Design of fuzzy PID controllers using modified triangular membership functions

A design method for fuzzy proportional-integral-derivative (PID) controllers is investigated in this study. Based on conventional triangular membership functions used in fuzzy inference systems, the modified triangular membership functions are proposed to improve a system’s performance according to knowledge-based reasonings. The parameters of the considered controllers are tuned by means of genetic algorithms (GAs) using a fitness function associated with the system’s performance indices. The merits of the proposed controllers are illustrated by considering a model of the induction motor control system and a higher-order numerical model.     

Intelligent forecasting system based on integration of electromagnetism-like mechanism and fuzzy neural network

Fuzzy neural network (FNN) architectures, in which fuzzy logic and artificial neural networks are integrated, have been proposed by many researchers. In addition to developing the architecture for the FNN models, evolution of the learning algorithms for the connection weights is also a very important. Researchers have proposed gradient descent methods such as the back propagation algorithm and evolution methods such as genetic algorithms (GA) for training FNN connection weights. In this paper, we integrate a new meta-heuristic algorithm, the electromagnetism-like mechanism (EM), into the FNN training process. The EM algorithm utilizes an attraction–repulsion mechanism to move the sample points towards the optimum. However, due to the characteristics of the repulsion mechanism, the EM algorithm does not settle easily into the local optimum. We use EM to develop an EM-based FNN (the EM-initialized FNN) model with fuzzy connection weights. Further, the EM-initialized FNN model is used to train fuzzy if–then rules for learning expert knowledge. The results of comparisons done of the performance of our EM-initialized FNN model to conventional FNN models and GA-initialized FNN models proposed by other researchers indicate that the performance of our EM-initialized FNN model is better than that of the other FNN models. In addition, our use of a fuzzy ranking method to eliminate redundant fuzzy connection weights in our FNN architecture results in improved performance over other FNN models.     

一种基于NFCS形态的模糊神经网络的学习算法

神经网络与模糊逻辑协同系统（NFCS）是神经网络与模型系统深度融合的一种形态，传统的BP算法也可作为NFCS的学习算法，但收敛性能不佳，针对NFCS形态的模糊神经网络提出了BP算法的一种新的改进算法（NFCS－BP），即在误差传播时不仅改变网络的连接权值，同时也改变模糊逻辑神经元模型的补偿参数，首先介绍了NFCS的协同机制和典型结构，然后详细推导了改进算法的迭代公式，实践证明，与传统BP算法相比，该算法具有收敛性能好，函数逼近精度高的优点。     

基于模糊控制律的遗传神经匝道协调控制

讨论了快速路匝道系统中智能控制技术问题。针对匝道系统特点,分析了模糊控制、人工神经网络、遗传算法的适用性,提出了一种基于模糊控制律的遗传神经匝道协调控制方案。在该方案中,对模糊控制输入输出数据进行线性修正,使用修正后的数据完成遗传神经网络训练,并用神经网络代替模糊控制器对匝道系统进行控制。给出了神经网络结构和遗传算法流程,并结合宏观交通流模型进行系统仿真。仿真结果表明,与模糊控制相比,控制效果显著提高。     

Adaptive fuzzy identification and predictive control for industrial processes

This paper proposes a method for adaptive identification and control for industrial applications. The learning of a T–S fuzzy model is performed from input/output data to approximate unknown nonlinear processes by a hierarchical genetic algorithm (HGA). The HGA approach is composed by five hierarchical levels where the following parameters of the T–S fuzzy system are learned: input variables and their respective time delays, antecedent fuzzy sets, consequent parameters, and fuzzy rules. In order to reduce the computational cost and increase the algorithm’s performance an initialization method is applied on HGA. To deal with nonlinear plants and time-varying processes, the T–S fuzzy model is adapted online to maintain the quality of the identification/control. The identification methodology is proposed for two application problems: (1) the design of data-driven soft sensors, and (2) the learning of a model for the Generalized predictive control (GPC) algorithm. The integration of the proposed adaptive identification method with the GPC results in an effective adaptive predictive fuzzy control methodology. To validate and demonstrate the performance and effectiveness of the proposed methodologies, they are applied on identification of a model for the estimation of the flour concentration in the effluent of a real-world wastewater treatment system; and on control of a simulated continuous stirred tank reactor (CSTR) and on a real experimental setup composed of two coupled DC motors. The results are presented, showing that the developed evolving T–S fuzzy model can identify the nonlinear systems satisfactorily and it can be used successfully as a prediction model of the process for the GPC controller.     

