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.     

Robust and novel two degree of freedom fractional controller based on two-loop topology for inverted pendulum

A rotary single inverted pendulum (RSIP) typically represents a space booster rocket, Segway and similar systems with unstable equilibrium. This paper proposes a novel two degree of freedom (2-DOF) fractional control strategy based on 2-loop topology for RSIP system which can be extended to control the systems with unstable equilibrium. It comprises feedback and feed-forward paths. Primary controller relates the perturbation attenuation while the secondary controller is accountable for set point tracking. To tune the parameters of proposed fractional controller a simple graphical tuning method based on frequency response is used. The study will serve the outstanding experimental results for both, stabilization and trajectory tracking tasks. The study will also serve to present a comparison of the performance of the proposed controller with the 1-DOF FOPID controller and sliding mode controller (SMC) for the RSIP system. Further to confirm the usability of the proposed controller and to avoid the random perturbations sensitivity, robustness, and stability analysis through fractional root-locus and Bode-plot is investigated.     

Design of interval type-2 fuzzy precompensated PID controller applied to two-DOF robotic manipulator with variable payload

The interval type-2 fuzzy logic controller (IT2-FLC), with footprint of uncertainty (FOU) in membership functions (MF), has increasingly recognized for controlling uncertainties and nonlinearities. Within the ambit of this, the efficient interval type-2 fuzzy precompensated PID (IT2FP-PID) controller is designed for trajectory tracking of 2-DOF robotic manipulator with variable payload. A systematic strategy for optimizing the controller parameters along with scaling factors and the antecedent MF parameters for minimization of performance metric integral time absolute error (ITAE) is presented. Prominently, recently proposed optimization technique hybridizing grey wolf optimizer and artificial bee colony algorithm (GWO–ABC) is utilized for solving this high-dimensional constrained optimization problem. In order to witness effectiveness, the performance is compared with type-1 fuzzy precompensated PID (T1FP-PID), fuzzy PID (FPID), and conventional PID controllers. More significantly, the robustness of IT2FP-PID is examined for payload variation, model uncertainties, external disturbance, and noise cancellation. After experimental outcome, it is inferred that IT2FP-PID controller outperforms others and can be referred as a viable alternative for controlling nonlinear complex systems with higher uncertainties.     

Trajectory and vibration control of a flexible joint manipulator using interval type-2 fuzzy logic

This study presents the development of a novel interval type-2 fuzzy logic controller for real time trajectory and vibration control of a flexible joint manipulator. The controller is designed on the Mamdani based interval type-2 fuzzy logic toolbox, which is developed by the authors, using interval triangular membership functions and Karnik–Mendel type reduction algorithm. The closed-loop stability of the system is proved based on Lyapunov stability theorem. In order to observe the effectiveness and robustness of the proposed controller to variations of system parameters (change in link length and payload), the experimental results of interval type-2 and conventional type-1 fuzzy logic controllers are compared. The results show that proposed controller clearly improves the link vibration and trajectory tracking behavior of the system.     

Optimal interval type-2 fuzzy fractional order super twisting algorithm: A second order sliding mode controller for fully-actuated and under-actuated nonlinear systems

In this paper, a novel interval type-2 fuzzy fractional order super twisting algorithm (IT2FFOSTA) which is essentially a second order sliding mode controller is presented. The proposed IT2FFOSTA enhances fractional order super twisting algorithm (FOSTA) by taking advantage of an interval type-2 fuzzy fractional order sliding surface (IT2FFOSS) for some classes of fully-actuated and under-actuated nonlinear systems in presence of uncertainty. The FOSTA significantly reduces the amount of chattering and the IT2FFOSS results in decreasing the tracking error, control effort, and chattering level. In order to control under-actuated systems, a hierarchical sliding surface is employed. The multi-tracker optimization algorithm is utilized to adjust the controller’s parameters; this leads to an optimal performance for the IT2FFOSTA. To examine the performance of the IT2FFOSTA, some simulation and experimental tests on three examples of different classes of fully-actuated and under-actuated systems, including ball and plate, inverted pendulum, and ball and beam systems are carried out. The simulation and experimental results demonstrate the superiority of the IT2FFOSTA in reducing the amount of chattering, tracking error, and control effort compared to those of the other control methods.     

