scholarly journals Analysis and Comparison of Fuzzy Models and Observers for DC-DC Converters Applied to a Distillation Column Heating Actuator

2020 ◽  
Vol 25 (3) ◽  
pp. 55
Author(s):  
Mario Heras-Cervantes ◽  
Adriana del Carmen Téllez-Anguiano ◽  
Juan Anzurez-Marín ◽  
Elisa Espinosa-Juárez
Keyword(s):  
Distillation Column ◽  
Control Strategies ◽  
Power Converter ◽  
Heating Power ◽  
Linear Matrix ◽  
State Variables ◽  
Distillation Process ◽  
Online Measurements ◽  
The Stability ◽  
Takagi Sugeno

In this paper, as an introduction, the nonlinear model of a distillation column is presented in order to understand the fundamental paper that the column heating actuator has in the distillation process dynamics as well as in the quality and safety of the process. In order to facilitate the implementation control strategies to maintain the heating power regulated in the distillation process, it is necessary to represent adequately the heating power actuator behavior; therefore, three different models (switching, nonlinear and fuzzy Takagi–Sugeno) of a DC-DC Buck-Boost power converter, selected to regulate the electric power regarding the heating power, are presented and compared. Considering that the online measurements of the two main variables of the converter, the inductor current and the capacitor voltage, are not always available, two different fuzzy observers (with and without sliding modes) are developed to allow monitoring the physical variables in the converter. The observers response is compared to determine which has a better performance. The role of the observer in estimating the state variables with the purpose of using them in the sensors fault diagnosis, using the analytical redundancy concept, likewise, from the estimation of these variables other non-measurable can be determined; for example, the caloric power. The stability analysis and observers gains are obtained by linear matrix inequalities (LMIs). The observers are validated by MATLAB® simulations to verify the observers convergence and analyze their response under system disturbances.

scholarly journals Takagi-Sugeno Fuzzy Modeling and PSO-Based Robust LQR Anti-Swing Control for Overhead Crane

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Xuejuan Shao ◽  
Jinggang Zhang ◽  
Xueliang Zhang
Keyword(s):  
Linear Quadratic Regulator ◽  
Pso Algorithm ◽  
Fuzzy Modeling ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Overhead Crane ◽  
Linear Quadratic ◽  
Highly Nonlinear ◽  
The Stability ◽  
Takagi Sugeno

The dynamic model of overhead crane is highly nonlinear and uncertain. In this paper, Takagi-Sugeno (T-S) fuzzy modeling and PSO-based robust linear quadratic regulator (LQR) are proposed for anti-swing and positioning control of the system. First, on the basis of sector nonlinear theory, the two T-S fuzzy models are established by using the virtual control variables and approximate method. Then, considering the uncertainty of the model, robust LQR controllers with parallel distributed compensation (PDC) structure are designed. The feedback gain matrices are obtained by transforming the stability and robustness of the system into linear matrix inequalities (LMIs) problem. In addition, particle swarm optimization (PSO) algorithm is used to overcome the blindness of LQR weight matrix selection in the design process. The proposed control methods are simple, feasible, and robust. Finally, the numeral simulations are carried out to prove the effectiveness of the methods.

Improved Delay-Dependent Stability of Nonlinear Quadratic TS Fuzzy Systems

2019 ◽  
Vol 29 (09) ◽  
pp. 2050134 ◽  
Author(s):  
Khadija Naamane ◽  
El Houssaine Tissir
Keyword(s):  
Fuzzy Systems ◽  
Model Transformation ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Small Gain ◽  
The Stability ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper focuses on the problem of delay-dependent stability for nonlinear quadratic Takagi–Sugeno (TS) fuzzy systems with time-varying delay using the input–output approach. The results are based on the model transformation by employing a three-terms approximation of delayed state vector. By applying the scaled small-gain theorem and Lyapunov–Krasovskii functional, the stability criteria is obtained in terms of linear matrix inequalities. Furthermore, the Wirtinger-based integral inequality approach has been employed to derive less conservative results. Finally, the numerical examples are provided to demonstrate the effectiveness of the obtained results and for comparison with previous work.

scholarly journals Improved Delay-Dependent Stability and Stabilization Conditions of T-S Fuzzy Time-Delay Systems via an Augmented Lyapunov-Krasovskii Functional Approach

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Zifan Gao ◽  
Jiaxiu Yang ◽  
Shuqian Zhu
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Stability Conditions ◽  
State Variables ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Stability And Stabilization ◽  
The Stability ◽  
Delay Dependent

This paper develops some improved stability and stabilization conditions of T-S fuzzy system with constant time-delay and interval time-varying delay with its derivative bounds available, respectively. These conditions are presented by linear matrix inequalities (LMIs) and derived by applying an augmented Lyapunov-Krasovskii functional (LKF) approach combined with a canonical Bessel-Legendre (B-L) inequality. Different from the existing LKFs, the proposed LKF involves more state variables in an augmented way resorting to the form of the B-L inequality. The B-L inequality is also applied in ensuring the positiveness of the constructed LKF and the negativeness of derivative of the LKF. By numerical examples, it is verified that the obtained stability conditions can ensure a larger upper bound of time-delay, the larger number of Legendre polynomials in the stability conditions can lead to less conservative results, and the stabilization condition is effective, respectively.

