Takagi-Sugeno Fuzzy Model Research Articles

상태 양자화를 고려한 쿼드로터의 샘플치 퍼지 상태 조정기 설계

In this paper, a method to design a sampled-data fuzzy regulator is proposed under state quantization. To this end, the attitude and altitude systems of a quadrotor are represented as the Takagi-Sugeno (T-S) fuzzy model. And then, the state regularization condition of each system are derived in the form of the linear matrix inequality (LMI) based on the Lyapunov-Krasovskii functional (LKF). When deriving the condition, we use the robust control technique to handle the uncertainties raised by the state quantization. Finally, the effectiveness of the proposed method is validated through the simulation example.

Attitude Control of a Flexible Spacecraft via Fuzzy Optimal Variance Technique

This paper investigates the performance of a fuzzy optimal variance control technique for attitude stability and vibration attenuation with regard to a spacecraft made of a rigid platform and multiple flexible appendages that can be retargeted to the line of sight. The proposed technique addresses the problem of actuators’ amplitude and rate constraints. The fuzzy model of the spacecraft is developed based on the Takagi-Sugeno(T-S) fuzzy model with disturbances, and the control input is designed using the Parallel Distributed Compensation technique (PDC). The problem is presented as an optimization problem in the form of Linear Matrix Inequalities (LMIs). The performance and the stability of the proposed controller are investigated through numerical simulation.

On the nonlinear output regulation for systems described by Takagi-Sugeno fuzzy descriptor models with a steady-state mapping as an LMI optimization problem


 
 
 This paper is devoted to provide a numerical solution the nonlinear output regulation problem for descriptor systems. The control law under design is a nonlinear one, it consists on a nonlinear stabilizer combined with linear steady-state mapping as well as nonlinear steady-state input mapping; all of them are computed via linear matrix inequalities. A numerical example as well as a mechanical system as well are used to illustrate the viability of the proposed approach.
 
 

Fuzzy observer-based fault detection for wind turbines using the finite-frequency approach

ABSTRACT This research investigates the synthesis of a new Finite Frequency Observer (FFO) to detect faults affecting wind turbines. First, the wind turbine nonlinear behaviour is approximated using Takagi-Sugeno (T-S) fuzzy modelling technique for observer design purposes. Then, through the H-/H∞ optimisation technique with Finite Frequency (FF) specification, the FFO design conditions are formulated using the Lyapunov method as a set of LMIs. Finally, to assess the efficiency of the FFO-based detection approach, simulations results are applied to a dynamic 4.8 MW WT model, where an Unknown Input Observer method is used for comparison.

Adaptive Optimal Multi-Surface Back-Stepping Sliding Mode Control Design for the Takagi-Sugeno Fuzzy Model of Uncertain Nonlinear System With External Disturbance

This paper proposes a novel scheme of the multi-objective robust control design for a class of uncertain nonlinear systems in strict-feedback-form based on Takagi–Sugeno fuzzy model (TSFM). The nonlinear system contains both the matched and the unmatched uncertainties and also subjected to the external disturbances. The TSFM provides the generalization of the linear systems concepts to the nonlinear systems field in a convex framework. First, a new sliding surface is defined using a convex combination of the surfaces which are defined for each fuzzy rule consequence local linear subsystems. Then, their gains are designed optimally via a generalized eigenvalue problem (GEVP). Also, the upper-bounds of the matched and unmatched uncertainties are estimated using the adaptive update laws. The multi-objective control aims not only to satisfy the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization performance, but also, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability region is formulated to improve the transient response performance. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{2}$ </tex-math></inline-formula> -optimization characterization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> -stability design conditions are derived in terms of new linear matrix inequalities (LMIs) conditions. Finally, the effectiveness of the proposed approach is demonstrated by considering a comparative practical example.

Local Stabilization of Discrete-Time Nonlinear Systems

This article considers local stability analysis and local stabilization of discrete-time nonlinear systems represented by Takagi–Sugeno fuzzy models. Conditions are established using Lyapunov functions and controller gains that depend also on past samples. Together with the stability and design conditions, an estimate of the region of attraction is also determined. The developed conditions are discussed and illustrated on several examples.

