Search results for: probabilistic fuzzy neural network

Authors: Hataitep Wongsuwarn, Djitt Laowattana

Abstract:

This paper summaries basic principles and concepts of intelligent controls, implemented in humanoid robotics as well as recent algorithms being devised for advanced control of humanoid robots. Secondly, this paper presents a new approach neuro-fuzzy system. We have included some simulating results from our computational intelligence technique that will be applied to our humanoid robot. Subsequently, we determine a relationship between joint trajectories and located forces on robot-s foot through a proposed neuro-fuzzy technique.

Keywords: Biped Robot, Computational Intelligence, Static and Dynamic Walking, Gait Synthesis, Neuro-Fuzzy System.

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Authors: Shashank N. Mathur, Anil K. Ahlawat, Virendra P. Vishwakarma

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In this paper, a comparative study of application of supervised and unsupervised learning algorithms on illumination invariant face recognition has been carried out. The supervised learning has been carried out with the help of using a bi-layered artificial neural network having one input, two hidden and one output layer. The gradient descent with momentum and adaptive learning rate back propagation learning algorithm has been used to implement the supervised learning in a way that both the inputs and corresponding outputs are provided at the time of training the network, thus here is an inherent clustering and optimized learning of weights which provide us with efficient results.. The unsupervised learning has been implemented with the help of a modified Counterpropagation network. The Counterpropagation network involves the process of clustering followed by application of Outstar rule to obtain the recognized face. The face recognition system has been developed for recognizing faces which have varying illumination intensities, where the database images vary in lighting with respect to angle of illumination with horizontal and vertical planes. The supervised and unsupervised learning algorithms have been implemented and have been tested exhaustively, with and without application of histogram equalization to get efficient results.

Keywords: Artificial Neural Networks, back propagation, Counterpropagation networks, face recognition, learning algorithms.

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Authors: Igor Astrov, Natalya Berezovski

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This paper focuses on a critical component of the situational awareness (SA), the control of autonomous vertical flight for vectored thrust aerial vehicle (VTAV). With the SA strategy, we proposed a neural network motion control procedure to address the dynamics variation and performance requirement difference of flight trajectory for a VTAV. This control strategy with using of NARMAL2 neurocontroller for chosen model of VTAV has been verified by simulation of take-off and forward maneuvers using software package Simulink and demonstrated good performance for fast stabilization of motors, consequently, fast SA with economy in energy can be asserted during search-and-rescue operations.

Keywords: NARMA-L2 neurocontroller, situational awareness, vectored thrust aerial vehicle.

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Authors: Ahmad Aljaafreh

Abstract:

This paper proposes a hierarchical hidden Markov model (HHMM) to model the detection of M vehicles in a wireless sensor network (WSN). The HHMM model contains an extra level of hidden Markov model to model the temporal transitions of each state of the first HMM. By modeling the temporal transitions, only those hypothesis with nonzero transition probabilities needs to be tested. Thus, this method efficiently reduces the computation load, which is preferable in WSN applications.This paper integrates several techniques to optimize the detection performance. The output of the states of the first HMM is modeled as Gaussian Mixture Model (GMM), where the number of states and the number of Gaussians are experimentally determined, while the other parameters are estimated using Expectation Maximization (EM). HHMM is used to model the sequence of the local decisions which are based on multiple hypothesis testing with maximum likelihood approach. The states in the HHMM represent various combinations of vehicles of different types. Due to the statistical advantages of multisensor data fusion, we propose a heuristic based on fuzzy weighted majority voting to enhance cooperative classification of moving vehicles within a region that is monitored by a wireless sensor network. A fuzzy inference system weighs each local decision based on the signal to noise ratio of the acoustic signal for target detection and the signal to noise ratio of the radio signal for sensor communication. The spatial correlation among the observations of neighboring sensor nodes is efficiently utilized as well as the temporal correlation. Simulation results demonstrate the efficiency of this scheme.

