Search results for: Adaptive fuzzy controller

Authors: A. El Ougli, I. Lagrat, I. Boumhidi

Abstract:

In this paper we propose a robust adaptive fuzzy controller for a class of nonlinear system with unknown dynamic. The method is based on type-2 fuzzy logic system to approximate unknown non-linear function. The design of the on-line adaptive scheme of the proposed controller is based on Lyapunov technique. Simulation results are given to illustrate the effectiveness of the proposed approach.

Keywords: Fuzzy set type-2, Adaptive fuzzy control, Nonlinear system.

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Authors: Leehter Yao, Chin-Chin Lin

Abstract:

An adaptive fuzzy PID controller with gain scheduling is proposed in this paper. The structure of the proposed gain scheduled fuzzy PID (GS_FPID) controller consists of both fuzzy PI-like controller and fuzzy PD-like controller. Both of fuzzy PI-like and PD-like controllers are weighted through adaptive gain scheduling, which are also determined by fuzzy logic inference. A modified genetic algorithm called accumulated genetic algorithm is designed to learn the parameters of fuzzy inference system. In order to learn the number of fuzzy rules required for the TSK model, the fuzzy rules are learned in an accumulated way. In other words, the parameters learned in the previous rules are accumulated and updated along with the parameters in the current rule. It will be shown that the proposed GS_FPID controllers learned by the accumulated GA perform well for not only the regular linear systems but also the higher order and time-delayed systems.

Keywords: Gain scheduling, fuzzy PID controller, adaptive control, genetic algorithm.

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Authors: Sudeept Mohan, Surekha Bhanot

Abstract:

The problem of manipulator control is a highly complex problem of controlling a system which is multi-input, multioutput, non-linear and time variant. In this paper some adaptive fuzzy, and a new hybrid fuzzy control algorithm have been comparatively evaluated through simulations, for manipulator control. The adaptive fuzzy controllers consist of self-organizing, self-tuning, and coarse/fine adaptive fuzzy schemes. These controllers are tested for different trajectories and for varying manipulator parameters through simulations. Various performance indices like the RMS error, steady state error and maximum error are used for comparison. It is observed that the self-organizing fuzzy controller gives the best performance. The proposed hybrid fuzzy plus integral error controller also performs remarkably well, given its simple structure.

Keywords: Hybrid fuzzy, Self-organizing, Self-tuning, Trajectory tracking.

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Authors: A. R. Tavakolpour-Saleh, H. Jokar

Abstract:

Liquid level control of conical tank system is known to be a great challenge in many industries such as food processing, hydrometallurgical industries and wastewater treatment plant due to its highly nonlinear characteristics. In this research, an adaptive fuzzy PID control scheme is applied to the problem of liquid level control in a nonlinear tank process. A conical tank process is first modeled and primarily simulated. A PID controller is then applied to the plant model as a suitable benchmark for comparison and the dynamic responses of the control system to different step inputs were investigated. It is found that the conventional PID controller is not able to fulfill the controller design criteria such as desired time constant due to highly nonlinear characteristics of the plant model. Consequently, a nonlinear control strategy based on gain-scheduling adaptive control incorporating a fuzzy logic observer is proposed to accurately control the nonlinear tank system. The simulation results clearly demonstrated the superiority of the proposed adaptive fuzzy control method over the conventional PID controller.

Keywords: Adaptive control, fuzzy logic, conical tank, PID controller.

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Authors: Yang Li, Xiaorong Guan, Cheng Xu

Abstract:

In order to design a suitable control scheme for human extremity exoskeleton, the interaction force control scheme with traditional PI controller was presented, and the simulation study of the electromechanical system of the human extremity exoskeleton was carried out by using a MATLAB/Simulink module. By analyzing the simulation calculation results, it was shown that the traditional PI controller is not very suitable for every movement speed of human body. So, at last the fuzzy self-adaptive PI controller was presented to solve this problem. Eventually, the superiority and feasibility of the fuzzy self-adaptive PI controller was proved by the simulation results and experimental results.