基于LPC2103的模糊PID温度控制器设计

为使温度控制器的动态性能和稳态精度满足控制系统的要求,控制器采用了一种新型的模糊PID控制算法;温度测量采用Pt100,信号调理采用高精度运算放大器OP07,采用控制器LPC2103处理器制作了温度控制器;温度控制器采用PWM控制,控制器经模糊PID控制算法确定PWM脉冲宽度。为更好确定电阻炉温度控制系统的控制参数,采用实验的方法对电阻炉的数学模型进行了识别。在matlab仿真的基础上确定模糊PID控制参数,电阻炉的温度控制实验结果表明该温度控制器满足系统控制要求。     

A fuzzy model based adaptive PID controller design for nonlinear and uncertain processes

We develop a novel adaptive tuning method for classical proportional–integral–derivative (PID) controller to control nonlinear processes to adjust PID gains, a problem which is very difficult to overcome in the classical PID controllers. By incorporating classical PID control, which is well-known in industry, to the control of nonlinear processes, we introduce a method which can readily be used by the industry. In this method, controller design does not require a first principal model of the process which is usually very difficult to obtain. Instead, it depends on a fuzzy process model which is constructed from the measured input–output data of the process. A soft limiter is used to impose industrial limits on the control input. The performance of the system is successfully tested on the bioreactor, a highly nonlinear process involving instabilities. Several tests showed the method's success in tracking, robustness to noise, and adaptation properties. We as well compared our system's performance to those of a plant with altered parameters with measurement noise, and obtained less ringing and better tracking. To conclude, we present a novel adaptive control method that is built upon the well-known PID architecture that successfully controls highly nonlinear industrial processes, even under conditions such as strong parameter variations, noise, and instabilities.     

A simplified type-2 fuzzy logic controller for real-time control

Increasingly, genetic algorithms (GAs) are used to optimize the parameters of fuzzy logic controllers (FLCs). Although GAs provide a systematic design approach, the optimization process is generally performed off-line using a plant model. Differences between the model and physical plant may result in unsatisfactory control performance when the FLCs are deployed in practice. Type-2 FLCs are an attractive alternative because they can better cope with modeling uncertainties. Unfortunately, type-2 FLCs are computationally intensive. This paper presents a simplified type-2 FLC that is suitable for real-time applications. The key idea is to only replace some critical type-1 fuzzy sets by type-2 sets. Experimental results indicate that the proposed simplified type-2 FLC is as robust as a conventional type-2 FLC, while lowering the computational cost.     

一种模糊规范化PID控制器混沌优化设计

基于混沌变量，提出了一种FNPID参数混沌优化设计。文中将混沌动力学特性与退火策略结合起来实现混沌优化搜索，体现出具有更强的FNPID参数全局最优值的搜索能力。仿真实验表明能有效地实现FNPID控制器参数优化，控制结果具有稳定、无振荡、无超调、响应快、调节时间短的优点，算法结构简单，编程容易。     

基于模糊遗传算法的二自由度PID控制器优化设计

针对一般遗传算法中交叉概率和变异概率存在的选择困难问题，利用模糊推理系统来自适应估计交叉概率和变异概率，提出了模糊遗传算法（FGAs），并用于二自由度PID控制器参数寻优设计。仿真和实验表明，所设计的二自由度PID控制器可以使系统同时具有良好的目标值跟随特性和干扰抑制特性。     

基于模糊PID控制器的流量控制设计

现今流量控制系统很多都使用常规PID控制器,这样虽然比较方便,但不能在线整定参数,因而不能很好地控制非线性等复杂系统.在本系统中,采用模糊PID控制器来设计控制流量.模糊PID控制器将PID控制和模糊控制两种方法结合起来,既能消除稳态误差,又能对复杂系统进行简单有效的控制,从而达到控制要求.     

