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 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.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

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.

Disturbance Rejection of Interval Type-2 Fuzzy Systems Based on Equivalence-Input-Disturbance Approach

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
P. Selvaraj ◽  
R. Sakthivel ◽  
O. M. Kwon ◽  
M. Muslim
Keyword(s):  
Disturbance Rejection ◽  
Fuzzy Systems ◽  
Fuzzy Controller ◽  
Reference Signal ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Input Disturbance ◽  
Interval Type ◽  
Fuzzy State

This paper focuses on the problem of disturbance rejection for a class of interval type-2 (IT-2) fuzzy systems via equivalence-input-disturbance (EID)-based approach. The main objective of this work is to design a fuzzy state-feedback controller combined with a disturbance estimator such that the output of the fuzzy system perfectly tracks the given reference signal without steady-state error and produces an EID to eliminate the influence of the actual disturbances. By constructing a suitable Lyapunov function and using linear matrix inequality (LMI) technique, a new set of sufficient conditions is established in terms of linear matrix inequalities for the existence of fuzzy controller. Finally, a simple pendulum model is considered to illustrate the effectiveness and applicability of the proposed EID-based control design.

Finite Time Passive Reliable Filtering for Fuzzy Systems With Missing Measurements

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
S. Vimal Kumar ◽  
R. Sakthivel ◽  
M. Sathishkumar ◽  
S. Marshal Anthoni
Keyword(s):  
Finite Time ◽  
Fuzzy Systems ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Missing Measurements ◽  
Randomly Occurring Uncertainties ◽  
Error System ◽  
Takagi Sugeno ◽  
Reliable Filtering

This paper investigates the problem of robust finite time extended passive reliable filtering for Takagi–Sugeno (T–S) fuzzy systems with randomly occurring uncertainties, missing measurements, and time-varying delays. Moreover, two stochastic variables satisfying the Bernoulli random distribution are introduced to characterize the phenomenon of the randomly occurring uncertainties and missing measurements. By skillfully choosing a proper Lyapunov–Krasovskii functional (LKF), a new set of sufficient conditions in terms of linear matrix inequalities (LMI) is derived to ensure that the filtering error system is robustly stochastically finite time bounded (SFTB) with a desired extended passive performance index. Based on the obtained sufficient conditions, an explicit expression for the desired filter can be computed. Finally, two numerical examples are provided to show the effectiveness of the proposed filter design technique.

New Sufficient Conditions on H∞ Filter Design for Nonlinear T-S Fuzzy Systems with Time Delays

2012 ◽  
Vol 263-266 ◽  
pp. 162-166
Author(s):  
Su Huan Yi ◽  
Sheng Juan Huang
Keyword(s):  
Fuzzy Systems ◽  
Time Delays ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Decoupling Approach ◽  
Takagi Sugeno ◽  
Varying Delay

This paper focuses on the problem of H∞ filter design for continuous Takagi-Sugeno (T-S) fuzzy systems with an interval time-varying delay in the state. Based on the free weighting matrix method combined with a matrix decoupling approach, some new sufficient results are proposed in forms of linear matrix inequalities (LMIs), which can achieve much less conservative feasibility conditions. Finally, the effectiveness of the proposed method is demonstrated ba an example.

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 Relaxed State and Fault Estimation for Vehicle Lateral Dynamics Represented by T–S Fuzzy Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
N. El Youssfi ◽  
R. El Bachtiri ◽  
T. Zoulagh ◽  
H. El Aiss
Keyword(s):  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
State Equation ◽  
Observer Design ◽  
Fault Estimation ◽  
Linear Matrix ◽  
Vehicle Model ◽  
Lateral Dynamics ◽  
Takagi Sugeno ◽  
Vehicle Lateral Dynamics

This paper deals with the problem of observer design of the vehicle model which is represented by Takagi–Sugeno (T–S) fuzzy systems with the presence of uncertainties. A relaxed observer design is presented to estimate the unmeasurable states and the faults of the vehicle lateral dynamics model, simultaneously. The vehicle model is transformed into a system with unknown inputs. Then, it is rebuilt by adding the default to the system state equation. Based on the Lyapunov function approach and the introduction of some slack variables, sufficient conditions of unknown input observer design are formulated as Linear Matrix Inequalities (LMIs). Finally, the simulation section clearly shows the importance and effectiveness of the proposed strategy.

Further Results on Stability and Stabilization of T–S Fuzzy Neutral Systems with Time-Varying Delays Using Delay Dividing Approach

2014 ◽  
Vol 11 (04) ◽  
pp. 1442007
Author(s):  
Min Kook Song ◽  
Jin Bae Park ◽  
Young Hoon Joo
Keyword(s):  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Time Varying ◽  
Neutral Systems ◽  
Sufficient Stability ◽  
Stability And Stabilization ◽  
The Stability ◽  
Takagi Sugeno

This paper is concerned with the stability and the stabilization problem for Takagi–Sugeno (T–S) fuzzy systems with neutral time delays. The sufficient stability conditions are derived using novel Lyapunov–Krasovskii functionals (LKFs). The stability conditions are expressed as linear matrix inequalities (LMIs) and hence easily tractable numerically. These conditions are easily extended to the sufficient conditions for the existence of stabilizing state-feedback fuzzy gains for T–S fuzzy neutral systems with time-varying delays. An example is given to illustrate the effectiveness of the proposed methods.

Finite-Frequency Static Output Feedback H∞ Control of Continuous-Time T–S Fuzzy Systems

2018 ◽  
Vol 28 (02) ◽  
pp. 1950023 ◽  
Author(s):  
Redouane Chaibi ◽  
Ismail Er Rachid ◽  
El Houssaine Tissir ◽  
Abdelaziz Hmamed
Keyword(s):  
Output Feedback ◽  
Continuous Time ◽  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Static Output Feedback ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Takagi Sugeno ◽  
Static Output

This paper is concerned with finite-frequency static output feedback (SOF) [Formula: see text] control for a class of continuous-time Takagi–Sugeno (T–S) fuzzy systems. With the aid of the generalized Kalman–Yakubovich–Popov (GKYP) lemma, sufficient conditions for the existence of the finite-frequency SOF [Formula: see text] control are presented. The bilinear matrix inequalities are converted to a set of linear matrix inequalities, with the aid of some special derivations. Two practical examples are given to demonstrate the effectiveness of the proposed method.

Sign in / Sign up

Export Citation Format

Share Document