Keywords: Human extremity exoskeleton, interaction force control scheme, simulation study, fuzzy self-adaptive pi controller, man-machine coordinated walking, bear payload.

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Authors: Sathans, A. Swarup

Abstract:

This paper presents the development and application of an adaptive neuro fuzzy inference system (ANFIS) based intelligent hybrid neuro fuzzy controller for automatic generation control (AGC) of two-area interconnected thermal power system with reheat non linearity. The dynamic response of the system has been studied for 1% step load perturbation in area-1. The performance of the proposed neuro fuzzy controller is compared against conventional proportional-integral (PI) controller, state feedback linear quadratic regulator (LQR) controller and fuzzy gain scheduled proportionalintegral (FGSPI) controller. Comparative analysis demonstrates that the proposed intelligent neuro fuzzy controller is the most effective of all in improving the transients of frequency and tie-line power deviations against small step load disturbances. Simulations have been performed using Matlab®.

Keywords: Automatic generation control, ANFIS, LQR, Hybrid neuro fuzzy controller

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Authors: Dongsu Wu, Hongbin Gu, Peng Li

Abstract:

A novel adaptive fuzzy trajectory tracking algorithm of Stewart platform based motion platform is proposed to compensate path deviation and degradation of controller-s performance due to actuator torque limit. The algorithm can be divided into two parts: the real-time trajectory shaping part and the joint space adaptive fuzzy controller part. For a reference trajectory in task space whenever any of the actuators is saturated, the desired acceleration of the reference trajectory is modified on-line by using dynamic model of motion platform. Meanwhile an additional action with respect to the difference between the nominal and modified trajectories is utilized in the non-saturated region of actuators to reduce the path error. Using modified trajectory as input, the joint space controller incorporates compute torque controller, leg velocity observer and fuzzy disturbance observer with saturation compensation. It can ensure stability and tracking performance of controller in present of external disturbance and position only measurement. Simulation results verify the effectiveness of proposed control scheme.

Keywords: Actuator saturation, adaptive fuzzy control, Stewartplatform, trajectory shaping, flight simulator

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Authors: A. Ghaffari, A. Meghdari, D. Naderi, S. Eslami

Abstract:

In this paper an algorithm based on the adaptive neuro-fuzzy controller is provided to enhance the tipover stability of mobile manipulators when they are subjected to predefined trajectories for the end-effector and the vehicle. The controller creates proper configurations for the manipulator to prevent the robot from being overturned. The optimal configuration and thus the most favorable control are obtained through soft computing approaches including a combination of genetic algorithm, neural networks, and fuzzy logic. The proposed algorithm, in this paper, is that a look-up table is designed by employing the obtained values from the genetic algorithm in order to minimize the performance index and by using this data base, rule bases are designed for the ANFIS controller and will be exerted on the actuators to enhance the tipover stability of the mobile manipulator. A numerical example is presented to demonstrate the effectiveness of the proposed algorithm.

Keywords: Mobile Manipulator, Tipover Stability Enhancement, Adaptive Neuro-Fuzzy Inference Controller System, Soft Computing.

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Authors: S. Leghmizi, S. Liu, F. Naeim

Abstract:

This paper presents a fuzzy control system for a three degree of freedom (3-DOF) stabilized platform with explicit decoupling scheme. The system under consideration is a system with strong interactions between three channels. By using the concept of decentralized control, a control structure is developed that is composed of three control loops, each of which is associated with a single-variable fuzzy controller and a decoupling unit. Takagi-Sugeno (TS) fuzzy control algorithm is used to implement the fuzzy controller. The decoupling units design is based on the adaptive theory reasoning. Simulation tests were established using Simulink of Matlab. The obtained results have demonstrated the feasibility and effectiveness of the proposed approach. Simulation results are represented in this paper.

Keywords: 3-DOF platform of a ship carried antenna, the concept of decentralized control, Takagi-Sugeno (TS) fuzzy control algorithm, Simulink.