Fuzzy financial profitability analyses of demand side management alternatives from participant perspective

This paper derives fuzzy profitability models for the financial evaluation of different demand side management (DSM) alternatives. The present value of cost (PVC) and equivalent uniform annual cost (EUAC) models are selected to determine the least-cost solution, while the net present value (NPV), pay back year (PBY) and benefit/cost ratio (BCR) models are proposed for the execution of cost–benefit analysis. Since fuzzy results are in the form of a complex non-linear representation, and do not always provide a totally ordered set in the same way that crisp numbers do, the current paper approximates the resulting fuzzy profitability indexes by a triangular fuzzy number initially, and then uses the Mellin transform to obtain the means and variances of the approximated fuzzy numbers in order to determine their relative ranking in a decision-making process. The performance of the proposed models is verified through the simulation of a numerical example and by considering their application to two practical DSM programs in Taiwan. In the first case study, the fuzzy least-cost solution is used to decide upon the installation of either a conventional air conditioning system or a cooling energy storage (CES) air conditioning system. In the second case study relating to cogeneration, a fuzzy cost–benefit analysis is applied to compare the relative profitabilities of an Extracted Condensing Steam Turbine Generator system and a Backpressure Steam Turbine Generator system. These investigations confirm not only that the results of the proposed fuzzy economic models are consistent with those of the conventional crisp models, but also demonstrate that the proposed methods represent readily implemented possibility analysis tools for use in the arena of uncertain financial decision-making.     

Improving the interpretability of TSK fuzzy models by combiningglobal learning and local learning

The fuzzy inference system proposed by Takagi, Sugeno, and Kang, known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is essentially a multimodel approach in which simple submodels (typically linear models) are combined to describe the global behavior of the system. Most existing learning algorithms for identifying the TSK model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model. Although these algorithms can generate a TSK model with good global performance (i.e., the model is capable of approximating the given system with arbitrary accuracy, provided that sufficient rules are used and sufficient training data are available), they cannot guarantee the resulting model to have a good local performance. Often, the submodels in the TSK model may exhibit an erratic local behavior, which is difficult to interpret. Since one of the important motivations of using the TSK model (also other fuzzy models) is to gain insights into the model, it is important to investigate the interpretability issue of the TSK model. We propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework. This algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics, but remains the component of global fitting in the existing learning algorithms. The algorithm is capable of adjusting its parameters based on the user's preference, generating models with good tradeoff in terms of global fitting and local interpretation. We illustrate the performance of the proposed algorithm using a motorcycle crash modeling example     

基于逆系统方法的内模控制在吊车消摆运动中的应用

针对非线性、欠驱动的桥式吊车水平运动系统，先运用非线性逆系统方法将其转化为伪线性系统，然后按照线性系统理论设计内模控制器来控制吊车的水平定位．同时设计了一个角度反馈控制器来确保摆角迅速衰减．最后和常规PID、模糊控制做了比较．实验结果表明，本方案能保证定位无静差、摆角迅速衰减，同时具有良好的抗干扰能力和较强的鲁棒性，控制效果优于PID和模糊控制．     

在线知识获得智能模糊控制器研究

对一些复杂的系统。传统PID或模糊控制很难得到满意控制效果,本文提出采用基于RBF神经网络和遗传算法的自适应模糊控制器来进行控制。由遗传算法在线优化模糊控制器的比例因子、模糊推理规则和隶属函数。并由RBF网络辨识被控对象的动态特性,以评价模糊控制器控制性能。仿真实验表明。优化后的Fuzzy控制器具有较强的学习和自适应控制能力,控制效果优于没有寻优的Fuzzy控制。     

Growing fuzzy topology adaptive resonance theory models with a push-pull learning algorithm

A new incrementally growing neural network model, called the growing fuzzy topology ART (GFTART) model, is proposed based on integrating the conventional fuzzy ART model with the incremental topology-preserving mechanism of the growing cell structure (GCS) model. This is in addition, to a new training algorithm, called the push-pull learning algorithm. The proposed GFTART model has two purposes: First, to reduce the proliferation of incrementally generated nodes in the F2 layer by the conventional fuzzy ART model based on replacing each F2 node with a GCS. Second, to enhance the class-dependent clustering representation ability of the GCS model by including the categorization property of the conventional fuzzy ART model. In addition, the proposed push-pull training algorithm enhances the cluster discriminating property and partially improves the forgetting problem of the training algorithm in the GCS model.     

