Takagi Sugeno Fuzzy Models for Wind Turbine Driving a DFI-Generator via Linear Matrix Inequalities

The paper proposes a new design method based on linear matrix inequalities (LMIs) for tracking constant signals (regulation) considering nonlinear plants described by the Takagi-Sugeno fuzzy models. The procedure consists in designing a single controller that stabilizes the system at operation points belonging to a certain range or region, without the need of remaking the design of the controller gains at each new chosen equilibrium point. The control system design of a magnetic levitator illustrates the proposed methodology.

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Finite frequency model reduction for 2-D fuzzy systems in FM model

E3S Web of Conferences ◽

10.1051/e3sconf/202129701035 ◽

2021 ◽

Vol 297 ◽

pp. 01035

Author(s):

Rachid Naoual ◽

Abderrahim El-Amrani ◽

Ismail Boumhidi

Keyword(s):

Model Reduction ◽

State Space ◽

Linear Matrix Inequalities ◽

Fuzzy Systems ◽

Linear Matrix ◽

Two Dimensional ◽

Matrix Inequalities ◽

Finite Frequency ◽

Frequency Model ◽

Takagi Sugeno

This paper deals with the problem of H∞ model reduction for two-dimensional (2D) discrete Takagi-Sugeno (T-S) fuzzy systems described by Fornasini-Marchesini local state-space (FM LSS) models, over finite frequency (FF) domain. New design conditions guaranteeing the FF H∞ model reduction are established in terms of Linear Matrix Inequalities (LMIs). To highlight the effectiveness of the proposed H∞ model reduction design, a numerical example is given.

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

Energies ◽

10.3390/en12112221 ◽

2019 ◽

Vol 12 (11) ◽

pp. 2221 ◽

Cited By ~ 8

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.

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Stabilization of Nonlinear Systems Using Quasi-Linear Models

10.1115/imece2000-2343 ◽

2000 ◽

Author(s):

Kiriakos Kiriakidis

Keyword(s):

Linear Matrix Inequalities ◽

Linear Models ◽

Nonlinear Models ◽

Linear Matrix ◽

Matrix Inequalities ◽

Analysis And Design ◽

Linear Differential Inclusions ◽

Linear Differential ◽

Generalized Lyapunov Functions ◽

Takagi Sugeno

Abstract Unconventional nonlinear models such as nonlinear ARMAX, Takagi-Sugeno fuzzy models, global linearizations, and linear hybrid systems are, at the highest level of abstraction, a sort of quasi-linear models, namely, Polytopic Linear Differential Inclusions (PLDIs). At present, quadratic stability has enabled, mainly via linear matrix inequalities, the analysis and design of a nonlinear system from the vertex matrices of its PLDI model. Proving stability by a globally quadratic Lyapunov function, however, entails conservatism. This paper proposes a less conservative framework by using piecewise-quadratic generalized Lyapunov functions. Further manipulation of the problem within such framework yields a set of bilinear rather than linear matrix inequalities.

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Delay-Dependent H∞ Control for T-S Fuzzy Systems with Local Nonlinear Models: An LMI Approach

Mathematical Problems in Engineering ◽

10.1155/2020/2301085 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Zhile Xia

Keyword(s):

Linear Matrix Inequalities ◽

Nonlinear Models ◽

Linear Matrix ◽

Matrix Inequalities ◽

Switching Model ◽

Delay Dependent ◽

S Model ◽

Takagi Sugeno ◽

Time Systems ◽

The Relationship

This paper studies the stabilization design scheme with H∞ performance for a large class of nonlinear discrete-time systems. The system under study is modeled by Takagi-Sugeno (T-S) model with local nonlinearity and state delay. First, the model is changed into an equivalent fuzzy switching model. And then, according to projection theorem and piecewise Lyapunov function (PLF), two new H∞ control methods are proposed for fuzzy switched systems, which consider the time delay information of the system. Finally, the relationship among all fuzzy subsystems is considered. Because the results are only expressed by a series of linear matrix inequalities (LMIs), the controller can be directly designed by the linear matrix inequalities toolbox of MATLAB.

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