Robust Tracking Control for Takagi–Sugeno Fuzzy Systems With Unmeasurable Premise Variables: Application to Tank System

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
H. Ghorbel ◽  
A. El Hajjaji ◽  
M. Souissi ◽  
M. Chaabane
Keyword(s):  
Tracking Control ◽  
Fuzzy Systems ◽  
Design Procedure ◽  
Control Design ◽  
Linear Matrix ◽  
Robust Tracking Control ◽  
Fuzzy Observer ◽  
Tank System ◽  
System States ◽  
Takagi Sugeno

In this paper, a robust fuzzy observer-based tracking controller for continuous-time nonlinear systems presented by Takagi–Sugeno (TS) models with unmeasurable premise variables, is synthesized. Using the H∞ norm and Lyapunov approach, the control design for TS fuzzy systems with both unmeasurable premises and system states is developed to guarantee tracking performance of closed loop systems. Sufficient relaxed conditions for synthesis of the fuzzy observer and the fuzzy control are driven in terms of linear matrix inequalities (LMIs) constraints. The proposed method allows simplifying the design procedure and gives the observer and controller gains in only one step. Numerical simulation on a two tank system is provided to illustrate the tracking control design procedure and to confirm the efficiency of the proposed method.

Fault Estimation and Fault-Tolerant Control Via a Novel Proportional–Integral Observer in Singular Takagi-Sugeno Fuzzy Systems

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Min Li ◽  
Ming Liu ◽  
Yingchun Zhang ◽  
Zhuo Chen
Keyword(s):  
Fuzzy Systems ◽  
Controller Design ◽  
Fault Tolerant ◽  
Sufficient Conditions ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Proportional Integral ◽  
System States ◽  
Takagi Sugeno

This paper deals with the fault observer and fault-tolerant controller design for singular Takagi–Sugeno (T–S) fuzzy systems subject to actuator faults. First, a novel proportional-integral observer is constructed to estimate the system states and faults. Sufficient conditions for the existence of the proposed observer are given in linear matrix inequality (LMI) terms. Furthermore, based on the state and fault estimation (FE), a fault-tolerant controller (FTC) is designed to effectively accommodate the influence of fault upon state and ensure that the closed-loop system is stable. Finally, a numerical example is given to show the effectiveness of the presented method.

scholarly journals Robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774539 ◽  
Author(s):  
Min Xu
Keyword(s):  
Fuzzy Systems ◽  
Design Procedure ◽  
Linear Matrix ◽  
Delta Operator ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Operator Approach ◽  
Time Varying Delay ◽  
Takagi Sugeno ◽  
Varying Delay

The problem of robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach is investigated. The time-varying delay and parameter uncertainties are assumed to be of an internal-like type and a structured linear fractional form, respectively. Based on a Lyapunov–Krasovskii functional in delta domain, robust ℋ∞ filter scheme is proposed. Then, a sufficient condition is established for the existence of the desired filter in terms of linear-matrix inequalities. A numerical example is provided to illustrate the design procedure of the present method.

scholarly journals Observer based robust H∞ fuzzy tracking control: application to an activated sludge process

2021 ◽  
Vol 7 ◽  
pp. e458
Author(s):  
Abdelmounaim Khallouq ◽  
Asma Karama ◽  
Mohamed Abyad
Keyword(s):  
Activated Sludge ◽  
Fuzzy Systems ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Activated Sludge Process ◽  
Fuzzy Observer ◽  
Control Application ◽  
Takagi Sugeno ◽  
Substrate Concentrations

The design of an observer-based robust tracking controller is investigated and successfully applied to control an Activated Sludge Process (ASP) in this study. To this end, the Takagi–Sugeno (TS) fuzzy modeling is used to describe the dynamics of a nonlinear system with disturbance. Since the states of the system are not fully available, a fuzzy observer is designed. Based on the observed states and a reference state model, a reduced fuzzy controller for trajectory tracking purposes is then proposed. While the controller and the observer are developed, the design goal is to achieve the convergence and a guaranteed H∞ performance. By using Lyapunov and H∞ theories, sufficient conditions for synthesis of a fuzzy observer and a fuzzy controller for TS fuzzy systems are derived. Using some special manipulations, these conditions are reformulated in terms of linear matrix inequalities (LMIs) problem. Finally, the robust and effective tracking performance of the proposed controller is tested through simulations to control the dissolved oxygen and the substrate concentrations in an activated sludge process.

Robust Fuzzy Tracking Control Design for a Class of Nonlinear Stochastic Markovian Jump Systems

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Ran Huang ◽  
Yan Lin ◽  
Zhongwei Lin
Keyword(s):  
Tracking Control ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Control Design ◽  
Type Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Approximation ◽  
Jump Systems ◽  
Bounded Uncertainties

This paper deals with the problem of robust fuzzy tracking control design for a class of nonlinear stochastic Itô-type systems with Markovian jumps. Considering the fuzzy approximation errors as norm-bounded uncertainties, we derive two sufficient conditions for the nonlinear stochastic robust fuzzy tracking control in terms of coupled matrix inequalities, which ensure the globally asymptotical stability in probability and L2 property for the augmented system, respectively. Then, a systematic algorithm is developed to construct the robust fuzzy tracking controller by reformulating the coupled matrix inequalities into two intertwined linear matrix inequalities (LMIs). Finally, a simulation example is presented to illustrate the design procedure.

scholarly journals Control Design for Discrete-Time Fuzzy Systems with Disturbance Inputs via Delta Operator Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Qi Zhou ◽  
Yabin Gao ◽  
Hongyi Li ◽  
Hamid Reza Karimi
Keyword(s):  
Discrete Time ◽  
Fuzzy Systems ◽  
Passive Control ◽  
Control Design ◽  
Linear Matrix ◽  
Delta Operator ◽  
Operator Approach ◽  
New Type ◽  
Existence Conditions ◽  
Takagi Sugeno

This paper is concerned with the problem of passive control design for discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay and disturbance input via delta operator approach. The discrete-time passive performance index is established in this paper for the control design problem. By constructing a new type ofLyapunov-Krasovskii function (LKF) in delta domain, and utilizing some fuzzy weighing matrices, a new passive performance condition is proposed for the system under consideration. Based on the condition, a state-feedback passive controller is designed to guarantee that the resulting closed-loop system is very-strictly passive. The existence conditions of the controller can be expressed by linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the feasibility and effectiveness of the proposed method.

scholarly journals Optimal Fuzzy Control for a Class of Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Design Procedure ◽  
Control Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Stabilizing Controllers ◽  
Simulation Results ◽  
Takagi Sugeno ◽  
Slack Matrices

The paper presents conditions suitable in design giving quadratic performances to stabilizing controllers for given class of continuous-time nonlinear systems, represented by Takagi-Sugeno models. Based on extended Lyapunov function and slack matrices, the design conditions are outlined in the terms of linear matrix inequalities to possess a stable structure closest to LQ performance, if premise variables are measurable. Simulation results illustrate the design procedure and demonstrate the performances of the proposed control design method.

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