scholarly journals Improved T-S Fuzzy Control for Uncertain Time-Delay Coronary Artery System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Zhenyu Zhu ◽  
Zhanshan Zhao ◽  
Haoliang Cui ◽  
Fengdong Shi
Keyword(s):  
Coronary Artery ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Practical Significance ◽  
Linear Matrix ◽  
System State ◽  
Fuzzy Models ◽  
The Stability ◽  
Uncertain Time ◽  
Takagi Sugeno

This paper is based on the Takagi-Sugeno (T-S) fuzzy models to construct a coronary artery system (CAS) T-S fuzzy controller and considers the uncertainties of system state parameters in CAS. We propose the fuzzy model of CAS with uncertainties. By using T-S fuzzy model of CAS and the use of parallel distributed compensation (PDC) concept, the same fuzzy set is assigned to T-S fuzzy controller. Based on this, a PDC controller whose fuzzy rules correspond to the fuzzy model is designed. By constructing a suitable Lyapunov-Krasovskii function (LKF), the stability conditions of the linear matrix inequality (LMI) are exported. Simulation results show that the method proposed in this paper is correct and effective and has certain practical significance.

scholarly journals Actuator Saturated Fuzzy Controller Design for Interval Type-2 Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 823
Author(s):  
Wen-Jer Chang ◽  
Yu-Wei Lin ◽  
Yann-Horng Lin ◽  
Chin-Lin Pen ◽  
Ming-Hsuan Tsai
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Fuzzy Model ◽  
The Stability ◽  
Interval Type ◽  
Takagi Sugeno

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

scholarly journals Further results on robust fuzzy dynamic systems with LMI D-stability constraints

2014 ◽  
Vol 24 (4) ◽  
pp. 785-794 ◽  
Author(s):  
Wudhichai Assawinchaichote
Keyword(s):  
Dynamic Systems ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Local System ◽  
Linear Matrix ◽  
Fuzzy Modelling ◽  
Ts Fuzzy Model ◽  
Input Noise ◽  
Takagi Sugeno

Abstract This paper examines the problem of designing a robust H∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H∞ fuzzy controller that guarantees (i) the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

DELAYED FUZZY CONTROLLER DESIGN FOR HYPERCHAOS WITH APPLICATION TO HYPERCHAOTIC CHEN'S SYSTEM

2007 ◽  
Vol 18 (07) ◽  
pp. 1095-1105 ◽  
Author(s):  
XINGWEN LIU ◽  
XIN GAO
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed State Feedback ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Compensation Design ◽  
Hyperchaotic Systems ◽  
Control Criterion

Studied in this paper is the control problem of hyperchaotic systems. By combining Takagi–Sugeno (T–S) fuzzy model with parallel distributed compensation design technique, we propose a delay-dependent control criterion via pure delayed state feedback. Because the result is expressed in terms of linear matrix inequalities (LMIs), it is quite convenient to check in practice. Based on this criterion, a procedure is provided for designing fuzzy controller for such systems. This method is a universal one for controlling continuous hyperchaotic systems. As illustrated by its application to hyperchaotic Chen's system, the controller design is quite effective.

Takagi-Sugeno Fuzzy Load-Following Control of Nuclear Reactors Based on Reactor Point Kinetics Equations

2014 ◽  
Author(s):  
Xiuchun Luan ◽  
Jie Zhou ◽  
Yu Zhai
Keyword(s):  
Control System ◽  
Linear Models ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Neutron Density ◽  
Load Following ◽  
Wide Range ◽  
Takagi Sugeno ◽  
Operating Points

A state differential feedback control system based Takagi-Sugeno (T-S) fuzzy model is designed for load-following operation of nonlinear nuclear reactor whose operating points vary within a wide range. Linear models are first derived from the original nonlinear model on several operating points. Next the fuzzy controller is designed via using the parallel distributed compensation (PDC) scheme with the relative neutron density at the equilibrium point as the premise variable. Last the stability analysis is given by means of linear matrix inequality (LMI) approach, thus the control system is guaranteed to be stable within a large range. The simulation results demonstrate that the control system works well over a wide region of operation.

