Design of interval type-2 fuzzy sliding-mode controller

In this paper, an interval type-2 fuzzy sliding-mode controller (IT2FSMC) is proposed for linear and nonlinear systems. The proposed IT2FSMC is a combination of the interval type-2 fuzzy logic control (IT2FLC) and the sliding-mode control (SMC) which inherits the benefits of these two methods. The objective of the controller is to allow the system to move to the sliding surface and remain in on it so as to ensure the asymptotic stability of the closed-loop system. The Lyapunov stability method is adopted to verify the stability of the interval type-2 fuzzy sliding-mode controller system. The design procedure of the IT2FSMC is explored in detail. A typical second order linear interval system with 50% parameter variations, an inverted pendulum with variation of pole characteristics, and a Duffing forced oscillation with uncertainty and disturbance are adopted to illustrate the validity of the proposed method. The simulation results show that the IT2FSMC achieves the best tracking performance in comparison with the type-1 Fuzzy logic controller (T1FLC), the IT2FLC, and the type-1 fuzzy sliding-mode controller (T1FSMC).     

A simple design method for interval type-2 fuzzy pid controllers

In this study, a design method for single Input interval type-2 fuzzy PID controller has been developed. The most important feature of the proposed type-2 fuzzy controller is its simple structure consisting of a single input variable. The presented simple structure gives an opportunity to the designer to form the type-2 fuzzy controller output in closed form formulation for the first time in literature. This formulation cannot be achieved with present type-2 fuzzy PID controller structures which have employed the Karnik-Mendel type reduction. The closed form solution is derived in terms of the tuning parameters which are chosen as the heights of lower membership functions of the antecedent interval type-2 fuzzy sets. Elaborations are done on the derived closed form output and a simple strategy is presented for a single input type-2 fuzzy PID controller design. The presented interval type-2 fuzzy controller structure still keeps the most preferred features of the PID controller such as simplicity and easy design. We will illustrate how the extra degrees of freedom provided by the antecedent interval type-2 fuzzy sets can be used to enhance the control performance on linear and nonlinear benchmark systems by simulations. Moreover, the type-2 fuzzy controller structure has been implemented on experimental pH neutralization. The simulation and experimental results will illustrate that the proposed type-2 fuzzy controller produces superior control performance and can handle nonlinear dynamics, parameter uncertainties, noise and disturbances better in comparison with the standard PID controllers. Hence, the results and analyses of this study will give the control engineers an opportunity to draw a bridge and connect the type-2 fuzzy logic and control theory.     

多输入–多输出非线性系统的特征模型及在挠性卫星姿态控制中的应用

研究多输入–多输出（MIMO）高阶非仿射非线性系统的特征建模问题.首先证明了MIMO高阶非仿射非线性系统的特征模型可用二阶时变差分方程组描述,并给出了特征模型的建模误差.然后设计了基于特征模型的自适应模糊广义预测控制器,利用Lyapunov方法分析了闭环系统的稳定性.由于控制结构中使用了分层模糊逻辑系统,从而极大减少了模糊规则和可调参数的个数,提高了控制的实时性.通过对挠性卫星姿态控制的仿真研究验证了所给控制方案的有效性,可实现高精度的姿态控制,且该方法具有较强的鲁棒性.     

高速公路非线性反馈模糊逻辑匝道控制器

入口匝道控制是高速公路交通控制和智能运输系统的重要组成部分,但现有的入口匝道控制效果尚不理想.为此,本文提出一种非线性反馈方法用模糊逻辑进行入口匝道控制.建立了高速公路交通流动态模型,在此基础上,结合模糊逻辑理论设计了非线性反馈匝道控制器,根据密度误差和误差变化用模糊控制决定匝道调节率,模糊变量选用三角形隶属度函数,并制定了包含56条模糊规则的规则库,最后用MATLAB软件进行系统仿真.结果表明该控制器具有优越的动态和稳态性能,它能使高速公路主线交通流密度保持为设定的期望密度,该方法用在高速公路入口匝道控制中效果良好.     

