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.

Design of Robust Double-Fuzzy-Summation Nonparallel Distributed Compensation Controller for Chaotic Power Systems

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Navid Vafamand ◽  
Mohammad Hassan Khooban ◽  
Alireza Khayatian ◽  
Frede Blabbjerg
Keyword(s):  
Power Systems ◽  
Controller Design ◽  
Chaotic Behavior ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Ts Fuzzy Model ◽  
Fuzzy Membership Functions ◽  
Local Controller ◽  
Takagi Sugeno

This paper studies a systematic linear matrix inequality (LMI) approach for controller design of nonlinear chaotic power systems. The presented method is based on a Takagi–Sugeno (TS) fuzzy model, a double-fuzzy-summation nonparallel distributed compensation (non-PDC) controller, and a double-fuzzy-summation nonquadratic Lyapunov function (NQLF). Since time derivatives of fuzzy membership functions (MFs) appear in the NQLF-based controller design conditions, local controller design criteria is considered, and sufficient conditions are formulated in terms of LMIs. Compared with the existing works in hand, the proposed LMI conditions provide less conservative results due to the special structure of the NQLF and the non-PDC controller in which two fuzzy summations are employed. To evaluate the effectiveness of the presented approach, two practical benchmark power systems, which exhibit chaotic behavior, are considered. Simulation results and hardware-in-the-loop illustrate the advantages of the proposed method compared with the recently published works.

scholarly journals Design of Takagi-Sugeno Fuzzy Control Scheme for Real World System Control

2019 ◽  
Vol 11 (14) ◽  
pp. 3855 ◽  
Author(s):  
Chiu ◽  
Peng
Keyword(s):  
Fuzzy Control ◽  
Real World ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
World System ◽  
Linear Matrix ◽  
System Control ◽  
Ts Fuzzy Model ◽  
Control Scheme ◽  
Takagi Sugeno

In this study, a novelty dual Takagi-Sugeno (TS) fuzzy control scheme (DTSFCS) is proposed for real world system control. We propose using a ball robot (BR) system control problem, where the BR has the ability to move omnidirectionally. The proposed control scheme combines two fuzzy control approaches for a BR. In this fuzzy control approach, the TS fuzzy model was adopted for the fuzzy modeling of the BR. The concept of parallel distributed compensation (PDC) was utilized to develop a fuzzy control scheme from the TS fuzzy models. The linear matrix inequalities (LMIs) can formulate sufficient conditions. Moreover, in this study, the motors of the BR were mounted on two orthogonal axes. Then, the dual TS fuzzy controller was designed to independently operate without coupling. Finally, the efficiency of the proposed control scheme is illustrated by the experimental and simulation results that are presented in this study.

Quadrotor UAV attitude stabilization using fuzzy robust control

2021 ◽  
pp. 014233122110025
Author(s):  
David Lara Alabazares ◽  
Abdelhamid Rabhi ◽  
Claude Pegard ◽  
Fernando Torres Garcia ◽  
Gerardo Romero Galvan
Keyword(s):  
Robust Control ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Ts Fuzzy Model ◽  
Attitude Stabilization ◽  
Numerical Tools ◽  
Robust Fuzzy Controller ◽  
Takagi Sugeno ◽  
The Given

In this paper, a robust controller for attitude stabilization of a small quadrotor helicopter is developed. The TS (Takagi-Sugeno) fuzzy model approach and the [Formula: see text] robust control are combined to produce the proposed algorithm. Besides, disturbances and parametric uncertainties are considered. First, the nonlinear model of the vehicle is linearized around several operating points to obtain the representation of a TS fuzzy model, which represents the nonlinearity of the system dynamics. Then, a robust fuzzy controller is synthesized which guarantees desired control performances. The given controller is designed using numerical tools such as linear matrix inequalities (LMI). Finally, simulation results and real-time experiments are presented to validate the performance of the proposed scheme to robustly stabilize the quadrotor dynamics at the desired reference.

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 Dissipativity-Based Controller Design for Time-Delayed T-S Fuzzy Switched Distributed Parameter Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaona Song ◽  
Mi Wang ◽  
Shuai Song ◽  
Jingtao Man
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Distributed Parameter Systems ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Varying Delay ◽  
Closed Loop Systems ◽  
Control Gain

This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

DELAYED FUZZY CONTROLLER DESIGN FOR HYPERCHAOS WITH APPLICATION TO HYPERCHAOTIC CHEN'S SYSTEM

2007 ◽  
Vol 18 (07) ◽  
pp. 1095-1105 ◽  
Author(s):  
XINGWEN LIU ◽  
XIN GAO
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed State Feedback ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Compensation Design ◽  
Hyperchaotic Systems ◽  
Control Criterion

Studied in this paper is the control problem of hyperchaotic systems. By combining Takagi–Sugeno (T–S) fuzzy model with parallel distributed compensation design technique, we propose a delay-dependent control criterion via pure delayed state feedback. Because the result is expressed in terms of linear matrix inequalities (LMIs), it is quite convenient to check in practice. Based on this criterion, a procedure is provided for designing fuzzy controller for such systems. This method is a universal one for controlling continuous hyperchaotic systems. As illustrated by its application to hyperchaotic Chen's system, the controller design is quite effective.

