position measurement system are developed as a physical model of the magnetic suspension. A nonlinear mathematical model is presented and linearized. This model has been used to design a discrete linear PID controller with optimal parameters. The physical real-time model was constructed in order to compare the performance of the linear discrete PID controller and the proposed fuzzy logic based PID controller. The decomposed fuzzy PID controller has proportional, integral, and derivative separate parts which are tuned independently. When testing it becomes clear that the decomposed fuzzy PID controller gives better performance over a typical operational range than a traditional linear PID controller.     

在分散控制系统上实现的PID参数模糊自整定控制

本文将给定相角裕度（ＰＭ）的参数自整定ＰＩＤ控制器与模糊参数自调整控制融合起来,提出一种基于给下相角裕度整定规则的模糊参数自整定控制。模拟推理控制器通过在线调整Ｐ、Ｉ、Ｄ参数,使其按不同的过程状态在最小及最大相角裕度两组参数间合理的变化,使系统得到比以往ＰＩＤ控制更好的控制效果。针对锅炉被控对象的仿真结果表明,这种控制器能很好的解决电厂的有关控制问题。     

Fuzzy Gain Scheduled Continuous Stirred Tank Reactor with Particle Swarm Optimization based PID control Minimizing Integral Square Error

In this paper, a new control scheme, the gain scheduled Particle Swarm Optimization (PSO) based PID, is proposed for a continuous stirred tank reactor (CSTR). CSTR is a highly nonlinear process that exhibits stability in certain regions and instability in some regions. Generally, PID controllers are used in these processes. Tuning of the PID controller is required to guarantee the best performance of the CSTR. The proposed scheme implements the characteristics of the PSO's global optimization to tune the PID's control parameters: k_p, k_i, k_d, to obtain the best control effect by minimizing Integral Square Error online. The PID controller parameters tuned for each region using PSO are gain scheduled using fuzzy control. Fuzzy gain-scheduling is a special form of fuzzy control that uses linguistic rules and fuzzy reasoning to determine the controller parameter transition policy for the dynamic plant subject to large changes in its operating state. Simulation results show the feasibility of using the proposed controller for the control of the dynamic nonlinear CSTR.     

基于模糊神经网络的精密角度定位PID控制

针对精密角度定位系统存在非线性、时变性,传统PID控制难以获得理想控制效果的问题,提出一种基于模糊神经网络的PID控制方法,将模糊控制、神经网络与PID控制相结合,采用3层前向网络、动态BP算法,利用神经网络的自学习和自适应能力,实时调整网络的权值,改变PID控制器的控制参数,整定出一组适用于控制对象的kp、ki、kd参数,实现精密角度定位PID控制的自适应和智能化。实验结果表明,采用BP神经网络整定的PID控制较传统的PID控制,控制性能有较大的提高,能有效提高定位精度,缩短定位时间。     

烧结混合料加水的模糊自适应分数阶PI~λD~u控制

烧结混合料加水系统具有大滞后、模型复杂的特性,且客观环境中存在干扰因素,传统的控制方法很难取得理想的控制效果。分数阶PIλDu控制器比常规PID控制器多了两个可调参数,具有更好的控制效果。在分析分数阶微积分的基础上,给出了分数阶微积分的数字实现,用分数阶PIλDu控制代替常规PID控制,结合模糊控制,首次提出了一种针对烧结混合料加水系统的模糊自适应分数阶PIλDu控制方法,利用模糊逻辑实现分数阶PIλDu控制参数的在线调整。并用MATLAB/simulink进行建模仿真。仿真结果验证该控制算法的有效性,能取得较好的控制效果。     

基于Matlab的无刷直流电机Fuzzy-PID控制研究及其建模仿真

针对PID控制下的无刷直流电机(BLDCM)抗干扰能力差的问题,提出了Fuzzy-PID控制方法,该方法利用模糊逻辑控制器(FLC)在线调整PID的控制参数。在Matlab/Simulink环境下建立了基于Fuzzy-PID控制的无刷直流电机模型,并对转速误差进行归一化处理。仿真结果显示Fuzzy-PID控制与传统PID控制相比,在超调量、稳态时间、电流波动和转矩波动等方面有明显改善。     

PID参数模糊自整定控制器的设计与研究

在常规PID控制和模糊控制研究的基础上,提出了一种PID参数模糊自整定控制器,采用模糊推理对PID控制器的控制参数进行在线调整,给出了参数整定的基本原则。并用MATLAB中SIMULINK和FUZZY工具箱对三种控制方式进行了仿真。仿真结果表明,PID参数模糊自整定控制器的控制性能优于常规PID控制和模糊控制,具有良好的抗干扰性和鲁棒性。     

Design of a fractional order PID controller using GBMO algorithm for load–frequency control with governor saturation consideration

Load–frequency control is one of the most important issues in power system operation. In this paper, a Fractional Order PID (FOPID) controller based on Gases Brownian Motion Optimization (GBMO) is used in order to mitigate frequency and exchanged power deviation in two-area power system with considering governor saturation limit. In a FOPID controller derivative and integrator parts have non-integer orders which should be determined by designer. FOPID controller has more flexibility than PID controller. The GBMO algorithm is a recently introduced search method that has suitable accuracy and convergence rate. Thus, this paper uses the advantages of FOPID controller as well as GBMO algorithm to solve load–frequency control. However, computational load will higher than conventional controllers due to more complexity of design procedure. Also, a GBMO based fuzzy controller is designed and analyzed in detail. The performance of the proposed controller in time domain and its robustness are verified according to comparison with other controllers like GBMO based fuzzy controller and PI controller that used for load–frequency control system in confronting with model parameters variations.     

四相平板式TFPM模糊PID控制系统的设计

针对四相平板式横向磁场永磁电机非线性、时变性的特点,采用单一传统的PID控制无法达到满意的控制效果,提出了一种复合控制即模糊PID控制算法。借助于模块化建模仿真工具搭建系统仿真模型,进行模糊PID与传统PID控制的对比研究,仿真结果表明模糊PID控制精度高,动态响应速度快,静态误差小,对外部扰动(负载扰动)具有很强抑制能力并且对电机参数变化也具有较强的自适应性。解决了四相平板式横向磁场永磁电机非线性、时变性特点的控制问题。     

一种MIMO的柴油机模糊智能控制器和改进算法

提出一种具有多输入和多输出(MIMO)结构,在线修正PID参数的柴油机模糊控制器和改进算法.在算法中建立了柴油机模糊PID控制器的三维模糊数学模型,提出用载荷和增压器进气流量作为新的模糊控制变量,并用模糊控制芯片F100实现了实时在线调整柴油机电子调速器PID参数.仿真结果和Z6135柴油机调速性能试验表明,模糊智能控制器可以实现实时多目标控制,改善调速器带载条件下的动态响应,实用可靠,适于工程应用.     

液压机械手电液比例系统模糊PID控制研究

针对液压机械手的电液比例系统存在较大程度的系统参数变化和负载干扰等特点,一般控制方法难以全部满足性能要求。常规PID控制方法虽然算法简单、可靠性好、鲁棒性高,但由于参数整定繁杂,往往造成参数整定不良、性能欠佳、适用性能差。为了改善这些缺陷,将模糊控制理论与PID控制理论相结合,设计了模糊PID控制器,实现了对PID参数的在线整定。利用MATLAB/Simulink进行仿真,比较常规PID控制与模糊PID控制下电液比例系统的控制效果,发现模糊PID控制器较好地克服了系统的非线性和负载干扰的影响,提高了系统的稳定性和动态性能。