Application of type-2 fuzzy logic system for load frequency control using feedback error learning approaches

In this paper, the type-2 fuzzy logic system (T2FLS) controller using the feedback error learning (FEL) strategy has been proposed for load frequency control (LFC) in the restructure power system. The original FEL strategy consists of an intelligent feedforward controller (INFC) (i.e. artificial neural network (ANN)) and the conventional feedback controller (CFC). The CFC acting as a general feedback controller to guarantee the stability of the system plays a crucial role in the transient state. The INFC is adopted in forward path to take over the control problem in the steady state. In this work, to improve the performance of the FEL strategy, the T2FLS is adopted instead of ANN in the INFC part due to its ability to model uncertainties, which may exist in the rules and measured data of sensors more effectively. The proposed FEL controller has been compared with a type-1 fuzzy logic system (T1FLS) – based FEL controller and the proportional, integral and derivative (PID) controller to highlight the effectiveness of the proposed method.     

Finishing mill strip gage setup and control by interval type-1 non-singleton type-2 fuzzy logic systems

The setup and control of the finishing mill roll gap positions required to achieve the desired strip head thickness as measured by the finish mill exit X-ray gauge sensor is made by an intelligent controller based on an interval type-2 fuzzy logic system. The controller calculates the finishing mill stand screw positions required to achieve the strip finishing mill exit target thickness. The interval type-2 fuzzy head gage controller uses as inputs the transfer bar thickness, the width and the temperature at finishing mill entry, the strip target thickness, the width and the temperature at finishing mill exit, the stand work roll diameter, the stand work roll speed, the stand entry thickness, the stand exit thickness, the stand rolling force, and the %C of the strip. Taking into account that the measurements and inputs to the proposed system are modeled as type-1 non-singleton fuzzy numbers, we present the so called interval type-1 non-singleton type-2 fuzzy logic roll gap controller. As reported in the literature, interval type-2 fuzzy logic systems have greater non-linear approximation capacity than that of its type-1 counterpart and it has the advantage to develop more robust and reliable solutions than the latter. The experiments of these applications were carried out for three different types of coils, from a real hot strip mill. The results proved the feasibility of the developed system for roll gap control. Comparison against the mathematical based model shows that the proposed interval type-2 fuzzy logic system equalizes the performance in finishing mill stand screw positions setup and enhances the achieved strip thickness under the tested conditions characterized by high uncertainty levels.     

Interval Type-2 Fuzzy Hierarchical Adaptive Cruise Following-Control for Intelligent Vehicles

Intelligent vehicles can effectively improve traffic congestion and road traffic safety. Adaptive cruise following-control (ACFC) is a vital part of intelligent vehicles. In this paper, a new hierarchical vehicle-following control strategy is presented by synthesizing the variable time headway model, type-2 fuzzy control, feedforward + fuzzy proportion integration (PI) feedback (F+FPIF) control, and inverse longitudinal dynamics model of vehicles. Firstly, a traditional variable time headway model is improved considering the acceleration of the lead car. Secondly, an interval type-2 fuzzy logic controller (IT2 FLC) is designed for the upper structure of the ACFC system to simulate the driver’s operating habits. To reduce the nonlinear influence and improve the tracking accuracy for the desired acceleration, the control strategy of F+FPIF is given for the lower control structure. Thirdly, the lower control method proposed in this paper is compared with the fuzzy PI control and the traditional method (no lower controller for tracking desired acceleration) separately. Meanwhile, the proportion integration differentiation (PID), linear quadratic regulator (LQR), subsection function control (SFC) and type-1 fuzzy logic control (T1 FLC) are respectively compared with the IT2 FLC in control performance under different scenes. Finally, the simulation results show the effectiveness of IT2 FLC for the upper structure and F+FPIF control for the lower structure.      

基于跟踪误差调节的非线性自适应模糊预测控制

将模糊逻辑系统引入预测控制,对一类非线性离散系统提出了直接自适应模糊预测控制的方法,此方法首先建立被控对象的预测模型;然后基于此模型直接利用模糊逻辑系统设计预测控制器,并基于跟踪误差对控制器参数中的未知向量进行自适应调整;最后证明了此方法可使跟踪误差收敛到原点的一个小邻域内。     

基于TS模型的二型模糊控制器和观测器分析与设计

主要探讨一种新的系统方法——二型模糊系统在控制上的应用．文章先介绍了二型模糊集合和系统的基本概念和基本方法，然后集中推导TS模型下规则的输出形式，推广一型系统的特性，从而获得二型模糊控制器和观测器的表达式、稳定性以及其它特性分析方法，并以小车倒立摆仿真验证．最后文章从整体上分析和比较了传统系统、一型模糊系统和二型模糊系统的主要特点和不同点．     