Takagi–Sugeno Fuzzy Modeling and Control for Effective Robotic Manipulator Motion

Robotic manipulators are widely used in applications that require fast and precise motion. Such devices, however, are prompt to nonlinear control issues due to the flexibility in joints and the friction in the motors within the dynamics of their rigid part. To address these issues, the Linear Matrix Inequalities (LMIs) and Parallel Distributed Compensation (PDC) approaches are implemented in the Takagy-Sugeno Fuzzy Model (T-SFM). We propose the following methodology; initially, the state space equations of the nonlinear manipulator model are derived. Next, a Takagy-Sugeno Fuzzy Model (T-SFM) technique is used for linearizing the state space equations of the nonlinear manipulator. The T-SFM controller is developed using the Parallel Distributed Compensation (PDC) method. The prime concept of the designed controller is to compensate for all the fuzzy rules. Furthermore, the Linear Matrix Inequalities (LMIs) are applied to generate adequate cases to ensure stability and control. Convex programming methods are applied to solve the developed LMIs problems. Simulations developed for the proposed model show that the proposed controller stabilized the system with zero tracking error in less than 1.5 s.

Modelling of Iron Ore Processing in Technological Units Based on the Hybrid Approach

Abstract The process line of concentrating iron ore materials is considered as a sequence of connected concentration units, some of which partially return ore materials to the previous unit. The output product of the final concentration unit in the process line is the end product of the whole line. Characteristics of ore, such as distribution of ore particles by size and distribution of iron content by size classes, are considered. Processing of iron ore materials by process units (a cycle, a scheme) is characterised by a separation characteristic – namely the function of extracting elementary fractions depending on physical properties of ore particles. The results of fraction analysis of ore samples in different points of the process line provide an experimental definition of separation characteristics and numerical values of the Rosin–Rammler equation factors. To identify dependencies that cannot be analytically described, the hybrid approach accompanied by the Takagi–Sugeno fuzzy models, in accompaniment with triangular membership functions determining fuzzy sets in preconditions, are used. To identify fuzzy sets in rule preconditions, triangular membership functions are used. Introduction of a-priori data on iron ore concentration as constraints for model parameters is a promising trend of further research, since it enables increased accuracy of identification despite limited availability of experimental data.

Identification and control of a heat flow system based on the Takagi-Sugeno fuzzy model using the grey wolf optimization algorithm

Even though, it is mostly used by process control engineers, the temperature control remains an important task for researchers. This paper addressed two separate issues concerning model optimization and control. Firstly, the linear models for the three different operating points of the heat flow system were found. From these identified models a Takagi-Sugeno model is obtained using fixed membership functions in the premises of the rules. According to the chosen objective function, parameters in the premise part of Takagi-Sugeno fuzzy model were optimized using the grey wolf algorithm. Furthermore, by using the parallel distributed compensation a fuzzy controller is developed via the fuzzy blending of three proportional + sum controllers designed for each of the operating points. In order to evaluate performance, a comparison is made between the fuzzy controller and local linear controllers. Moreover, the fuzzy controllers from the optimized and initial Takagi-Sugeno plant models are compared. The experimental results on a heat flow platform are presented to validate efficiency of the proposed method.

Nonlinear Time-Delay Observer-Based Control to Estimate Vehicle States: Lateral Vehicle Model

This paper deals with the state estimation and control problem for nonlinear lateral vehicle dynamics with time delays. First, a novel time-varying delay vehicle model described as a Takagi-Sugeno fuzzy model is presented. In particular, it is considered that the lateral force contains an air resistance term which is assumed to be a quadratic function of the lateral vehicle velocity. A time-varying delay has been included in the vehicle states by a simple formula in order to capture brake actuation aspects or other practical aspects that may generate a delayed response, while the nonlinear part of the vehicle model is described as a Lipschitz function. A Takagi-Sugeno time-delay observer-based control that satisfies the Lipschitz condition is proposed to get closed-loop stability conditions. These results generalize existing ones in the literature on lateral dynamics control. Additionally, we provide a new methodology for the controller and observer gains design that can be cast as linear matrix inequality constraints. Finally, we illustrate our results with numerical examples, which also reveal the negative effect of not considering the presence of delays in the controller design.

Dynamics and Model Predictive Control of Current-Fed Dickson Voltage Multiplier: TS Fuzzy Approach

This study presents a new approach to modeling and control the current-fed Dickson voltage multiplier (CF-DVM). The capacitor voltage relation and the input current are obtained. As all switching intervals are considered in detail, a highly accurate dynamic model is obtained, which can be easily extended for a CF-DVM with an arbitrary number of stages. Using the precise extracted model, the Takagi-Sugeno fuzzy model (TSFM) of the CF-DVM is provided, which is an exact equivalent representation of the CF-DVM nonlinear model. Then, a highly accurate and responsive model predictive controller (MPC) is designed based on an obtained TSFM of the CF-DVM to control the output voltage in an optimal and constrained manner. To obtain the control signal, the suggested optimization problem is converted to a quadratic programming (QP)-based problem which has a low online computational burden. Moreover, the performance of the proposed MPC is compared with the PI controller and the linear MPC. Finally, the simulation and experimental results demonstrate the promising merits of the proposed model and control approaches.

