scholarly journals LMI-Fuzzy Control Design for Non-Minimum-Phase DC-DC Converters: An Application for Output Regulation

2021 ◽  
Vol 11 (5) ◽  
pp. 2286
Author(s):  
Carlos Andrés Torres-Pinzón ◽  
Leonel Paredes-Madrid ◽  
Freddy Flores-Bahamonde ◽  
Harrynson Ramirez-Murillo
Keyword(s):  
Fuzzy Control ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Voltage Regulation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Minimum Phase ◽  
State Variables ◽  
Large Signal ◽  
Takagi Sugeno

Robust control techniques for power converters are becoming more attractive because they can meet with most demanding control goals like uncertainties. In this sense, the Takagi-Sugeno (T-S) fuzzy controller based on linear matrix inequalities (LMI) is a linear control by intervals that has been relatively unexplored for the output-voltage regulation problem in switching converters. Through this technique it is possible to minimize the disturbance rejection level, satisfying constraints over the decay rate of state variables as well as the control effort. Therefore, it is possible to guarantee, a priori, the stability of the large-signal converters in a broad operation domain. This work presents the design of a fuzzy control synthesis based on a T-S fuzzy model for non-minimum phase dc-dc converters, such as boost and buck-boost. First, starting from the canonical bilinear converters expression, a Takagi-Sugeno (T-S) fuzzy model is obtained, allowing to define the fuzzy controller structure through the parallel distributed compensation technique (PDC). Finally, the fuzzy controller design based on LMIs is solved for the defined specification in close loop through MATLAB toolbox LMI. Simulations and experimental results of a 60 W prototype are presented to verify theoretical predictions.

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.

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.

Finite time takagi-sugeno fuzzy control for hydro-turbine governing system

2016 ◽  
Vol 24 (5) ◽  
pp. 1001-1010 ◽  
Author(s):  
Bin Wang ◽  
Jianyi Xue ◽  
Fengjiao Wu ◽  
Delan Zhu
Keyword(s):  
Fuzzy Control ◽  
Finite Time ◽  
Control Method ◽  
Fuzzy Model ◽  
Schur Complement ◽  
Stability Control ◽  
Linear Matrix ◽  
Hydro Turbine ◽  
Governing System ◽  
Takagi Sugeno

In this study, a robust finite time Takagi-Sugeno fuzzy control method for hydro-turbine governing system (HTGS) is investigated. Firstly, the mathematical model of HTGS is introduced, and on the basis of Takagi-Sugeno (T-S) fuzzy rules, the T-S fuzzy model of HTGS is presented. Secondly, based on finite time stability theory, a novel finite time Takagi-Sugeno fuzzy control method is designed for the stability control of HTGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed finite time T-S fuzzy control scheme works well compared with the conventional method. The approach proposed in this paper is easy to implement and also provides reference for relevant hydropower systems.

Reliable Robust H∞ Fuzzy Control for Uncertain Nonlinear Systems With Markovian Jumping Actuator Faults

2006 ◽  
Vol 129 (3) ◽  
pp. 252-261 ◽  
Author(s):  
Huai-Ning Wu
Keyword(s):  
Fuzzy Control ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Actuator Faults ◽  
Markovian Jumping ◽  
Stochastically Stable ◽  
The Stability ◽  
Time Systems

This paper is concerned with the design of reliable robust H∞ fuzzy control for uncertain nonlinear continuous-time systems with Markovian jumping actuator faults. The Takagi and Sugeno fuzzy model is employed to represent an uncertain nonlinear system with Markovian jumping actuator faults. First, based on the parallel distributed compensation (PDC) scheme, a sufficient condition such that the closed-loop fuzzy system is robustly stochastically stable and satisfies a prescribed level of H∞-disturbance attenuation is derived. In the derivation process, a stochastic Lyapunov function is used to test the stability and H∞ performance of the system. Then, a new improved linear matrix inequality (LMI) formulation is applied to this condition to alleviate the interrelation between the stochastic Lyapunov matrix and system matrices containing controller variables, which results in a tractable LMI-based condition for the existence of reliable and robust H∞ fuzzy controllers. A suboptimal fuzzy controller is proposed to minimize the level of disturbance attenuation subject to the LMI constraints. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Shared Fuzzy Control of Multiple Quadrotor UAVs With Time-Dependent Delay and Bounded Control-Input Constraint

2015 ◽  
Author(s):  
Mark D. Johnson ◽  
Mohammad A. Ayoubi
Keyword(s):  
Fuzzy Control ◽  
Attitude Control ◽  
Fuzzy Controller ◽  
Equations Of Motion ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Control Input ◽  
Maximum Magnitude ◽  
Time Varying ◽  
Bounded Control

We propose a shared fuzzy controller for position and attitude control of multiple quadrotor unmanned aerial vehicles (UAVs). Using the nonlinear governing equations of motion and kinematics of a quadrotor, we develop a Takagi-Sugeno (T-S) fuzzy model for a quadrotor. Then, we consider time-varying delays due to wireless connectioninto the T-S fuzzy model. We use the sufficient stability condition based on the Lyapunov-Krasovskii stability theorem and the parallel distributed compensation (PDC) technique to determine the fuzzy control law. For practical purposes, we include actuator amplitude constraint into the design process. The problem of designing a shared fuzzy controller is cast in the form of linear matrix inequalities (LMIs). A feasible solution region is found in terms of maximum magnitude and rate of time-varying delay. In the end, the stability, performance, and robustness of the proposed shared fuzzy controller are examined via numerical simulation.