基于模糊BP网络的自适应PID控制

针对经典PID控制的参数不能在线调整的缺陷,提出了一种基于模糊BP神经网络的PID控制算法,采用模糊规则自动地调节BP神经网络训练过程的学习参数,利用神经网络较强的学习能力和模糊控制在模型未知或不精确前提下的控制能力,将其应用到PID控制中[1],实现了PID控制参数的在线调整和优化,并对其在非线性离散系统中的应用进行了仿真。实验结果表明该算法性能优良,加快了系统响应速度,减少了超调量,适用于纯滞后非线性系统。     

一种用于1/2汽车半主动悬架的模糊PID控制器

设计了一种用于1/2车体四自由度的液压半主动悬架的参数自整定模糊PID控制器,利用模糊控制规则对PID参数进行在线修改.应用MATLAB/Simulink控制系统仿真软件,以正弦信号路面、脉冲信号路面和C级路面三种典型路面作为输入信号对该半主动悬架模型进行计算机仿真,仿真结果表明具有模糊PID控制器的半主动悬架在提高车辆乘坐的舒适性方面明显优于被动悬架和单纯的模糊控制悬架,具有较好的自适应能力.     

Fault tolerant control based on interval type-2 fuzzy sliding mode controller for coaxial trirotor aircraft

In this paper, a robust controller for a Six Degrees of Freedom (6 DOF) coaxial trirotor helicopter control is proposed in presence of defects in the system. A control strategy based on the coupling of the interval type-2 fuzzy logic control and sliding mode control technique are used to design a controller. The main purpose of this work is to eliminate the chattering phenomenon and guaranteeing the stability and the robustness of the system. In order to achieve this goal, interval type-2 fuzzy logic control has been used to generate the discontinuous control signal. The simulation results have shown that the proposed control strategy can greatly alleviate the chattering effect, and perform good reference tracking in presence of defects in the system.     

A novel optimized hybrid fuzzy logic intelligent PID controller for an interconnected multi-area power system with physical constraints and boiler dynamics

In the fast developing world nowadays, load frequency control (LFC) is considered to be a most significant role for providing the power supply with good quality in the power system. To deliver a reliable power, LFC system requires highly competent and intelligent control technique. Hence, in this article, a novel hybrid fuzzy logic intelligent proportional-integral-derivative (FLiPID) controller has been proposed for LFC of interconnected multi-area power systems. A four-area interconnected thermal power system incorporated with physical constraints and boiler dynamics is considered and the adjustable parameters of the FLiPID controller are optimized using particle swarm optimization (PSO) scheme employing an integral square error (ISE) criterion. The proposed method has been established to enhance the power system performances as well as to reduce the oscillations of uncertainties due to variations in the system parameters and load perturbations. The supremacy of the suggested method is demonstrated by comparing the simulation results with some recently reported heuristic methods such as fuzzy logic proportional-integral (FLPI) and intelligent proportional-integral-derivative (PID) controllers for the same electrical power system. the investigations showed that the FLiPID controller provides a better dynamic performance and outperform compared to the other approaches in terms of the settling time, and minimum undershoots of the frequency as well as tie-line power flow deviations following a perturbation, in addition to perform appropriate settlement of integral absolute error (IAE). Finally, the sensitivity analysis of the plant is inspected by varying the system parameters and operating load conditions from their nominal values. It is observed that the suggested controller based optimization algorithm is robust and perform satisfactorily with the variations in operating load condition, system parameters and load pattern.     

Calculation of PID controller parameters by using a fuzzy neural network

In this paper, we use the fuzzy neural network (FNN) to develop a formula for designing the proportional-integral-derivative (PID) controller. This PID controller satisfies the criteria of minimum integrated absolute error (IAE) and maximum of sensitivity (Ms). The FNN system is used to identify the relationship between plant model and controller parameters based on IAE and Ms. To derive the tuning rule, the dominant pole assignment method is applied to simplify our optimization processes. Therefore, the FNN system is used to automatically tune the PID controller for different system parameters so that neither theoretical methods nor numerical methods need be used. Moreover, the FNN-based formula can modify the controller to meet our specification when the system model changes. A simulation result for applying to the motor position control problem is given to demonstrate the effectiveness of our approach.     