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Authors: Aqeel S. Jaber, Abu Zaharin Ahmad, Ahmed N. Abdalla

Abstract:

The artificial intelligent controller in power system plays as most important rule for many applications such as system operation and its control specially Load Frequency Controller (LFC). The main objective of LFC is to keep the frequency and tie-line power close to their decidable bounds in case of disturbance. In this paper, parallel fuzzy PI adaptive with conventional PD technique for Load Frequency Control system was proposed. PSO optimization method used to optimize both of scale fuzzy PI and tuning of PD. Two equal interconnected power system areas were used as a test system. Simulation results show the effectiveness of the proposed controller compared with different PID and classical fuzzy PI controllers in terms of speed response and damping frequency.

Keywords: Load frequency control, PSO, fuzzy control.

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Authors: Seungwoo Kim, Hyojune Chae, Yongrae Jung, Jongwook Kim

Abstract:

Recent medical studies have investigated the importance of enteral feeding and the use of feeding pumps for recovering patients unable to feed themselves or gain nourishment and nutrients by natural means. The most of enteral feeding system uses a peristaltic tube pump. A peristaltic pump is a form of positive displacement pump in which a flexible tube is progressively squeezed externally to allow the resulting enclosed pillow of fluid to progress along it. The squeezing of the tube requires a precise and robust controller of the geared motor to overcome parametric uncertainty of the pumping system which generates due to a wide variation of friction and slip between tube and roller. So, this paper proposes fuzzy adaptive controller for the robust control of the peristaltic tube pump. This new adaptive controller uses a fuzzy multi-layered architecture which has several independent fuzzy controllers in parallel, each with different robust stability area. Out of several independent fuzzy controllers, the most suited one is selected by a system identifier which observes variations in the controlled system parameter. This paper proposes a design procedure which can be carried out mathematically and systematically from the model of a controlled system. Finally, the good control performance, accurate dose rate and robust system stability, of the developed feeding pump is confirmed through experimental and clinic testing.

Keywords: Enteral Feeding Pump, Peristaltic Tube Pump, Fuzzy Adaptive Control, Fuzzy Multi-layered Controller, Look-up Table..

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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: P.-W. Tsai, C.-Y. Chen, C.-W. Chen

Abstract:

In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

Keywords: Adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm.

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Authors: R. Ghasemi, M. R. Rahimi Khoygani

Abstract:

This paper proposes the designing direct adaptive neural controller to apply for a class of a nonlinear pendulum dynamic system. The radial basis function (RBF) neural adaptive controller is robust in presence of external and internal uncertainties. Both the effectiveness of the controller and robustness against disturbances are importance of this paper. The simulation results show the promising performance of the proposed controller.

Keywords: Adaptive Neural Controller, Nonlinear Dynamical, Neural Network, RBF, Driven Pendulum, Position Control.

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Authors: Jinsiang Shaw, Ray Pan, Yin-Chieh Chang

Abstract:

In this paper, an magnetorheological (MR) mount with fuzzy sliding mode controller (FSMC) is studied for vibration suppression when the system is subject to base excitations. In recent years, magnetorheological fluids are becoming a popular material in the field of the semi-active control. However, the dynamic equation of an MR mount is highly nonlinear and it is difficult to identify. FSMC provides a simple method to achieve vibration attenuation of the nonlinear system with uncertain disturbances. This method is capable of handling the chattering problem of sliding mode control effectively and the fuzzy control rules are obtained by using the Lyapunov stability theory. The numerical simulations using one-dimension and two-dimension FSMC show effectiveness of the proposed controller for vibration suppression. Further, the well-known skyhook control scheme and an adaptive sliding mode controller are also included in the simulation for comparison with the proposed FSMC.

Keywords: adaptive sliding mode controller, fuzzy sliding modecontroller, magnetorheological mount, skyhook control.

