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 Design of Explicit Fuzzy Prediction Controller for Constrained Nonlinear Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Yan Yan ◽  
Baili Su
Keyword(s):  
Nonlinear Systems ◽  
Predictive Control ◽  
Control Method ◽  
Fuzzy Model ◽  
Main Idea ◽  
Closed Loop System ◽  
Nonlinear Predictive Control ◽  
Predictive Controller ◽  
Constrained Nonlinear Systems ◽  
Fuzzy Predictive Control

This paper presents an explicit fuzzy predictive control method for a class of nonlinear systems with constrained inputs. The main idea is to construct a terminal invariant set and explicit predictive controller with affine input on the basis of T-S fuzzy model. This method need not compute the complex nonconvex nonlinear programming problem of earlier nonlinear predictive control methods and decreases the number of optimization variables and guarantees stability of the closed-loop system. The simulation results on a numerical example show the validity of the method presented in this paper.

Fuzzy Based Model Predictive Control for Uncertain Nonlinear System

2011 ◽  
Vol 383-390 ◽  
pp. 2404-2410
Author(s):  
Li Xu ◽  
Fei Liu
Keyword(s):  
Nonlinear System ◽  
Model Predictive Control ◽  
Predictive Control ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Uncertain Nonlinear System ◽  
Predictive Controller ◽  
The Stability ◽  
Takagi Sugeno ◽  
Parameter Dependent

In this paper, a model predictive control (MPC) scheme is investigated for uncertain nonlinear system with time delay and input constraint. First, the Takagi-Sugeno (T-S) fuzzy model is used to approximate the dynamics of nonlinear processes and the parallel distributed compensation (PDC) controllers which are parameter dependent and mirror the structure of the T-S plant model are proposed. Then a novel feedback PDC predictive controller obtained from the linear matrix inequality (LMI) solutions which can guarantee the stability of the closed-loop overall fuzzy system is put forward. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed method.

Direct Adaptive Fuzzy Predictive Control and its Application to CSTR Process

2012 ◽  
Vol 241-244 ◽  
pp. 1191-1194
Author(s):  
Cheng Li Su ◽  
Ma Lina ◽  
Ping Li
Keyword(s):  
Predictive Control ◽  
Fuzzy Model ◽  
Least Square ◽  
Effective Control ◽  
Continuous Stirred Tank Reactor ◽  
Recursive Least Square ◽  
On Line ◽  
S Model ◽  
Takagi Sugeno ◽  
Fuzzy Predictive Control

In order to obtain accurate prediction model and avoid solving nonlinear programming problem, a direct adaptive predictive control (DAPC) method is proposed. Firstly, a nonlinear system was described based on Takagi-Sugeno (T-S) fuzzy models. Assuming that that the antecedent parameters of T-S models were kept, the consequent parameters were identified on-line by using the weighted recursive least square (WRLS) method. Secondly, the identified parameters of fuzzy model were used to directly receive the model predicted output with direct iterative for the T-S model. Finally, the application results for continuous stirred tank reactor (CSTR) process show that the proposed algorithm is an effective control strategy with excellent tracing ability. The proposed algorithm is a good way to resolve the two major problems, modeling and optimization, and provides a guarantee for high-precision control of nonlinear systems.

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.

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.

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