Keywords: Classification, decision fusion, fuzzy logic, hidden Markov model

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Authors: Engin Yesil, Leon Urbas

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Modeling of complex dynamic systems, which are very complicated to establish mathematical models, requires new and modern methodologies that will exploit the existing expert knowledge, human experience and historical data. Fuzzy cognitive maps are very suitable, simple, and powerful tools for simulation and analysis of these kinds of dynamic systems. However, human experts are subjective and can handle only relatively simple fuzzy cognitive maps; therefore, there is a need of developing new approaches for an automated generation of fuzzy cognitive maps using historical data. In this study, a new learning algorithm, which is called Big Bang-Big Crunch, is proposed for the first time in literature for an automated generation of fuzzy cognitive maps from data. Two real-world examples; namely a process control system and radiation therapy process, and one synthetic model are used to emphasize the effectiveness and usefulness of the proposed methodology.

Keywords: Big Bang-Big Crunch optimization, Dynamic Systems, Fuzzy Cognitive Maps, Learning.

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Authors: M. Sedighizadeh, A. Rezazadeh

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In this paper a PID control strategy using neural network adaptive RASP1 wavelet for WECS-s control is proposed. It is based on single layer feedforward neural networks with hidden nodes of adaptive RASP1 wavelet functions controller and an infinite impulse response (IIR) recurrent structure. The IIR is combined by cascading to the network to provide double local structure resulting in improving speed of learning. This particular neuro PID controller assumes a certain model structure to approximately identify the system dynamics of the unknown plant (WECS-s) and generate the control signal. The results are applied to a typical turbine/generator pair, showing the feasibility of the proposed solution.

Keywords: Adaptive PID Control, RASP1 Wavelets, WindEnergy Conversion Systems.

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Authors: A. Salmanpour, Sh. Mohammad Nejad

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One of the methods for detecting the target position error in the laser tracking systems is using Four Quadrant (4Q) detectors. If the coordinates of the target center is yielded through the usual relations of the detector outputs, the results will be nonlinear, dependent on the shape, target size and its position on the detector screen. In this paper we have designed an algorithm with using neural network that coordinates of the target center in laser tracking systems is calculated by using detector outputs obtained from visual modeling. With this method, the results except from the part related to the detector intrinsic limitation, are linear and dependent from the shape and target size.

Keywords: four quadrant detector, laser tracking system, rangefinder, tracking sensor

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Authors: M. Zerikat, S. Chekroun

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This paper proposes an effective algorithm approach to hybrid control systems combining fuzzy logic and conventional control techniques of controlling the speed of induction motor assumed to operate in high-performance drives environment. The introducing of fuzzy logic in the control systems helps to achieve good dynamical response, disturbance rejection and low sensibility to parameter variations and external influences. Some fundamentals of the fuzzy logic control are preliminary illustrated. The developed control algorithm is robust, efficient and simple. It also assures precise trajectory tracking with the prescribed dynamics. Experimental results have shown excellent tracking performance of the proposed control system, and have convincingly demonstrated the validity and the usefulness of the hybrid fuzzy controller in high-performance drives with parameter and load uncertainties. Satisfactory performance was observed for most reference tracks.

Keywords: Fuzzy controller, high-performance, inductionmotor, intelligent control, robustness.

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Authors: Meredith Stevenson, John E. Porter

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Since the pioneering work of Zadeh, fuzzy set theory has been applied to a myriad of areas. Song and Chissom introduced the concept of fuzzy time series and applied some methods to the enrollments of the University of Alabama. In recent years, a number of techniques have been proposed for forecasting based on fuzzy set theory methods. These methods have either used enrollment numbers or differences of enrollments as the universe of discourse. We propose using the year to year percentage change as the universe of discourse. In this communication, the approach of Jilani, Burney, and Ardil is modified by using the year to year percentage change as the universe of discourse. We use enrollment figures for the University of Alabama to illustrate our proposed method. The proposed method results in better forecasting accuracy than existing models.

Keywords: Fuzzy forecasting, fuzzy time series, fuzzified enrollments, time-invariant model

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Authors: Shunzuo Wu, Xudong Luo, Yuanxiu Liao

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Recently, the rapid development of deep learning makes artificial intelligence (AI) penetrate into many fields, replacing manual work there. In particular, AI systems also become a research focus in the field of automatic office. To meet real needs in automatic officiating, in this paper we develop an automatic form filling system. Specifically, it uses two classical neural network models and several word embedding models to classify various relevant information elicited from the Internet. When training the neural network models, we use less noisy and balanced data for training. We conduct a series of experiments to test my systems and the results show that our system can achieve better classification results.