Takagi-Sugeno Fuzzy Load-Following Control of Nuclear Reactors Based on Reactor Point Kinetics Equations

2014 ◽  
Author(s):  
Xiuchun Luan ◽  
Jie Zhou ◽  
Yu Zhai
Keyword(s):  
Control System ◽  
Linear Models ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Neutron Density ◽  
Load Following ◽  
Wide Range ◽  
Takagi Sugeno ◽  
Operating Points

A state differential feedback control system based Takagi-Sugeno (T-S) fuzzy model is designed for load-following operation of nonlinear nuclear reactor whose operating points vary within a wide range. Linear models are first derived from the original nonlinear model on several operating points. Next the fuzzy controller is designed via using the parallel distributed compensation (PDC) scheme with the relative neutron density at the equilibrium point as the premise variable. Last the stability analysis is given by means of linear matrix inequality (LMI) approach, thus the control system is guaranteed to be stable within a large range. The simulation results demonstrate that the control system works well over a wide region of operation.

scholarly journals T-S Fuzzy Modelling and H∞ Attitude Control for Hypersonic Gliding Vehicles

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Weidong Zhang ◽  
Xianlin Huang ◽  
Xiao-Zhi Gao
Keyword(s):  
Attitude Control ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Attitude Dynamics ◽  
Approximation Accuracy ◽  
Fuzzy Modelling ◽  
Original Plant ◽  
Operating Points

This paper addresses the T-S fuzzy modelling and H∞ attitude control in three channels for hypersonic gliding vehicles (HGVs). First, the control-oriented affine nonlinear model has been established which is transformed from the reentry dynamics. Then, based on Taylor’s expansion approach and the fuzzy linearization approach, the homogeneous T-S local modelling technique for HGVs is proposed. Given the approximation accuracy and controller design complexity, appropriate fuzzy premise variables and operating points of interest are selected to construct the T-S homogeneous submodels. With so-called fuzzy blending, the original plant is transformed into the overall T-S fuzzy model with disturbance. By utilizing Lyapunov functional approach, a state feedback fuzzy controller has been designed based on relaxed linear matrix inequality (LMI) conditions to stable the original plants with a prescribed H∞ performance of disturbance. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed H∞ T-S fuzzy controller for the original attitude dynamics; the superiority of the designed T-S fuzzy controller compared with other local controllers based on the constructed fuzzy model is shown as well.

scholarly journals Model reduction design for continuous systems with finite frequency specifications

2021 ◽  
Vol 11 (5) ◽  
pp. 3956
Author(s):  
Miloud Koumir ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Model Reduction ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Continuous Systems ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Error System ◽  
Takagi Sugeno

<p>This paper is concerned with the problem of model reduction design for continuous systems in Takagi-Sugeno fuzzy model. Through the defined FF H∞ gain performance, sufficient conditions are derived to design model reduction and to assure the fuzzy error system to be asymptotically stable with a FF H∞ gain performance index. The explicit conditions of fuzzy model reduction are developed by solving linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.</p>

Fuzzy H∞ Synchronization for Chaotic Systems with Time-Varying Delay

2011 ◽  
Vol 66 (3-4) ◽  
pp. 151-160
Author(s):  
Choon Ki Ahn
Keyword(s):  
Chaotic Systems ◽  
External Disturbance ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Time Varying ◽  
Ts Fuzzy Model ◽  
Time Varying Delay ◽  
Norm Constraint ◽  
Takagi Sugeno ◽  
Varying Delay

In this paper, we propose a newH∞ synchronization method for fuzzy model based chaotic systems with external disturbance and time-varying delay. Based on Lyapunov-Krasovskii theory, Takagi- Sugeno (TS) fuzzy model, and linear matrix inequality (LMI) approach, the H∞ synchronization controller is presented to not only guarantee stable synchronization but also reduce the effect of external disturbance to an H∞ norm constraint. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. A simulation study is presented to demonstrate the validity of the proposed approach.

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