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Authors: S.R. Khuntia, K.B. Mohanty, S. Panda, C. Ardil

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This paper presents a comparative study of various controllers for the speed control of DC motor. The most commonly used controller for the speed control of dc motor is Proportional- Integral (P-I) controller. However, the P-I controller has some disadvantages such as: the high starting overshoot, sensitivity to controller gains and sluggish response due to sudden disturbance. So, the relatively new Integral-Proportional (I-P) controller is proposed to overcome the disadvantages of the P-I controller. Further, two Fuzzy logic based controllers namely; Fuzzy control and Neuro-fuzzy control are proposed and the performance these controllers are compared with both P-I and I-P controllers. Simulation results are presented and analyzed for all the controllers. It is observed that fuzzy logic based controllers give better responses than the traditional P-I as well as I-P controller for the speed control of dc motor drives.

Keywords: Proportional-Integral (P-I) controller, Integral- Proportional (I-P) controller, Fuzzy logic control, Neuro-fuzzy control, Speed control, DC Motor drive.

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Authors: S. Yaman, S. Rostami

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In this study, a black box modeling of the coupled-tank system is obtained by using fuzzy sets. The derived model is tested via adaptive neuro fuzzy inference system (ANFIS). In order to achieve a better control performance, the parameters of three different controller types, classical proportional integral controller (PID), fuzzy PID and function tuner method, are tuned by one of the evolutionary computation method, genetic algorithm. All tuned controllers are applied to the fuzzy model of the coupled-tank experimental setup and analyzed under the different reference input values. According to the results, it is seen that function tuner method demonstrates better robust control performance and guarantees the closed loop stability.

Keywords: Function tuner method, fuzzy modeling, fuzzy PID controller, genetic algorithm.

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Authors: Shiuh-Jer Huang, Ming-Tien Su

Abstract:

Since the driving speed and control accuracy of commercial optical disk are increasing significantly, it needs an efficient controller to monitor the track seeking and following operations of the servo system for achieving the desired data extracting response. The nonlinear behaviors of the actuator and servo system of the optical disk drive will influence the laser spot positioning. Here, the model-free fuzzy control scheme is employed to design the track seeking servo controller for a d.c. motor driving optical disk drive system. In addition, the sliding model control strategy is introduced into the fuzzy control structure to construct a 1-D adaptive fuzzy rule intelligent controller for simplifying the implementation problem and improving the control performance. The experimental results show that the steady state error of the track seeking by using this fuzzy controller can maintain within the track width (1.6 μm ). It can be used in the track seeking and track following servo control operations.

Keywords: Fuzzy control, gain tuning and optical disk drive.

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Authors: Mazin Z. Othman

Abstract:

This paper presents the idea of a rough controller with application to control the overhead traveling crane system. The structure of such a controller is based on a suggested concept of a fuzzy logic controller. A measure of fuzziness in rough sets is introduced. A comparison between fuzzy logic controller and rough controller has been demonstrated. The results of a simulation comparing the performance of both controllers are shown. From these results we infer that the performance of the proposed rough controller is satisfactory.

Keywords: Accuracy measure, Fuzzy Logic Controller (FLC), Overhead Traveling Crane (OTC), Rough Set Theory (RST), Roughness measure

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Authors: Chidentree Treesatayapun

Abstract:

A direct adaptive controller for a class of unknown nonlinear discrete-time systems is presented in this article. The proposed controller is constructed by fuzzy rules emulated network (FREN). With its simple structure, the human knowledge about the plant is transferred to be if-then rules for setting the network. These adjustable parameters inside FREN are tuned by the learning mechanism with time varying step size or learning rate. The variation of learning rate is introduced by main theorem to improve the system performance and stabilization. Furthermore, the boundary of adjustable parameters is guaranteed through the on-line learning and membership functions properties. The validation of the theoretical findings is represented by some illustrated examples.

Keywords: Neuro-Fuzzy, learning algorithm, nonlinear discrete time.