Keywords: Personal information, deep learning, auto fill, NLP, document analysis.

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Authors: Hong Choon Ong

Abstract:

Naïve Bayes classifiers are simple probabilistic classifiers. Classification extracts patterns by using data file with a set of labeled training examples and is currently one of the most significant areas in data mining. However, Naïve Bayes assumes the independence among the features. Structural learning among the features thus helps in the classification problem. In this study, the use of structural learning in Bayesian Network is proposed to be applied where there are relationships between the features when using the Naïve Bayes. The improvement in the classification using structural learning is shown if there exist relationship between the features or when they are not independent.

Keywords: Bayesian Network, Classification, Naïve Bayes, Structural Learning.

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Authors: Chien-Hua Wang, Meng-Ying Chou, Chin-Tzong Pang

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This paper applies fuzzy AHP to evaluate the service quality of online auction. Service quality is a composition of various criteria. Among them many intangible attributes are difficult to measure. This characteristic introduces the obstacles for respondents on reply in the survey. So as to overcome this problem, we invite fuzzy set theory into the measurement of performance and use AHP in obtaining criteria. We found the most concerned dimension of service quality is Transaction Safety Mechanism and the least is Charge Item. Other criteria such as information security, accuracy and information are too vital.

Keywords: Fuzzy set theory, AHP, Online auction, Service quality

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Authors: A. Majeed, P. Ali

Abstract:

Before designing an electrical system, the estimation of load is necessary for unit sizing and demand-generation balancing. The system could be a stand-alone system for a village or grid connected or integrated renewable energy to grid connection, especially as there are non–electrified villages in developing countries. In the classical model, the energy demand was found by estimating the household appliances multiplied with the amount of their rating and the duration of their operation, but in this paper, information exists for electrified villages could be used to predict the demand, as villages almost have the same life style. This paper describes a method used to predict the average energy consumed in each two months for every consumer living in a village by Artificial Neural Network (ANN). The input data are collected using a regional survey for samples of consumers representing typical types of different living, household appliances and energy consumption by a list of information, and the output data are collected from administration office of Piramagrun for each corresponding consumer. The result of this study shows that the average demand for different consumers from four villages in different months throughout the year is approximately 12 kWh/day, this model estimates the average demand/day for every consumer with a mean absolute percent error of 11.8%, and MathWorks software package MATLAB version 7.6.0 that contains and facilitate Neural Network Toolbox was used.

Keywords: Artificial neural network, load estimation, regional survey, rural electrification.

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Authors: Saeed Vaneshani, Hooshang Jazayeri-Rad

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Fuzzy logic control (FLC) systems have been tested in many technical and industrial applications as a useful modeling tool that can handle the uncertainties and nonlinearities of modern control systems. The main drawback of the FLC methodologies in the industrial environment is challenging for selecting the number of optimum tuning parameters. In this paper, a method has been proposed for finding the optimum membership functions of a fuzzy system using particle swarm optimization (PSO) algorithm. A synthetic algorithm combined from fuzzy logic control and PSO algorithm is used to design a controller for a continuous stirred tank reactor (CSTR) with the aim of achieving the accurate and acceptable desired results. To exhibit the effectiveness of proposed algorithm, it is used to optimize the Gaussian membership functions of the fuzzy model of a nonlinear CSTR system as a case study. It is clearly proved that the optimized membership functions (MFs) provided better performance than a fuzzy model for the same system, when the MFs were heuristically defined.

Keywords: continuous stirred tank reactor (CSTR), fuzzy logiccontrol (FLC), membership function(MF), particle swarmoptimization (PSO)

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Authors: Nadia M. G. AL-Sa'idi, Muhammad Rushdan Md. Sd., Adil M. Ahmed

Abstract:

The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.

Keywords: Fuzzy metric space, Fuzzy fractal space, Multi fuzzy fractal space.

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Authors: Rami El-Hajj Mohamad, Mahmoud Skafi, Ali Massoud Haidar

Abstract:

Several meteorological parameters were used for the  prediction of monthly average daily global solar radiation on  horizontal using recurrent neural networks (RNNs). Climatological  data and measures, mainly air temperature, humidity, sunshine  duration, and wind speed between 1995 and 2007 were used to design  and validate a feed forward and recurrent neural network based  prediction systems. In this paper we present our reference system  based on a feed-forward multilayer perceptron (MLP) as well as the  proposed approach based on an RNN model. The obtained results  were promising and comparable to those obtained by other existing  empirical and neural models. The experimental results showed the  advantage of RNNs over simple MLPs when we deal with time series  solar radiation predictions based on daily climatological data.

