scholarly journals H∞ Control for T-S Fuzzy Singularly Perturbed Switched Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Qianjin Wang ◽  
Linna Zhou ◽  
Wei Dai ◽  
Xiaoping Ma
Keyword(s):  
Switched Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Design Method ◽  
Average Dwell Time ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Function Technique ◽  
Pendulum System ◽  
Inverted Pendulum System

This paper is concerned with the design of fuzzy controller with guaranteed H∞ performance for a class of Takagi-Sugeno (T-S) fuzzy singularly perturbed switched systems. First, by using the average dwell time approach together with the piecewise Lyapunov function technique, a state feedback controller that depends on the singular perturbation parameter ε is developed. This controller is shown to work well for all ε∈(0,ε0]. Then, for sufficiently small ε, an ε-independent controller design method is proposed. Furthermore, under the ε-independent controller, the ε-bound estimation problem of the overall switched closed-loop system is solved. Finally, an inverted pendulum system is used to evaluate the feasibility and effectiveness of the obtained results.

scholarly journals Fuzzy Controllers for Nonaffine-in-Control Singularly Perturbed Switched Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Linna Zhou ◽  
Qianjin Wang ◽  
Xiaoping Ma ◽  
Chunyu Yang
Keyword(s):  
Switched Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Design Method ◽  
Singularly Perturbed ◽  
Dynamic State ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Stability Bound ◽  
Takagi Sugeno

This paper investigates the problem of fuzzy controller design for nonaffine-in-control singularly perturbed switched systems (NCSPSSs). First, the NCSPSS is approximated by Takagi-Sugeno (T-S) models which include not only state but also control variables in the premise part of the rules. Then, a dynamic state feedback controller design method is proposed in terms of linear matrix inequalities. Under the controller, stability bound estimation problem of the closed-loop system is solved. Finally, an example is given to show the feasibility and effectiveness of the obtained methods.

Model-Based Fuzzy Controller Design With Common Observability Gramian Assignment

1998 ◽  
Vol 123 (1) ◽  
pp. 113-116 ◽  
Author(s):  
Wen-Jer Chang
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Design Method ◽  
Pendulum System ◽  
Model Based ◽  
Inverted Pendulum System ◽  
Present Design ◽  
Almost All ◽  
Observability Gramian

Almost all robust properties of linear systems can be related directly to properties of the controllability or observability Gramian. A model-based fuzzy controller for a class of uncertain nonlinear systems will be developed in this paper to achieve a common observability Gramian. Design of a model-based fuzzy controller begins by assigning a certain common observability Gramian. The nonlinear systems considered in this paper are represented by Takagi-Sugeno fuzzy models. An application to the inverted pendulum system will be given to demonstrate the effects of the present design method.

scholarly journals Passive Control andε-Bound Estimation of Singularly Perturbed Systems with Nonlinear Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Linna Zhou ◽  
Chunyu Yang
Keyword(s):  
Singular Perturbation ◽  
Passive Control ◽  
Controller Design ◽  
Design Method ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Storage Function ◽  
Rlc Circuit ◽  
Perturbed Systems

This paper considers the problems of passivity analysis and synthesis of singularly perturbed systems with nonlinear uncertainties. By a novel storage function depending on the singular perturbation parameterε, a new method is proposed to estimate theε-bound, such that the system is passive when the singular perturbation parameter is lower than theε-bound. Furthermore, a controller design method is proposed to achieve a predefinedε-bound. The proposed results are shown to be less conservative than the existing ones because the adopted storage function is more general. Finally, an RLC circuit is presented to illustrate the advantages and effectiveness of the proposed methods.