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Authors: Abduladheem A. Ali, Easa A. Abd

Abstract:

The robot is a repeated task plant. The control of such a plant under parameter variations and load disturbances is one of the important problems. The aim of this work is to design Geno-Fuzzy controller suitable for online applications to control single link rigid robot arm plant. The genetic-fuzzy online controller (indirect controller) has two genetic-fuzzy blocks, the first as controller, the second as identifier. The identification method is based on inverse identification technique. The proposed controller it tested in normal and load disturbance conditions.

Keywords: Fuzzy network, genetic algorithm, robot control, online genetic control, parameter identification.

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Authors: H. Mansor, S. B. Mohd-Noor, T. S. Gunawan, S. Khan, N. I. Othman, N. Tazali, R. B. Islam

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This paper provides a comparative study on the performances of standard PID and adaptive PID controllers tested on travel angle of a 3-Degree-of-Freedom (3-DOF) Quanser bench-top helicopter. Quanser, a well-known manufacturer of educational bench-top helicopter has developed Proportional Integration Derivative (PID) controller with Linear Quadratic Regulator (LQR) for all travel, pitch and yaw angle of the bench-top helicopter. The performance of the PID controller is relatively good; however, its performance could also be improved if the controller is combined with adaptive element. The objective of this research is to design adaptive PID controller and then compare the performances of the adaptive PID with the standard PID. The controller design and test is focused on travel angle control only. Adaptive method used in this project is self-tuning controller, which controller’s parameters are updated online. Two adaptive algorithms those are pole-placement and deadbeat have been chosen as the method to achieve optimal controller’s parameters. Performance comparisons have shown that the adaptive (deadbeat) PID controller has produced more desirable performance compared to standard PID and adaptive (poleplacement). The adaptive (deadbeat) PID controller attained very fast settling time (5 seconds) and very small percentage of overshoot (5% to 7.5%) for 10° to 30° step change of travel angle.

Keywords: Adaptive control, bench-top helicopter, deadbeat, pole-placement, self-tuning control.

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Authors: Ahmed Abbas, M.R. M Rizk, Mohamed El-Sayed

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This paper presents a new adaptive DMC controller that improves the controller performance in case of plant-model mismatch. The new controller monitors the plant measured output, compares it with the model output and calculates weights applied to the controller move. Simulations show that the new controller can help improve control performance and avoid instability in case of severe model mismatches.

Keywords: Adaptive control, dynamic matrix control, DMC, model predictive control

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Authors: Allouche Moez, Souissi Mansour, Chaabane Mohamed, Mehdi Driss

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This paper deals with the synthesis of fuzzy state feedback controller of induction motor with optimal performance. First, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate a non linear system in the synchronous d-q frame rotating with electromagnetic field-oriented. Next, a fuzzy controller is designed to stabilise the induction motor and guaranteed a minimum disturbance attenuation level for the closed-loop system. The gains of fuzzy control are obtained by solving a set of Linear Matrix Inequality (LMI). Finally, simulation results are given to demonstrate the controller-s effectiveness.

Keywords: Rejection disturbance, fuzzy modelling, open-loop control, Fuzzy feedback controller, fuzzy observer, Linear Matrix Inequality (LMI)

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Authors: Om Prakash Verma, Rajesh Singla, Rajesh Kumar

Abstract:

Conventional controller’s usually required a prior knowledge of mathematical modelling of the process. The inaccuracy of mathematical modelling degrades the performance of the process, especially for non-linear and complex control problem. The process used is Water-Bath system, which is most widely used and nonlinear to some extent. For Water-Bath system, it is necessary to attain desired temperature within a specified period of time to avoid the overshoot and absolute error, with better temperature tracking capability, else the process is disturbed.

To overcome above difficulties intelligent controllers, Fuzzy Logic (FL) and Adaptive Neuro-Fuzzy Inference System (ANFIS), are proposed in this paper. The Fuzzy controller is designed to work with knowledge in the form of linguistic control rules. But the translation of these linguistic rules into the framework of fuzzy set theory depends on the choice of certain parameters, for which no formal method is known. To design ANFIS, Fuzzy-Inference-System is combined with learning capability of Neural-Network.