Keywords: Recurrent Neural Networks, Global Solar Radiation, Multi-layer perceptron, gradient, Root Mean Square Error.

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Authors: M. Boudjerda, B. Touaibia, M. K. Mihoubi

Abstract:

In Algeria agricultural irrigation is the primary water consuming sector followed by the domestic and industrial sectors. Economic development in the last decade has weighed heavily on water resources which are relatively limited and gradually decreasing to the detriment of agriculture. The research presented in this paper focuses on the optimization of irrigation water demand. Dynamic Programming-Neural Network (DPNN) method is applied to investigate reservoir optimization. The optimal operation rule is formulated to minimize the gap between water release and water irrigation demand. As a case study, Foum El-Gherza dam’s reservoir system in south of Algeria has been selected to examine our proposed optimization model. The application of DPNN method allowed increasing the satisfaction rate (SR) from 12.32% to 55%. In addition, the operation rule generated showed more reliable and resilience operation for the examined case study.

Keywords: ater management, agricultural demand, dam and reservoir operation, Foum el-Gherza dam, dynamic programming, artificial neural network.

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Authors: Liang-Hsuan Chen, Chia-Jung Chang

Abstract:

Fuzzy random variables have been introduced as an imprecise concept of numeric values for characterizing the imprecise knowledge. The descriptive parameters can be used to describe the primary features of a set of fuzzy random observations. In fuzzy environments, the expected values are usually represented as fuzzy-valued, interval-valued or numeric-valued descriptive parameters using various metrics. Instead of the concept of area metric that is usually adopted in the relevant studies, the numeric expected value is proposed by the concept of distance metric in this study based on two characters (fuzziness and randomness) of FRVs. Comparing with the existing measures, although the results show that the proposed numeric expected value is same with those using the different metric, if only triangular membership functions are used. However, the proposed approach has the advantages of intuitiveness and computational efficiency, when the membership functions are not triangular types. An example with three datasets is provided for verifying the proposed approach.

Keywords: Fuzzy random variables, Distance measure, Expected value.

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Authors: T. C. Kuo

Abstract:

In this paper, a novel adaptive fuzzy sliding mode control method is proposed for the robust tracking control of robotic manipulators. The proposed controller possesses the advantages of adaptive control, fuzzy control, and sliding mode control. First, system stability and robustness are guaranteed based on the sliding mode control. Further, fuzzy rules are developed incorporating with adaptation law to alleviate the input chattering effectively. Stability of the control system is proven by using the Lyapunov method. An application to a three-degree-of-freedom robotic manipulator is carried out. Accurate trajectory tracking as well as robustness is achieved. Input chattering is greatly eliminated.

Keywords: Fuzzy control, sliding mode control, roboticmanipulator, adaptive control.

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Authors: Miin-Shen Yang, Yee-Shan Pan

Abstract:

Although there have been many researches in cluster analysis to consider on feature weights, little effort is made on sample weights. Recently, Yu et al. (2011) considered a probability distribution over a data set to represent its sample weights and then proposed sample-weighted clustering algorithms. In this paper, we give a sample-weighted version of generalized fuzzy clustering regularization (GFCR), called the sample-weighted GFCR (SW-GFCR). Some experiments are considered. These experimental results and comparisons demonstrate that the proposed SW-GFCR is more effective than the most clustering algorithms.

Keywords: Clustering; fuzzy c-means, fuzzy clustering, sample weights, regularization.

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Authors: Ferenc Peter Pach, Janos Abonyi

Abstract:

This paper focuses on the data-driven generation of fuzzy IF...THEN rules. The resulted fuzzy rule base can be applied to build a classifier, a model used for prediction, or it can be applied to form a decision support system. Among the wide range of possible approaches, the decision tree and the association rule based algorithms are overviewed, and two new approaches are presented based on the a priori fuzzy clustering based partitioning of the continuous input variables. An application study is also presented, where the developed methods are tested on the well known Wisconsin Breast Cancer classification problem.