scholarly journals Nonlinear modelling and optimal control via Takagi-Sugeno fuzzy techniques: A quadrotor stabilization

2020 ◽  
Vol 71 (1) ◽  
pp. 1-10
Author(s):  
Miroslav Pokorný ◽  
Tomáš Dočekal ◽  
Danica Rosinová
Keyword(s):  
Closed Loop ◽  
Fuzzy Controller ◽  
Fitness Function ◽  
Fuzzy Model ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Fuzzy Aggregation ◽  
Takagi Sugeno

AbstractUsing the principles of Takagi-Sugeno fuzzy modelling allows the integration of flexible fuzzy approaches and rigorous mathematical tools of linear system theory into one common framework. The rule-based T-S fuzzy model splits a nonlinear system into several linear subsystems. Parallel Distributed Compensation (PDC) controller synthesis uses these T-S fuzzy model rules. The resulting fuzzy controller is nonlinear, based on fuzzy aggregation of state controllers of individual linear subsystems. The system is optimized by the linear quadratic control (LQC) method, its stability is analysed using the Lyapunov method. Stability conditions are guaranteed by a system of linear matrix inequalities (LMIs) formulated and solved for the closed loop system with the proposed PDC controller. The additional GA optimization procedure is introduced, and a new type of its fitness function is proposed to improve the closed-loop system performance.

scholarly journals A probabilistic robust mixed H2/H∞ fuzzy control method for hypersonic vehicles based on reliability theory

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141775415 ◽  
Author(s):  
Xiaomeng Yin ◽  
Xinming Li ◽  
Lei Liu ◽  
Yongji Wang ◽  
Xing Wei
Keyword(s):  
Fuzzy Control ◽  
Flight Control ◽  
Control Method ◽  
Fuzzy Controller ◽  
Fuzzy Model ◽  
Control Design ◽  
Hypersonic Vehicle ◽  
Linear Matrix ◽  
Hypersonic Vehicles ◽  
Robust Fuzzy Controller

Achieving balance between robustness and performance is always a challenge in the hypersonic vehicle flight control design. In this research, we focus on dealing with uncertainties of the fuzzy control system from the viewpoint of reliability. A probabilistic robust mixed H2/ H∞ fuzzy control method for hypersonic vehicles is presented by describing the uncertain parameters as random variables. First, a Takagi–Sugeno fuzzy model is employed for the hypersonic vehicle nonlinear dynamics characteristics. Next, a robust fuzzy controller is developed by solving a reliability-based multi-objective linear matrix inequality optimization problem, in which the H2/ H∞ performance is optimized under the condition that the system is robustly reliable to uncertainties. By this method, the system performance and reliability can be taken into account simultaneously, which reduces the conservatism in the robust fuzzy control design. Finally, simulation results of a hypersonic vehicle demonstrate the feasibility and effectiveness of the presented method.

Further Results on T-S Fuzzy Controller Design Subject to Input Constraint

2008 ◽  
Vol 12 (2) ◽  
pp. 190-197 ◽  
Author(s):  
Hugang Han ◽  
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Fuzzy Model ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Input Constraint ◽  
Initial State ◽  
Control Gain ◽  
Matrix Variable ◽  
Takagi Sugeno

In general, when using the Takagi-Sugeno (T-S) fuzzy model to develop a control system, the state feedback control gain can be obtained by solving some linear matrix inequalities (LMIs). In this paper, we consider a class of nonlinear systems with input constraint (saturation). To obtain the control gain, we require to employ certain extra LMIs besides the general ones. As a result, all the LMIs are more conservative. At the same time, one of the extra LMIs confines the initial state to a region, which is referred to as an ellipsoid, and is relevant to a matrix variable in the LMIs. Therefore, the goals of this paper are: 1) making the ellipsoid as large as possible so that the initial state can be confined to the region easily and; 2) making all the LMIs more feasible to obtain the control gain.

State Feedback Stabilization in Nonlinear Time-Delay Systems

2002 ◽  
Vol 6 (3) ◽  
pp. 109-114
Author(s):  
Tsuyoshi Hori ◽  
◽  
Kazuo Tanaka
Keyword(s):  
Time Delay ◽  
Controller Design ◽  
Fuzzy Model ◽  
Main Idea ◽  
Feedback Stabilization ◽  
Delay Systems ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Takagi Sugeno

In this paper, a class of nonlinear time-delay systems based on the Takagi-Sugeno (T-S) fuzzy model is defined. We investigate the delay-independent stability of this model. A model-based fuzzy stabilization design utilizing the concept of parallel distributed compensation (PDC) is employed. The main idea of the controller design is to derive each control rule to compensate each rule of a fuzzy system. Moreover, the problem of H∞ of this class of nonlinear time-delay systems is considered. The associated control synthesis problems are formulated as linear matrix inequality (LMI) problems.

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