It is analyzed that ANFIS is best suitable for adaptive temperature control of above system. As compared to PID and FLC, ANFIS produces a stable control signal. It has much better temperature tracking capability with almost zero overshoot and minimum absolute error.

Keywords: PID Controller, FLC, ANFIS, Non-Linear Control System, Water-Bath System, MATLAB-7.

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

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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: Surya Prakash, Sunil Kumar Sinha

Abstract:

This paper deals with the application of artificial neural network (ANN) and fuzzy based Adaptive Neuro Fuzzy Inference System(ANFIS) approach to Load Frequency Control (LFC) of multi unequal area hydro-thermal interconnected power system. The proposed ANFIS controller combines the advantages of fuzzy controller as well as quick response and adaptability nature of ANN. Area-1 and area-2 consists of thermal reheat power plant whereas area-3 and area-4 consists of hydro power plant with electric governor. Performance evaluation is carried out by using intelligent controller like ANFIS, ANN and Fuzzy controllers and conventional PI and PID control approaches. To enhance the performance of intelligent and conventional controller sliding surface is included. The performances of the controllers are simulated using MATLAB/SIMULINK package. A comparison of ANFIS, ANN, Fuzzy, PI and PID based approaches shows the superiority of proposed ANFIS over ANN & fuzzy, PI and PID controller for 1% step load variation.

Keywords: Load Frequency Control (LFC), ANFIS, ANN & Fuzzy, PI, PID Controllers, Area Control Error (ACE), Tie-line, MATLAB / SIMULINK.

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Authors: Mujde Turkkan, Nurkan Yagiz

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In this study an active controller is presented for vibration suppression of a full-bus model. The bus is modeled having seven degrees of freedom. Using the achieved model via Lagrange Equations the system equations of motion are derived. The suspensions of the bus model include air springs with two auxiliary chambers are used. Fuzzy logic controller is used to improve the ride comfort. The numerical results, verifies that the presented fuzzy logic controller improves the ride comfort.

Keywords: Ride comfort, air spring, bus, fuzzy logic controller.

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Authors: Mohamed Amine Haraoubia, Abdelaziz Hamzaoui, Najib Essounbouli

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The pursuit of the MPPT has led to the development of many kinds of controllers, one of which is the Fuzzy Logic controller, which has proven its worth. To further tune this controller this paper will discuss and analyze the use of Genetic Algorithms to tune the Fuzzy Logic Controller. It will provide an introduction to both systems, and test their compatibility and performance.

Keywords: Fuzzy logic controller (FLC), fuzzy logic (FL), genetic algorithm (GA), maximum power point (MPP), maximum power point tracking (MPPT).

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Authors: Ali Ghaffari, A. Hosein Shamekhi, Akbar Saki, Ehsan Kamrani

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In order to meet the limits imposed on automotive emissions, engine control systems are required to constrain air/fuel ratio (AFR) in a narrow band around the stoichiometric value, due to the strong decay of catalyst efficiency in case of rich or lean mixture. This paper presents a model of a sample spark ignition engine and demonstrates Simulink-s capabilities to model an internal combustion engine from the throttle to the crankshaft output. We used welldefined physical principles supplemented, where appropriate, with empirical relationships that describe the system-s dynamic behavior without introducing unnecessary complexity. We also presents a PID tuning method that uses an adaptive fuzzy system to model the relationship between the controller gains and the target output response, with the response specification set by desired percent overshoot and settling time. The adaptive fuzzy based input-output model is then used to tune on-line the PID gains for different response specifications. Experimental results demonstrate that better performance can be achieved with adaptive fuzzy tuning relative to similar alternative control strategies. The actual response specifications with adaptive fuzzy matched the desired response specifications.

Keywords: Modelling, Air–fuel ratio control, SI engine, Adaptive fuzzy Control.

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