Keywords:

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Authors: S. Sendilkumar, B. L. Mathur, Joseph Henry

Abstract:

A new approach for protection of power transformer is presented using a time-frequency transform known as Wavelet transform. Different operating conditions such as inrush, Normal, load, External fault and internal fault current are sampled and processed to obtain wavelet coefficients. Different Operating conditions provide variation in wavelet coefficients. Features like energy and Standard deviation are calculated using Parsevals theorem. These features are used as inputs to PNN (Probabilistic neural network) for fault classification. The proposed algorithm provides more accurate results even in the presence of noise inputs and accurately identifies inrush and fault currents. Overall classification accuracy of the proposed method is found to be 96.45%. Simulation of the fault (with and without noise) was done using MATLAB AND SIMULINK software taking 2 cycles of data window (40 m sec) containing 800 samples. The algorithm was evaluated by using 10 % Gaussian white noise.

Keywords: Power Transformer, differential Protection, internalfault, inrush current, Wavelet Energy, Db9.

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Authors: M.Stella, M. Russo, D. Begušić

Abstract:

Ability of accurate and reliable location estimation in indoor environment is the key issue in developing great number of context aware applications and Location Based Services (LBS). Today, the most viable solution for localization is the Received Signal Strength (RSS) fingerprinting based approach using wireless local area network (WLAN). This paper presents two RSS fingerprinting based approaches – first we employ widely used WLAN based positioning as a reference system and then investigate the possibility of using GSM signals for positioning. To compare them, we developed a positioning system in real world environment, where realistic RSS measurements were collected. Multi-Layer Perceptron (MLP) neural network was used as the approximation function that maps RSS fingerprints and locations. Experimental results indicate advantage of WLAN based approach in the sense of lower localization error compared to GSM based approach, but GSM signal coverage by far outreaches WLAN coverage and for some LBS services requiring less precise accuracy our results indicate that GSM positioning can also be a viable solution.

Keywords: Indoor positioning, WLAN, GSM, RSS, location fingerprints, neural network.

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Authors: A. Greco, N. Mammone, F.C. Morabito, M.Versaci

Abstract:

This paper is mainly concerned with the application of a novel technique of data interpretation to the characterization and classification of measurements of plasma columns in Tokamak reactors for nuclear fusion applications. The proposed method exploits several concepts derived from soft computing theory. In particular, Artifical Neural Networks have been exploited to classify magnetic variables useful to determine shape and position of the plasma with a reduced computational complexity. The proposed technique is used to analyze simulated databases of plasma equilibria based on ITER geometry configuration. As well as demonstrating the successful recovery of scalar equilibrium parameters, we show that the technique can yield practical advantages compares with earlier methods.

Keywords: Tokamak, sensors, artificial neural network.

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Authors: Yeong-Hwa Chang, Chia-Wen Chang, Hung-Wei Lin, C.W. Tao

Abstract:

In this paper, an improved ant colony optimization (ACO) algorithm is proposed to enhance the performance of global optimum search. The strategy of the proposed algorithm has the capability of fuzzy pheromone updating, adaptive parameter tuning, and mechanism resetting. The proposed method is utilized to tune the parameters of the fuzzy controller for a real beam and ball system. Simulation and experimental results indicate that better performance can be achieved compared to the conventional ACO algorithms in the aspect of convergence speed and accuracy.

Keywords: Ant colony algorithm, Fuzzy control, ball and beamsystem

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Authors: A. Doaa M. Atia, Faten H. Fahmy, Ninet M. Ahmed, Hassen T. Dorrah

Abstract:

Temperature is one of the most principle factors affects aquaculture system. It can cause stress and mortality or superior environment for growth and reproduction. This paper presents the control of pond water temperature using artificial intelligence technique. The water temperature is very important parameter for shrimp growth. The required temperature for optimal growth is 34oC, if temperature increase up to 38oC it cause death of the shrimp, so it is important to control water temperature. Solar thermal water heating system is designed to supply an aquaculture pond with the required hot water in Mersa Matruh in Egypt. Neural networks are massively parallel processors that have the ability to learn patterns through a training experience. Because of this feature, they are often well suited for modeling complex and non-linear processes such as those commonly found in the heating system. Artificial neural network is proposed to control water temperature due to Artificial intelligence (AI) techniques are becoming useful as alternate approaches to conventional techniques. They have been used to solve complicated practical problems. Moreover this paper introduces a complete mathematical modeling and MATLAB SIMULINK model for the aquaculture system. The simulation results indicate that, the control unit success in keeping water temperature constant at the desired temperature by controlling the hot water flow rate.