Optimization of interval type-2 fuzzy logic controllers using evolutionary algorithms

A method for designing optimal interval type-2 fuzzy logic controllers using evolutionary algorithms is presented in this paper. Interval type-2 fuzzy controllers can outperform conventional type-1 fuzzy controllers when the problem has a high degree of uncertainty. However, designing interval type-2 fuzzy controllers is more difficult because there are more parameters involved. In this paper, interval type-2 fuzzy systems are approximated with the average of two type-1 fuzzy systems, which has been shown to give good results in control if the type-1 fuzzy systems can be obtained appropriately. An evolutionary algorithm is applied to find the optimal interval type-2 fuzzy system as mentioned above. The human evolutionary model is applied for optimizing the interval type-2 fuzzy controller for a particular non-linear plant and results are compared against an optimal type-1 fuzzy controller. A comparative study of simulation results of the type-2 and type-1 fuzzy controllers, under different noise levels, is also presented. Simulation results show that interval type-2 fuzzy controllers obtained with the evolutionary algorithm outperform type-1 fuzzy controllers.     

Control of a distillation column by type-2 and type-1 fuzzy logic PID controllers

The aim of this paper is to develop a type-1 and a type-2 fuzzy logic PID controller (type-1 FLC and type-2 FLC, respectively) for the control of a binary distillation column, the mathematical model of which is characterized by both high nonlinearities and parameter uncertainties. Attention was focused on the tuning procedure proposed by the authors and representing a development of the original Jantzen [1] method for type-1 and type-2 fuzzy controllers, in particular including input type-2 Gaussian membership functions. A theoretical explanation of the differences in fuzzy controller performance was in fact provided in the light of simulation results. The performance of a type-1 FLC was then compared in simulation with the one of type-2 FLC. All the simulation results confirmed the robustness and the effective control action of each fuzzy controller, with evident advantages for the type-2 FLC.     

Adaptive type-2 fuzzy sliding mode controller for SISO nonlinear systems subject to actuator faults

In this paper, an adaptive type-2 fuzzy sliding mode control to tolerate actuator faults of unknown nonlinear systems with external disturbances is presented. Based on a redundant actuation structure, a novel type-2 adaptive fuzzy fault tolerant control scheme is proposed using sliding mode control. Two adaptive type-2 fuzzy logic systems are used to approximate the unknown functions, whose adaptation laws are deduced from the stability analysis. The proposed approach allows to ensure good tracking performance despite the presence of actuator failures and external disturbances, as illustrated through a simulation example.     

基于模糊模型的非线性内模控制策略研究

针对一类非线性动态过程提出了基于模糊模型的非线性内模控制算法(NFIMC)。NFIMC控制器包括逆模糊模型控制器和滤波器。过程的模糊模型和逆模糊模型均可由模糊辨识获得。CSTR的仿真结果表明:该算法可以对强非线性过程实现有效控制,并且具有结构简单、计算效率高等优点,有利于在线应用。     

Hybrid learning for interval type-2 fuzzy logic systems based on orthogonal least-squares and back-propagation methods

This paper presents a novel learning methodology based on a hybrid algorithm for interval type-2 fuzzy logic systems. Since only the back-propagation method has been proposed in the literature for the tuning of both the antecedent and the consequent parameters of type-2 fuzzy logic systems, a hybrid learning algorithm has been developed. The hybrid method uses a recursive orthogonal least-squares method for tuning the consequent parameters and the back-propagation method for tuning the antecedent parameters. Systems were tested for three types of inputs: (a) interval singleton, (b) interval type-1 non-singleton, and (c) interval type-2 non-singleton. Experiments were carried out on the application of hybrid interval type-2 fuzzy logic systems for prediction of the scale breaker entry temperature in a real hot strip mill for three different types of coil. The results proved the feasibility of the systems developed here for scale breaker entry temperature prediction. Comparison with type-1 fuzzy logic systems shows that hybrid learning interval type-2 fuzzy logic systems provide improved performance under the conditions tested.     