STABILITY ANALYSIS OF NONLINEAR INTERCONNECTED SYSTEMS VIA T–S FUZZY MODELS

2004 ◽  
Vol 04 (01) ◽  
pp. 41-55 ◽  
Author(s):  
WEI-LING CHIANG ◽  
CHENG-WU CHEN ◽  
FENG-HSIAG HSIAO
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Fuzzy Models ◽  
Fuzzy Techniques ◽  
The Stability ◽  
Takagi Sugeno

This paper is concerned with the stability problem of nonlinear interconnected systems. Each of them consists of a few interconnected subsystems which are approximated by Takagi–Sugeno (T–S) type fuzzy models. In terms of Lyapunov's direct method, a stability criterion is derived to guarantee the asymptotic stability of interconnected systems. It is shown that the stability analysis problems of nonlinear interconnected systems can be reduced to linear matrix inequality (LMI) problems via suitable Lyapunov functions and T–S fuzzy techniques. Finally, numerical examples with simulations are given to demonstrate the validity of the proposed approach.

SYNCHRONIZATION OF TIME-DELAYED T–S FUZZY CHAOTIC SYSTEMS VIA SCALAR OUTPUT VARIABLE

2005 ◽  
Vol 15 (08) ◽  
pp. 2593-2601 ◽  
Author(s):  
JAE-HUN KIM ◽  
HYUNSEOK SHIN ◽  
EUNTAI KIM ◽  
MIGNON PARK
Keyword(s):  
Time Delay ◽  
Fuzzy Model ◽  
Order System ◽  
Linear Matrix ◽  
Output Variable ◽  
First Order ◽  
Scalar Output ◽  
The Stability ◽  
Takagi Sugeno ◽  
System With Time Delay

It has been known that very complex chaotic behaviors can be observed in a simple first-order system with time-delay. This paper presents a fuzzy model-based approach for synchronization of time-delayed chaotic system via a scalar output variable. Takagi–Sugeno (T–S) fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive and response system with time-delay. Since only a scalar output variable is available for synchronization, a fuzzy observer based on T–S fuzzy model is designed and applied to chaotic synchronization. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov–Krasovskii theory and derive stability conditions by solving linear matrix inequalities (LMI's) problem. A numerical example is given to demonstrate the validity of the proposed synchronization approach.

scholarly journals Stable Fault Tolerant Controller Design for Takagi–Sugeno Fuzzy Model-Based Control Systems via Linear Matrix Inequalities: Three Conical Tank Case Study

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2221 ◽  
Author(s):  
Himanshukumar R. Patel ◽  
Vipul A. Shah
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Control Systems ◽  
Linear Models ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Models ◽  
Takagi Sugeno

This paper deals with a methodical design approach of fault-tolerant controller that gives assurance for the the stabilization and acceptable control performance of the nonlinear systems which can be described by Takagi–Sugeno (T–S) fuzzy models. Takagi–Sugeno fuzzy model gives a unique edge that allows us to apply the traditional linear system theory for the investigation and blend of nonlinear systems by linear models in a different state space region. The overall fuzzy model of the nonlinear system is obtained by fuzzy combination of the all linear models. After that, based on this linear model, we employ parallel distributed compensation for designing linear controllers for each linear model. Also this paper reports of the T–S fuzzy system with less conservative stabilization condition which gives decent performance. However, the controller synthesis for nonlinear systems described by the T–S fuzzy model is a complicated task, which can be reduced to convex problems linking with linear matrix inequalities (LMIs). Further sufficient conservative stabilization conditions are represented by a set of LMIs for the Takagi–Sugeno fuzzy control systems, which can be solved by using MATLAB software. Two-rule T–S fuzzy model is used to describe the nonlinear system and this system demonstrated with proposed fault-tolerant control scheme. The proposed fault-tolerant controller implemented and validated on three interconnected conical tank system with two constraints in terms of faults, one issed to build the actuator and sond is system component (leak) respectively. The MATLAB Simulink platform with linear fuzzy models and an LMI Toolbox was used to solve the LMIs and determine the controller gains subject to the proposed design approach.