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.

Design of Takagi-Sugeno Fuzzy Region Controller Based on Rule Reduction, Robust Control, and Switching Concept

2006 ◽  
Vol 129 (2) ◽  
pp. 163-170 ◽  
Author(s):  
Chein-Chung Sun ◽  
Sheng-Ming Wu ◽  
Hung-Yuan Chung ◽  
Wen-Jer Chang
Keyword(s):  
Robust Control ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Robot System ◽  
Uncertain Model ◽  
Lyapunov Stability Criterion ◽  
Fuzzy Regions ◽  
The Stability ◽  
Takagi Sugeno ◽  
Fuzzy Region

This paper presents a new structure of Takagi-Sugeno (T-S) fuzzy controllers, which is called T-S fuzzy region controller or TSFRC for short. The fuzzy region concept is used to partition the plant rules into several fuzzy regions so that only one region is fired at the instant of each input vector being coming. Because each fuzzy region contains several plant rules, the fuzzy region can be regarded as a polytopic uncertain model. Therefore, robust control techniques would be essential for designing the feedback gains of each fuzzy region. To improve the speed of response, the decay rate constraint is imposed when deriving the stability conditions with Lyapunov stability criterion. To design TSFRC with the linear matrix inequality (LMI) solver, all stability conditions are represented in terms of LMIs. Finally, a two-link robot system is used to prove the feasibility and validity of the proposed method.

Estimation of Steering Wheel Angle and Vehicle Lateral State from Measured Lateral Forces

2018 ◽  
Vol 39 ◽  
pp. 14-31 ◽  
Author(s):  
Fatima Ezzahra Saber ◽  
Mohamed Ouahi ◽  
Abdelmjid Saka
Keyword(s):  
Steering Wheel ◽  
Linear Matrix ◽  
Unknown Input ◽  
State Variables ◽  
Unknown Input Observer ◽  
Driver Assistance ◽  
Lateral Dynamics ◽  
Lateral Forces ◽  
Vehicle Simulator ◽  
The Stability

This paper introduces a method to estimate the lateral dynamics parameters,which are valuable to the development of more complex and powerful driver assistance system. In the assumption of measured lateral forces, three state observer methods are designed to simultaneously estimate the steering angleas unknown input and vehicle lateral state variables. The stability conditionsof such observers are derived in terms of Linear Matrix Inequalities (LMI). Simulation results through Matlab/Simulink software based on data of the CALLAS vehicle simulator is used to evaluate the performance of observersbased on Unknown Input Observer (OEI).

scholarly journals Robust Stabilization for Continuous Takagi-Sugeno Fuzzy System Based on Observer Design

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yassine Manai ◽  
Mohamed Benrejeb
Keyword(s):  
Robust Stabilization ◽  
Uncertain System ◽  
Observer Design ◽  
Linear Matrix ◽  
State Variables ◽  
Fuzzy Models ◽  
Distributed Controller ◽  
Numeric Simulation ◽  
Stabilization Condition ◽  
Takagi Sugeno

This paper investigates the influence of a new parallel distributed controller (PDC) on the stabilization region of continuous Takagi-Sugeno (T-S) fuzzy models. Using a nonquadratic Lyapunov function, a new sufficient stabilization criterion is established in terms of linear matrix inequality. The criterion examines the derivative membership function; an approach to determine state variables is given based on observer design. In addition, a stabilization condition for uncertain system is given. Finally, numeric simulation is given to validate the developed approach.

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 Nonlinear Dynamics of Controlled Synchronizations of Manipulator System

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Qingkai Han ◽  
Hao Zhang ◽  
Jinguo Liu
Keyword(s):  
Nonlinear Dynamics ◽  
Control Strategies ◽  
Adaptive Synchronization ◽  
State Variables ◽  
Motion Patterns ◽  
Joint Friction ◽  
Synchronization Errors ◽  
Robust Adaptive ◽  
The Stability ◽  
Neuron Synchronization

The nonlinear dynamics of the manipulator system which is controlled to achieve the synchronization motions is investigated in the paper. Firstly, the control strategies and modeling approaches of the manipulator system are given, in which the synchronization goal is defined by both synchronization errors and its derivatives. The synchronization controllers applied on the manipulator system include neuron synchronization controller, improved OPCL synchronization controller, and MRAC-PD synchronization controller. Then, an improved adaptive synchronized control strategy is proposed in order to estimate online the unknown structure parameters and state variables of the manipulator system and to realize the needed synchronous compensation. Furthermore, a robust adaptive synchronization controller is also researched to guarantee the dynamic stability of the system. Finally, the stability of motion synchronizations of the manipulator system possessing nonlinear component is discussed, together with the effect of control parameters and joint friction and others. Some typical motions such as motion bifurcations and the loss of synchronization of it are obtained and illustrated as periodic, multiperiodic, and/or chaotic motion patterns.

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