未知多变量非线性系统自适应模糊预测控制

对一类未知多变量非线性系统提出了直接自适应模糊预测控制方法,此方法首先对被控对象提出了线性时变子模型加非线性子模型的预测模型,然后直接用模糊逻辑系统组成的向量来设计预测控制器,并基于时变死区函数对控制器中的未知向量和广义误差估计值中的未知矩阵进行自适应调整．文中证明了此方法可使广义误差向量估计值收敛到原点的一个邻域内．     

State feedback control of interval type-2 Takagi–Sugeno fuzzy systems via interval type-2 regional switching fuzzy controllers

The interval type-2 Takagi–Sugeno fuzzy systems have been proposed to handle nonlinear systems subject to parameter uncertainties. In this paper, a new type of state feedback controller, namely, interval type-2 regional switching fuzzy controller, is proposed to conceive less-conservative stabilisation conditions, which is switched by basing on the values of system states. To further reduce the conservativeness in the stability analysis, the information of lower and upper membership functions is also considered. Stability conditions for the interval type-2 fuzzy closed-loop systems are presented in the form of linear matrix inequalities (LMIs). Simulation examples are provided to illustrate the effectiveness of the proposed method.     

输出约束的有限时间自适应区间二型模糊输出反馈PMSM伺服控制

针对永磁同步电机驱动的伺服系统在不确定性摩擦和未知负载的影响下难以达到高精度的控制效果,提出一种基于区间二型模糊系统的带有输出约束的有限时间自适应输出反馈控制方案.首先,构建一个基于非线性扰动观测器的区间二型模糊状态观测器,分别完成对于未知扰动和速度的估计,区间二型模糊系统完成对于非线性摩擦的逼近;然后,在此基础上,结合滤波误差补偿机制和有限时间技术,引入障碍Lyapunov函数和反步控制技术设计输出约束的自适应区间二型模糊输出反馈控制器;最后,根据Lyapunov稳定性理论提出严格的稳定性分析,保证闭环系统的所有信号均是有限时间内有界的,并通过数值仿真和实验验证了所提出方法的有效性.     

基于量子粒子群的斜坡上两轮移动机器人的广义二型模糊控制

两轮移动机器人(2WMR)本身具有多变量和非线性等特征,从而使其控制变得复杂。当2WMR在倾斜的表面上移动时,控制问题变得更加复杂。针对2WMR的非线性模型,设计2WMR的广义二型模糊逻辑平衡控制器和位置控制器。针对广义二型模糊逻辑控制器(GT2FLC)中前、后件中参数难以设定的问题,通过量子粒子群算法(QPSO)优化隶属函数中的参数。针对GT2FLC和区间二型模糊逻辑控制器(IT2FLC)在不同斜面上对移动2WMR的平衡和位置控制的效果进行进一步的对比分析,并干扰对控制效果的影响。仿真结果表明,GT2FLC具有更好的抗干扰能力。     

Adaptive fuzzy model based inverse controller design using BB-BC optimization algorithm

The use of inverse system model as a controller might be an efficient way in controlling non-linear systems. It is also a known fact that fuzzy logic modeling is a powerful tool in representing nonlinear systems. Therefore, inverse fuzzy model can be used as a controller for controlling nonlinear plants. In this context, firstly, a new fuzzy model based inverse controller design methodology is presented in this study. The design methodology introduced here is based on a recursive optimization procedure that searches for an optimal inverse model control signal at every sampling time. Since the task of optimization should be accomplished in between two sampling periods the use of a fast optimization algorithm becomes essential. For this reason, Big Bang-Big Crunch (BB-BC) optimization algorithm is used due to its low computational time and high global convergence properties. Even though, inverse model controllers may produce perfect control while operating in an open loop fashion, this open loop control would not be sufficient in the case of modeling mismatches or disturbances that might occur over the system. In order to overcome this problem, secondly, an on-line adaptation mechanism via BB-BC optimization algorithm is introduced in addition to BB-BC optimization based fuzzy model inverse controller. The adaptation mechanism is used to update the related parameters of the model while minimizing the absolute value of the instantaneous error between the system and model outputs. In this manner, the system output is somehow fed back, the overall control form can be considered as a closed-loop system. The new fuzzy model based inverse control scheme with the new online adaptation mechanism has been implemented and tested on the two real time processes; namely, heat transfer and pH processes and very satisfactory results has been reported.