scholarly journals A Note on Practical Stability of Nonlinear Vibration Systems with Impulsive Effects

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Qishui Zhong ◽  
Hongcai Li ◽  
Hui Liu ◽  
Juebang Yu
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Nonlinear Vibration ◽  
Stability Criterion ◽  
Fuzzy Model ◽  
Vibration Characteristics ◽  
Impulsive Effects ◽  
Practical Stability ◽  
Impulsive Systems ◽  
System A

This paper addresses the issue of vibration characteristics of nonlinear systems with impulsive effects. By utilizing a T-S fuzzy model to represent a nonlinear system, a general strict practical stability criterion is derived for nonlinear impulsive systems.

Switching Model Construction and Stability Analysis for Nonlinear Systems

2006 ◽  
Vol 10 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Hiroshi Ohtake ◽  
◽  
Kazuo Tanaka
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Fuzzy Model ◽  
Function Approach ◽  
Model Construction ◽  
Switching Model ◽  
Piecewise Lyapunov Function ◽  
System A ◽  
The Stability

This paper presents switching model construction and stability analysis for a class of nonlinear systems. A switching fuzzy model newly developed in this paper is employed to represent the dynamics of a nonlinear system. A key feature of the switching fuzzy model construction is to find the so-called minimum distance sector by solving a nonlinear optimization problem. Next, we discuss the stability of a switching fuzzy model. To take advantage of the switching fuzzy model, we introduce a piecewise Lyapunov function that mirrors its structure. We show that the piecewise Lyapunov function approach provides less conservative results for the typical quadratic Lyapunov function approach. Illustrative examples demonstrate the utility of the switching model construction and the stability analysis.

Takagi–Sugeno Fuzzy Predictive Control for a Class of Nonlinear System With Constrains and Disturbances

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Bin Wang ◽  
Jianwei Zhang ◽  
Delan Zhu ◽  
Diyi Chen
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Predictive Control ◽  
Three Dimensional ◽  
Fuzzy Model ◽  
Control Input ◽  
Chen System ◽  
External Disturbances ◽  
Takagi Sugeno ◽  
Fuzzy Predictive Control

This paper investigates the fuzzy predictive control for a class of nonlinear system with constrains under the condition of noise. Based on the fuzzy linearization theory, a class of nonlinear systems can be described by the Takagi–Sugeno (T–S) fuzzy model. The T–S fuzzy model and predictive control are combined to stabilize the proposed class of nonlinear system, and the detailed mathematical derivation is given. Moreover, the designed controller has been optimized even if the system is constrained by output and control input, or perturbed by external disturbances. Finally, numerical simulations including three-dimensional Lorenz system, four-dimensional Chen system and five-dimensional nonlinear system with external disturbances are presented to demonstrate the universality and effectiveness of the proposed scheme. The approach proposed in this paper is simple and easy to implement and also provides reference for relevant nonlinear systems.

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.

scholarly journals The Identification of Nonlinear Systems UsingCt-KtPlane Coordinates

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Ming-Fei Chen ◽  
Dyi-Cheng Chen ◽  
Chung-Heng Yang ◽  
Shih-Feng Tseng
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Dynamic Behavior ◽  
Pulse Response ◽  
Displacement Velocity ◽  
Viscous Damping ◽  
Dynamic Parameters ◽  
Coordinate Plane ◽  
Aerostatic Bearing ◽  
System A

In order to instantaneously distinguish theCt(coefficient of viscous damping) andKt(coefficient of stiffness), which are both functions of time in an M.C.K. nonlinear system, a new identification method is proposed in this paper. The graphs of theCt-Ktare analyzed and the dynamic behavior of M.C.K. systems in aCt-Ktcoordinate plane is discussed. This method calculates two adjacent sampling data, the displacement, velocity, and acceleration (which are obtained from the responses of a pulse response experiment) and then distinguishesCtandKtof an instantaneous system. Finally, this method is used to identify the aerostatic bearing dynamic parameters,CandK.

A Controller Design for a Class of Nonlinear Systems Using the Lyapunov-Bellman Approach

1992 ◽  
Vol 114 (3) ◽  
pp. 390-393 ◽  
Author(s):  
R. T. Yanushevsky
Keyword(s):  
Optimal Control ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Optimal Control Problem ◽  
Lyapunov Functions ◽  
Bellman Equation ◽  
Controller Design ◽  
Variable Structure ◽  
System A

The method of synthesis for a wide class of nonlinear systems affine in control is considered. The proposed approach is based on the solution of a special optimal control problem. The integrand of the optimized functional is chosen in such a way that the Bellman equation has a desired solution. The nonlinear system design is reduced to the examination of the integrand of the optimized functional. To extend the domain of asymptotic stability of the nonlinear system, a sequence of the Lyapunov functions is used. The whole system becomes a system with variable structure.

