Intelligent control of a class of nonlinear systems

The objective of this study is to improve and propose new fuzzy control algorithms for a class of nonlinear systems. In order to achieve the objectives, novel stability theorems as well as modeling techniques are also investigated. Fuzzy controllers in this work are designed based on the fuzzy basis function neural networks and the type-2 Takagi-Sugeno fuzzy models. For a class of single-input single-output nonlinear systems, a new stability condition is derived to facilitate the design process of proportional-integral Mamdani fuzzy controllers. The stability conditions require a new technique to calculate the dynamic gains of nonlinear systems represented by fuzzy basis function network models. The dynamic gain of a fuzzy basis function network can be approximated by finding the maximum of norm values of the locally linearized systems or by solving a non-smooth optimal control problem. Based on the new stability theorem, a multilevel fuzzy controller with self-tuning algorithm is proposed and simulated in a tower crane control system. For a class of multi-input multi-output nonlinear systems with measurable state variables, a new method for modeling unstructured uncertainties and robust control of unknown nonlinear dynamic systems is proposed by using a novel robust Takagi-Sugeno fuzzy controller. First, a new training algorithm for an interval type-2 fuzzy basis function network is presented. Next, a novel technique is derived to convert the interval type-2 fuzzy basis function network to an interval type-2 Takagi-Sugeno fuzzy model. Based on the interval type-2 Takagi-Sugeno and type-2 fuzzy basis function network models, a robust controller is presented with an adjustable convergence rate. Simulation results on an electrohydraulic actuator show that the robust Takagi-Sugeno fuzzy controller can reduce steady-state error under different conditions while maintaining better responses than the other robust sliding mode controllers can. Next, the study presents an implementation of type-2 fuzzy basis function networks and robust Takagi-Sugeno fuzzy controllers to data-driven modeling and robust control of a laser keyhole welding process. In this work, the variation of the keyhole diameter during the welding process is approximated by a type-2 fuzzy-basis-function network, while the keyhole penetration depth is modelled by a type-1 fuzzy basis function network. During the laser welding process, a CMOS camera integrated with the welding system was used to provide a feedback signal of the keyhole diameter. An observer was implemented to estimate the penetration depth in real time based on the adaptive divided difference filter and the feedback signal from the camera. A robust Takagi-Sugeno fuzzy controller was designed based on the fuzzy basis function networks representing the welding process with uncertainties to adjust the laser power to ensure that the penetration depth of the keyhole is maintained at a desired value. Experimental results demonstrated that the fuzzy models provided an accurate estimation of both the welding geometry and its variations due to uncertainties, and the robust Takagi-Sugeno fuzzy controller successfully reduced the penetration depth variation and improved the quality of the welding process

Устойчивость нечетких импульсных систем Такаги–Сугено: метод линейных матричных неравенств

The Lyapunov stability of impulsive Takagi-Sugeno fuzzy systems is considered. The sufficient conditions of stability for impulsive fuzzy systems are derived on the basis of Lyapunov’s direct method. They can be easily expressed as a system of linear matrix inequalities

Fuzzy Controller Design for Nonlinear Systems

In this article is studied problem of Fuzzy Controller Design For Nonlinear Systems With Case Study Of TORA System. Fuzzy control for nonlinear systems is proposed on the framework from model of Takagi-Sugeno fuzzy model and PDC(paralel distributed compensation) controller. A lyapanouv-based stabilizing fuzzy control design for nonlinear systems using Takagi-Sugeno fuzzy models is applied. The stability analysis and control design problems are reduced to linear of matrix inequality (LMI) problems. So that method of fuzzy controller design are solve a set of LMI. Approach of PDC, robust and optimal controller are applied to a nonlinear control benchmark problem with case study of TORA system. The designed fuzzy controllers are yield an asymtotic stable closed-loop system. The fuzzy controller Simulation results are given to ilustrate the utility of the present fuzzy control

A CENTER MANIFOLD THEORY-BASED APPROACH TO THE STABILITY ANALYSIS OF STATE FEEDBACK TAKAGI-SUGENO-KANG FUZZY CONTROL SYSTEMS

The aim of this paper is to propose a stability analysis approach based on the application of the center manifold theory and applied to state feedback Takagi-Sugeno-Kang fuzzy control systems. The approach is built upon a similar approach developed for Mamdani fuzzy controllers. It starts with a linearized mathematical model of the process that is accepted to belong to the family of single input second-order nonlinear systems which are linear with respect to the control signal. In addition, smooth right-hand terms of the state-space equations that model the processes are assumed. The paper includes the validation of the approach by application to stable state feedback Takagi-Sugeno-Kang fuzzy control system for the position control of an electro-hydraulic servo-system

Fuzzy Model Based Solving Nonlinear Systems with Case Study of Truck-trailer System

In this paper, we consider the fuzzy controller problem for nonlinear system using fuzzy models. The controller is constructed using a design model of the dynamical process to be controlled. The design model obtained from the truth model using a fuzzy modeling approach. The Takagi-Sugeno fuzzy model is adopted for fuzzy modeling of the nonlinear system. The truth model represents a detailed description of the process dynamic. The model is used in a simulation to evaluate the performance of the controller design. Stabilization of the closed-loop discrete Takagi-Sugeno systems using the well-known PDC (Paralel Distributed Compensation) technique is investigated. The design procedure we adopt is to convert the design of the controller to a Linear Matrix Inequality (LMI) problem so that the stability of the whole system can be assured

Robust Multi-Criteria Optimal Fuzzy Control of Continuous-Time Nonlinear Systems

This paper presents a novel fuzzy control design of continuous-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with inherent stability property together with dissipativity type of disturbance reduction. The Takagi– Sugeno fuzzy model is used in our control system design. By solving the linear matrix inequality at each time step, the control solution can be found to satisfy the mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system

О спектральных условиях устойчивости нечетких систем Такаги–Сугено

Одержано достатнi умови стiйкостi дискретних та iмпульсних нечiтких систем Такагi–Сугено. Умови стiйкостi одержанi у виглядi обмежень на спектри деяких лiнiйних операторiв.The sufficient conditions for the stability of discrete and impulsive Takagi–Sugeno fuzzy systems are derived. The stability conditions are expressed in the form of limitations on the spectra of some linear operators

On the interpretation and identification of dynamic Takagi-Sugenofuzzy models

Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples

Robust Multi-Criteria Optimal Fuzzy Control of Discrete-Time Nonlinear Systems

This paper presents a novel fuzzy control design of discrete-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with an inherent stability property together with a dissipativity type of disturbance reduction. The Takagi–Sugeno-type fuzzy model is used in our control system design. By solving a linear matrix inequality at each time step, the optimal control solution can be found to satisfy mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system on a cart