Keywords: artificial neural networks, aquaculture, forced circulation hot water system,

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Authors: X. Z. Gao, S. J. Ovaska, X. Wang

Abstract:

Prediction of sinusoidal signals with time-varying frequencies has been an important research topic in power electronics systems. To solve this problem, we propose a new fuzzy predictive filtering scheme, which is based on a Finite Impulse Response (FIR) filter bank. Fuzzy logic is introduced here to provide appropriate interpolation of individual filter outputs. Therefore, instead of regular 'hard' switching, our method has the advantageous 'soft' switching among different filters. Simulation comparisons between the fuzzy predictive filtering and conventional filter bank-based approach are made to demonstrate that the new scheme can achieve an enhanced prediction performance for slowly changing sinusoidal input signals.

Keywords: Predictive filtering, fuzzy logic, sinusoidal signals, time-varying frequencies.

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Authors: Ali Mirmohammadi, Arash Taheri, Meysam Mohammadi-Amin

Abstract:

One of the major parts of a jet engine is air intake, which provides proper and required amount of air for the engine to operate. There are several aerodynamic parameters which should be considered in design, such as distortion, pressure recovery, etc. In this research, the effects of lip ice accretion on pitot intake performance are investigated. For ice accretion phenomenon, two supervised multilayer neural networks (ANN) are designed, one for ice shape prediction and another one for ice roughness estimation based on experimental data. The Fourier coefficients of transformed ice shape and parameters include velocity, liquid water content (LWC), median volumetric diameter (MVD), spray time and temperature are used in neural network training. Then, the subsonic intake flow field is simulated numerically using 2D Navier-Stokes equations and Finite Volume approach with Hybrid mesh includes structured and unstructured meshes. The results are obtained in different angles of attack and the variations of intake aerodynamic parameters due to icing phenomenon are discussed. The results show noticeable effects of ice accretion phenomenon on intake behavior.

Keywords: Artificial Neural Network, Ice Accretion, IntakeAerodynamics, Design Parameters, Finite Volume Method.

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Authors: J. Hossen, A. Rahman, K. Samsudin, F. Rokhani, S. Sayeed, R. Hasan

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The Neuro-Fuzzy hybridization scheme has become of research interest in pattern classification over the past decade. The present paper proposes a novel Modified Adaptive Fuzzy Inference Engine (MAFIE) for pattern classification. A modified Apriori algorithm technique is utilized to reduce a minimal set of decision rules based on input output data sets. A TSK type fuzzy inference system is constructed by the automatic generation of membership functions and rules by the fuzzy c-means clustering and Apriori algorithm technique, respectively. The generated adaptive fuzzy inference engine is adjusted by the least-squares fit and a conjugate gradient descent algorithm towards better performance with a minimal set of rules. The proposed MAFIE is able to reduce the number of rules which increases exponentially when more input variables are involved. The performance of the proposed MAFIE is compared with other existing applications of pattern classification schemes using Fisher-s Iris and Wisconsin breast cancer data sets and shown to be very competitive.

Keywords: Apriori algorithm, Fuzzy C-means, MAFIE, TSK

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Authors: S. Gherbi, F. Bouchareb

Abstract:

This paper deals with the novel intelligent bio-inspired control strategies, it presents a novel approach based on an optimal fuzzy immune PID parameters tuning, it is a combination of a PID controller, inspired by the human immune mechanism with fuzzy logic. Such controller offers more possibilities to deal with the delayed systems control difficulties due to the delay term. Indeed, we use an optimization approach to tune the four parameters of the controller in addition to the fuzzy function; the obtained controller is implemented in a modified Smith predictor structure, which is well known that it is the most efficient to the control of delayed systems. The application of the presented approach to control a three tank delay system shows good performances and proves the efficiency of the method.

Keywords: Delayed systems, Fuzzy Immune PID, Optimization, Smith predictor.

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