Fuzzy Passivity Non-Fragile Control of Flexible Joint Robot

2013 ◽  
Vol 448-453 ◽  
pp. 3571-3575
Author(s):  
Bin Zhang
Keyword(s):  
Robot Control ◽  
Simulation Experiment ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Flexible Joint ◽  
Control Approach ◽  
Compensation Principle ◽  
The Stability

The paper proposes a fuzzy passivity non-fragile control approach for flexible joint robot. The T-S fuzzy model is applied to approximate the flexible joint robot at first, and then the fuzzy controller is developed based on parallel distributed compensation principle. The passivity non-fragile performance of controller is also employed to limit the influence of model error. The conditions for the stability of the flexible joint robot control system are proposed by using Lyapunov function, and linear matrix inequality is applied to resolve the controller parameter. The simulation experiment results show the effectiveness of the proposed method.

scholarly journals T-S Fuzzy Model Based Control Strategy for the Networked Suspension Control System of Maglev Train

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Guang He ◽  
Jie Li ◽  
Peng Cui ◽  
Yun Li
Keyword(s):  
Control System ◽  
Control Strategy ◽  
State Feedback ◽  
Fuzzy Model ◽  
Maglev Train ◽  
Fuzzy Models ◽  
Physical Experiments ◽  
Suspension Control ◽  
The Stability ◽  
Takagi Sugeno

The control problem for the networked suspension control system of maglev train with random induced time delay and packet dropouts is investigated. First, Takagi-Sugeno (T-S) fuzzy models are utilized to represent the discrete-time nonlinear networked suspension control system, and the parameters uncertainties of the nonlinear model have also been taken into account. The controllers take the form of parallel distributed compensation. Then, a sufficient condition for the stability of the networked suspension control system is derived. Based on the criteria, the state feedback fuzzy controllers are obtained, and the controller gains can be computed by using MATLAB LMI Toolbox directly. Finally, both the numerical simulations and physical experiments on the full-scale single bogie of CMS-04 maglev train have been accomplished to demonstrate the effectiveness of this proposed method.

Reliable Robust H∞ Fuzzy Control for Uncertain Nonlinear Systems With Markovian Jumping Actuator Faults

2006 ◽  
Vol 129 (3) ◽  
pp. 252-261 ◽  
Author(s):  
Huai-Ning Wu
Keyword(s):  
Fuzzy Control ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Actuator Faults ◽  
Markovian Jumping ◽  
Stochastically Stable ◽  
The Stability ◽  
Time Systems

This paper is concerned with the design of reliable robust H∞ fuzzy control for uncertain nonlinear continuous-time systems with Markovian jumping actuator faults. The Takagi and Sugeno fuzzy model is employed to represent an uncertain nonlinear system with Markovian jumping actuator faults. First, based on the parallel distributed compensation (PDC) scheme, a sufficient condition such that the closed-loop fuzzy system is robustly stochastically stable and satisfies a prescribed level of H∞-disturbance attenuation is derived. In the derivation process, a stochastic Lyapunov function is used to test the stability and H∞ performance of the system. Then, a new improved linear matrix inequality (LMI) formulation is applied to this condition to alleviate the interrelation between the stochastic Lyapunov matrix and system matrices containing controller variables, which results in a tractable LMI-based condition for the existence of reliable and robust H∞ fuzzy controllers. A suboptimal fuzzy controller is proposed to minimize the level of disturbance attenuation subject to the LMI constraints. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

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