Indirect Adaptive Fuzzy H∞ Tracking Control with Self-Structuring Algorithm for a Class of Uncertain Nonlinear SISO Systems

2013 ◽  
Vol 756-759 ◽  
pp. 622-626
Author(s):  
Sen Xu ◽  
Zhang Quan Wang ◽  
You Rong Chen ◽  
Ban Teng Liu ◽  
Lu Yao Xu
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Pendulum System ◽  
Single Input Single Output ◽  
Adaptive Fuzzy ◽  
Single Output ◽  
Inverted Pendulum System ◽  
Single Input ◽  
Indirect Adaptive Fuzzy Controller ◽  
Siso Systems

Indirect adaptive fuzzy controller with a self-structuring algorithm is proposed in this paper to achieve tracking performance for a class of uncertain nonlinear single-input single-output (SISO) systems with external disturbances. Selecting membership functions and the fuzzy rules are difficult in fuzzy controller design. As a result, self-structuring algorithm is used in this paper, which simplifies the design of fuzzy controller. Lyapunov analysis is used to prove asymptotic stability of the proposed approach. Application of the proposed control scheme to a second-order inverted pendulum system demonstrates the effectiveness of the proposed approach.

scholarly journals Actuator Saturated Fuzzy Controller Design for Interval Type-2 Takagi-Sugeno Fuzzy Models with Multiplicative Noises

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 823
Author(s):  
Wen-Jer Chang ◽  
Yu-Wei Lin ◽  
Yann-Horng Lin ◽  
Chin-Lin Pen ◽  
Ming-Hsuan Tsai
Keyword(s):  
Nonlinear Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Actuator Saturation ◽  
Design Method ◽  
Fuzzy Model ◽  
The Stability ◽  
Interval Type ◽  
Takagi Sugeno

In many practical systems, stochastic behaviors usually occur and need to be considered in the controller design. To ensure the system performance under the effect of stochastic behaviors, the controller may become bigger even beyond the capacity of practical applications. Therefore, the actuator saturation problem also must be considered in the controller design. The type-2 Takagi-Sugeno (T-S) fuzzy model can describe the parameter uncertainties more completely than the type-1 T-S fuzzy model for a class of nonlinear systems. A fuzzy controller design method is proposed in this paper based on the Interval Type-2 (IT2) T-S fuzzy model for stochastic nonlinear systems subject to actuator saturation. The stability analysis and some corresponding sufficient conditions for the IT2 T-S fuzzy model are developed using Lyapunov theory. Via transferring the stability and control problem into Linear Matrix Inequality (LMI) problem, the proposed fuzzy control problem can be solved by the convex optimization algorithm. Finally, a nonlinear ship steering system is considered in the simulations to verify the feasibility and efficiency of the proposed fuzzy controller design method.

Robust Stabilizing Controller Design for Inverted Pendulum System

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Hazem I. Ali
Keyword(s):  
Steady State ◽  
Time Domain ◽  
State Feedback ◽  
Inverted Pendulum ◽  
Controller Design ◽  
H Infinity ◽  
Pendulum System ◽  
Stabilizing Controller ◽  
Inverted Pendulum System ◽  
System Uncertainties

In this paper the design of robust stabilizing state feedback controller for inverted pendulum system is presented. The Ant Colony Optimization (ACO) method is used to tune the state feedback gains subject to different proposed cost functions comprise of H-infinity constraints and time domain specifications. The steady state and dynamic characteristics of the proposed controller are investigated by simulations and experiments. The results show the effectiveness of the proposed controller which offers a satisfactory robustness and a desirable time response specifications. Finally, the robustness of the controller is tested in the presence of system uncertainties and disturbance.

Fuzzy Control of an Inverted Pendulum

1996 ◽  
Author(s):  
Tuna Balkan ◽  
Mehmet Emin Ari
Keyword(s):  
Inverted Pendulum ◽  
Fuzzy Controller ◽  
Angular Position ◽  
Upright Position ◽  
Control Signal ◽  
Position Measurement ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
And Performance ◽  
The Stability

Abstract An inverted pendulum system has been designed and constructed as a physical model of inherently unstable mechanical systems. The vertical upright position of a pendulum is controlled by changing the horizontal position of a cart to which the pendulum is hinged. The stability of the system has been investigated when a fuzzy controller is used to produce the control signal, while making a single measurement. It has been shown that by using simple fuzzy rules to allow real time computation with a single angular position measurement, the system can not be made absolutely stable. However, the stability and performance of the system have been considerably improved by shrinking the membership functions of angular position, computed angular velocity and control signal when inverted pendulum is very close to the vertical upright position.

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