Hybrid Fuzzy Modelling for Model Predictive Control

Model predictive control (MPC) has become an important area of research and is also an approach that has been successfully used in many industrial applications. In order to implement a MPC algorithm, a model of the process we are dealing with is needed. Due to the complex hybrid and nonlinear nature of many industrial processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed. A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between the proposed modern intelligent (fuzzy) approach and a classic (linear) approach was made. It was established that the MPC algorithm employing the proposed hybrid fuzzy model clearly outperforms the approach where a hybrid linear model is used, which justifies the usability of the hybrid fuzzy model. The hybrid fuzzy formulation introduces a powerful model that can faithfully represent hybrid and nonlinear dynamics of systems met in industrial practice, therefore, this approach demonstrates a significant advantage for MPC resulting in a better control performance.     

Hybrid identification of fuzzy rule‐based models

In this study, we propose a hybrid identification algorithm for a class of fuzzy rule‐based systems. The rule‐based fuzzy modeling concerns structure optimization and parameter identification using the fuzzy inference methods and hybrid structure combined with two methods of optimization theories for nonlinear systems. Two types of inference methods of a fuzzy model concern a simplified and linear type of inference. The proposed hybrid optimal identification algorithm is carried out using a combination of genetic algorithms and an improved complex method. The genetic algorithms determine initial parameters of the membership function of the premise part of the fuzzy rules. In the sequel, the improved complex method (being in essence a powerful auto‐tuning algorithm) leads to fine‐tuning of the parameters of the respective membership functions. An aggregate performance index with a weighting factor is proposed in order to achieve a balance between performance of the fuzzy model obtained for the training and testing data. Numerical examples are included to evaluate the performance of the proposed model. They are also contrasted with the performance of the fuzzy models existing in the literature. © 2002 John Wiley & Sons, Inc.     

一种基于PFLC的可演化模糊逻辑控制器设计与实现

常规的模糊控制器主要通过计算机软件或单片机实现,但模糊控制器是一个高度并行的系统,实时性、自适应性要求较高,这种实现方式不能满足现代模糊控制器的设计要求。要解决这个问题必须从算法和器件结构入手。本文提出以可编程模糊逻辑控制器芯片（PFLC）作为可演化的部件,利用遗传算法优化生成模糊规则的演化硬件结构。模糊规则的自适应性是通过引入可调整因子,根据环境的变化自寻优获得。以典型二阶系统模糊控制为例进行仿真实验,其结果表明了这个可演化的模糊逻辑控制器结构的可行性。     

A Highly Accurate Model-Free Motion Control System with a Mamdani Fuzzy Feedback Controller combined with a TSK Fuzzy Feed-forward Controller

In this paper, a new intelligent robot motion control architecture – a highly accurate model-free fuzzy motion control- is proposed in order to achieve improved robot motion accuracy and dynamic performance. Its architecture combines a Mamdani fuzzy proportional (P) and a conventional integral (I) plus derivative (D) controller for the feedback part of the system, and a Takagi-Sugeno-Kang fuzzy controller for the feed-forward, nonlinear part. The fuzzy P + ID controller improves the performance of the nonlinear system, and the TSK fuzzy controller uses a TSK fuzzy inference system based on extended subtractive- clustering method which integrates information on joint angular displacement, velocity and acceleration for torque identification. The advantage of this kind of model-free control is that it uses the information directly from the input/output of the nonlinear system, without any complex robot model computation, in order to decrease the control system’s sensitivity to any dynamical uncertainty. Furthermore, parametric search for clustering parameters in extended subtractive clustering secures the high accuracy of the system identification. Consequently, this proposed model-free fuzzy motion control benefits from the advantages of two kinds of fuzzy system. It not only incorporates flexible design, good performance and simple conception but also ensures precise motion control and great robustness. Comparisons with other intelligent models and results from numerical studies on a 4-bar planar parallel mechanism show the effectiveness and competitiveness of the proposed control.     