Modeling and Control of Complex Nonlinear Systems Based on TS Model

2013 ◽  
Vol 380-384 ◽  
pp. 417-420
Author(s):  
Yu Chi Zhao ◽  
Jing Liu
Keyword(s):  
System Theory ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Fuzzy System ◽  
Fuzzy Systems ◽  
Fuzzy Model ◽  
Modeling And Control ◽  
Linear Control Theory ◽  
Complex Nonlinear Systems ◽  
And Control

The current theory of nonlinear systems is still not perfect. The modeling and control of nonlinear system problem has always been the difficulty. In a variety of methods of its study, fuzzy system theory because of having the language descriptive way similar to the human mind, can obtain and deal with the qualitative information intelligently. The theory itself also has non-linear characteristics. Therefore the use of fuzzy systems theory to establish the fuzzy model of nonlinear system can well describe the nonlinear characteristics. T-S fuzzy systems, due to the combination of the good performance of the fuzzy system to deal with nonlinear problems with the simple linear expressions, are not only suitable for modeling the nonlinear system, but also use T-S fuzzy model and the linear control theory method to design the controller. So it has been widely used in nonlinear system control problems, and has also greatly developed the T-S fuzzy system theory, appearing a lot of methods of structural and parameter identification. However, this study of T-S fuzzy rules makes us have to face the difference of different ways to select the number of rules as well as online self-adaptability of the number of rules which off-line method lacks when using T-S fuzzy model to deal with nonlinear system modeling and control problem. In view of this, this paper researches on modeling and controlling of complex nonlinear systems based on TS model from different perspectives.

Output Feedback Fuzzy Control for Uncertain Nonlinear Systems

2003 ◽  
Vol 125 (4) ◽  
pp. 521-530 ◽  
Author(s):  
Wook Chang ◽  
Jin Bae Park ◽  
Young Hoon Joo ◽  
Guanrong Chen
Keyword(s):  
Feedback Control ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Output Feedback ◽  
Fuzzy Model ◽  
Output Feedback Control ◽  
Static Output Feedback ◽  
Uncertain Nonlinear System ◽  
Switching Type ◽  
Static Output

In this paper, a fuzzy control scheme, which employs the output feedback control approach, is suggested for the stabilization of nonlinear systems with uncertainties. The uncertain nonlinear system can be represented by uncertain Takagi-Sugeno (TS) fuzzy model structure, which is further rearranged to give a set of uncertain linear systems. A switching-type fuzzy-model-based controller, which utilizes the static output feedback control strategy, is designed based on this preliminary study. Theoretical analysis guarantees that under the control of the proposed technique, the uncertain nonlinear system is stabilizable by the switching-type static output-feedback fuzzy-model-based controller. Finally, two computer simulation examples are provided to show the effectiveness and feasibility of the developed controller design method.

scholarly journals A Data-Driven Approach of Takagi-Sugeno Fuzzy Control of Unknown Nonlinear Systems

2020 ◽  
Vol 11 (1) ◽  
pp. 62
Author(s):  
Bin Zhang ◽  
Yung C. Shin
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Control Method ◽  
Approximation Error ◽  
Fuzzy Model ◽  
Evolutionary Strategy ◽  
Global Approximation ◽  
Fuzzy Models ◽  
Neuro Fuzzy ◽  
Takagi Sugeno

A novel approach to build a Takagi-Sugeno (T-S) fuzzy model of an unknown nonlinear system from experimental data is presented in the paper. The neuro-fuzzy models or, more specifically, fuzzy basis function networks (FBFNs) are trained from input–output data to approximate the nonlinear systems for which analytical mathematical models are not available. Then, the T-S fuzzy models are derived from the direct linearization of the neuro-fuzzy models. The operating points for linearization are chosen using the evolutionary strategy to minimize the global approximation error so that the T-S fuzzy models can closely approximate the original unknown nonlinear system with a reduced number of linearizations. Based on T-S fuzzy models, optimal controllers are designed and implemented for a nonlinear two-link flexible joint robot, which demonstrates the possibility of implementing the well-established model-based optimal control method onto unknown nonlinear dynamic systems.

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