Design and implementation of a new fuzzy PID controller for networked control systems

This paper presents a practical network platform to design and implement a networked-based cascade control system linking a Smar Foundation Fieldbus (FF) controller (DFI-302) and a Siemens programmable logic controller (PLC-S7-315-2DP) through Industrial Ethernet to a laboratory pilot plant. In the presented network configuration, the Smar OPC tag browser and Siemens WinCC OPC Channel provide the communicating interface between the two controllers. The paper investigates the performance of a PID controller implemented in two different possible configurations of FF function block (FB) and networked control system (NCS) via a remote Siemens PLC. In the FB control system implementation, the desired set-point is provided by the Siemens Human-Machine Interface (HMI) software (i.e, WinCC) via an Ethernet Modbus link. While, in the NCS implementation, the cascade loop is realized in remote Siemens PLC station and the final element set-point is sent to the Smar FF station via Ethernet bus. A new fuzzy PID control strategy is then proposed to improve the control performances of the networked-based control systems due to an induced transmission delay degradation effect. The proposed strategy utilizes an innovative idea based on sectionalizing the error signal of the step response into three different functional zones. The supporting philosophy behind these three functional zones is to decompose the desired control objectives in terms of rising time, settling time and steady-state error measures maintained by an appropriate PID-type controller in each zone. Then, fuzzy membership factors are defined to configure the control signal on the basis of the fuzzy weighted PID outputs of all three zones. The obtained results illustrate the effectiveness of the proposed fuzzy PID control scheme in improving the performances of the implemented NCS for different transportation delays.     

Design of nonlinear PID controller and nonlinear model predictive controller for a continuous stirred tank reactor

In this paper, the authors have represented the nonlinear system as a family of local linear state space models, local PID controllers have been designed on the basis of linear models, and the weighted sum of the output from the local PID controllers (Nonlinear PID controller) has been used to control the nonlinear process. Further, Nonlinear Model Predictive Controller using the family of local linear state space models (F-NMPC) has been developed. The effectiveness of the proposed control schemes has been demonstrated on a CSTR process, which exhibits dynamic nonlinearity.     

模糊自适应PID控制器在磁粉制动器加载系统中的应用研究

针对磁粉制动器在扭矩加载时,由于磁阻的磁滞、磁通的饱和性和磁导率的非恒定性,造成的加载精度低和系统响应滞后等问题,对磁粉制动器加载控制方法进行了研究,使用Matlab/Simulink设计了一种模糊自适应PID控制器,利用模糊规则在线对PID参数进行了优化调整,并对蜗轮蜗杆减速器扭矩加载系统中磁粉制动器的加载特性进行了仿真和实验。研究结果表明,模糊自适应PID控制器在磁粉制动器加载系统的控制中,大大提高了磁粉制动器的加载精度,且明显减小了系统响应的时间,表现出了良好的自适应性和稳定性,能够用来实现对磁粉制动器加载系统的有效控制。     

一类切换模糊PID控制器设计及其仿真

提出了一类高动态性能切换模糊PID控制器设计方法.通过对传统PID控制中比例控制和微分控制作用的分析,结合模糊PID控制器鲁棒性能和自适应性好的优点,设计了一类新的模糊控制器.由于该类控制器先后经历比例控制,微分控制和模糊PID控制的切换,使被控系统不仅具有一般模糊PID控制器的所具有的良好的鲁棒性能和自适应性,而且与一般模糊控制器相比具有更小的超调量和调节时间,是一类动态性能良好的控制器.最后将该控制器应用于一伺服系统进行仿真对比,并给出了Simulink仿真框图.仿真结果说明了该控制器的优越性.