两种优化训练的FNN在船舶柴油机故障诊断中的性能研究

本文针对船舶柴油机故障诊断系统,基于遗传算法（genetic algorithm,GA）和蚁群优化算法（ant colony optimization algorithm,ACOA）构造了2种优化训练的模糊神经网络（fuzzy neural network,FNN）智能故障诊断模式,给出了该模糊神经网络智能故障诊断系统的结构及其参数选取方法,通过对船舶柴油机燃烧子系统的FNN模型结构权值和阈值优化训练的故障诊断仿真研究,对两种方式的性能进行对比研究,仿真测试结果表明,基于ACOA的诊断模型具有更好的故障诊断知识表达准确性和较快的收敛速度等特点,具有较好的应用前景。     

Comparative Study of Different Decoupling Schemes for TITO Binary Distillation Column via PI Controller

This paper presents a comparative study of different decoupling control schemes for a two-input, two-output (TITO) binary distillation column via proportional-integral (PI) controller. The key idea behind this paper is designing two novel fuzzy decoupling schemes that depend on human knowledge, instead of the system mathematical model used in conventional decoupling schemes. Based on conventional and inverted decoupling schemes, fuzzy and inverted fuzzy decoupling schemes are developed. The control effect is compared using simulation results for the proposed two schemes with conventional decoupling and inverted decoupling. The proposed fuzzy decoupling schemes are easy to realize and simple to design, besides they have a good decoupling capability. Two methods are used to prove asymptotic stability of each loop and the entire closed-loop system by applying the proposed fuzzy decoupling-based PI controller. The Wood and Berry model of a binary distillation column is used to illustrate the applicability of the proposed schemes.      

Integration of PSO and GA for optimum design of fuzzy PID controllers in a pendubot system

In this paper, a novel auto-tuning method is proposed to design fuzzy PID controllers for asymptotical stabilization of a pendubot system. In the proposed method, a fuzzy PID controller is expressed in terms of fuzzy rules, in which the input variables are the error signals and their derivatives, while the output variables are the PID gains. In this manner, the PID gains are adaptive and the fuzzy PID controller has more flexibility and capability than the conventional ones with fixed gains. To tune the fuzzy PID controller simultaneously, an evolutionary learning algorithm integrating particle swarm optimization (PSO) and genetic algorithm (GA) methods is proposed. The simulation results illustrate that the proposed method is indeed more efficient in improving the asymptotical stability of the pendubot system. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Design of a multilevel fuzzy controller for nonlinear systems and stability analysis

In this paper, a multilevel fuzzy control (MLFC) system is developed and implemented to deal with the real-world nonlinear plants with intrinsic uncertainties and time-varying parameters. The proposed fuzzy control strategy has a hierarchical structure with an adaptation mechanism embedded in the lower level to tune the output membership functions (MFs) of the first layer fuzzy controller and can be used to control a system with an input-output monotonic relationship or a piecewise monotonic relationship. The stability of the closed-loop system under the proposed MLFC is theoretically proven. Simulations are carried out by applying the proposed multilevel fuzzy control (MLFC) to a uncertain nonlinear plants, and it is shown that much better system performances are achieved compared with conventional fuzzy logic controllers (FLC), even in presence of disturbance and noise.     

A PSO based integrated functional link net and interval type-2 fuzzy logic system for predicting stock market indices

This paper presents an integrated functional link interval type-2 fuzzy neural system (FLIT2FNS) for predicting the stock market indices. The hybrid model uses a TSK (Takagi-Sugano-Kang) type fuzzy rule base that employs type-2 fuzzy sets in the antecedent parts and the outputs from the Functional Link Artificial Neural Network (FLANN) in the consequent parts. Two other approaches, namely the integrated FLANN and type-1 fuzzy logic system and Local Linear Wavelet Neural Network (LLWNN) are also presented for a comparative study. Backpropagation and particle swarm optimization (PSO) learning algorithms have been used independently to optimize the parameters of all the forecasting models. To test the model performance, three well known stock market indices like the Standard's & Poor's 500 (S&P 500), Bombay stock exchange (BSE), and Dow Jones industrial average (DJIA) are used. The mean absolute percentage error (MAPE) and root mean square error (RMSE) are used to find out the performance of all the three models. Finally, it is observed that out of three methods, FLIT2FNS performs the best irrespective of the time horizons spanning from 1 day to 1 month.     

矢量量化的遗传k-均值算法

提出了一种遗传k-均值算法，该算法通过改进标准遗传操作及采用可变变异率，使其在矢量量化应用中表现出很好的性能．实验证明，该算法能够获得质量高于k-均值和模糊k-均值算法的矢量量化码书，为设计全局最优码书提供了新思路。