Observer-Based Output Feedback Control of Nonlinear 2-D Systems via Fuzzy-Affine Models

Through Takagi-Sugeno fuzzy affine models, the observer-based output feedback control of discrete-time nonlinear two-dimensional systems is investigated, where the two-dimensional system information evolves dynamically along two independent directions. A piecewise fuzzy affine observer is designed to estimate the unmeasurable system states, and two enhanced observer-based piecewise output feedback control approaches are then developed. By making sufficient use of Young&#x2019;s matrix inequality with its variant, novel and less conservative observer-based piecewise output feedback controller design results are proposed via piecewise quadratic Lyapunov functions. Simulation studies on a doubly-indexed nonlinear process are provided to illustrate the effectiveness of the developed approaches.

PI Observer-Based Fault-Tolerant Tracking Controller for Automobile Active Suspensions

The objective of this paper is to retain the desirable dynamics performances and improve ride quality for active suspensions with the actuator faults and unknown road disturbances. To that end, a novel proportional-integral observer (PIO)-based fault-tolerant tracking controller (FTTC) design is proposed for automobile active suspensions (ASSs) encountered with actuator faults and parameter uncertainties. First, the Takagi-Sugeno (T-S) fuzzy model approach is adopted to establish T-S representation of the faulty ASSs by describing vehicle dynamics system as the weighed summation of a common linear system. Afterwards, a nominal robust H∞ output feedback controller is developed to enhance the suspension performances under fault-free mode, whose output response indicators are taken as the prescribed reference trajectories. Then, a PIO-based fault estimator is designed to predict both the system states and the unmeasurable actuator faults, synchronously. On basis of this designed observer, the expected PIO-FTTC is synthesized to track the prescribed reference trajectories, and further to make up for the system performance deteriorations aroused by the actuator faults. Finally, a simulative investigation demonstrates the effectiveness and feasibility of the proposed PIO-FTTC compared to existing control approach.

Adaptive Internal Model Control of SCR Denitration System Based on Multi-Objective Optimization

Many thermal power plants use selective catalytic reduction (SCR) systems to complete flue gas denitration. The system has the characteristics of large inertia, large delay and nonlinearity. At the same time, it is difficult to use the controller under a single working condition to meet the control task of the system under the full working conditions. In order to solve the above control difficulties, This paper proposes a two-degree-of-freedom internal model control (2-DOF-IMC) method based on controller parameter adaptation and multi-model adaptation to realize the control of the full working conditions of the SCR system. First, the intelligent identification method based on Differential evolution quantum particle swarm optimization (DEQPSO) is used to obtain the sub-model of ammonia injection-SCR outlet Nitrogen Oxide (NOx) concentration in typical working conditions. A 2-DOF-IMC controller under each sub-model is established. Then, aiming at system set point tracking performance, anti-disturbance performance, and control energy consumption, the Pareto optimal solution of each controller is obtained by using the Non-dominated Sorting Genetic Algorithms-II (NSGA-II) algorithm based on chaotic mutation. Finally, the controller parameter adaptive strategy is designed based on the Takagi-Sugeno (T-S) fuzzy model, and the multi-model adaptive strategy is designed based on the recursive bayesian probability weighting. Through the dynamic performance test and the anti-disturbance performance test, it is verified that the 2-DOF-IMC based on controller parameter adaptation and multi-model adaptation has good control performance and adaptability to all working conditions. The method proposed in this paper combines the advantages of multi-parameter and multi-model strategies, further improves the control quality, and provides a new solution for the control of thermal power plant SCR system.

Control of Time Delay in Magnetic Levitation Systems

The high-performance control of magnetic levitation (maglev) vehicles has encountered challenges in the form of time delays. In this letter, we model a reliable control method based on a Takagi-Sugeno fuzzy model aimed at solving the problem of air gap control of a magnetic levitation system for a maglev vehicle under time-delay conditions. The key idea is based on the global fuzzy model derived through sector nonlinearity to design a global controller utilizing the parallel distributed compensation method and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> method. As a result, the stability of the system is guaranteed under conditions of mass parameter uncertainty, disturbance, and time delay. The theoretical analysis, numerical simulations, and experimental results consistently show the effectiveness of the control method.

Output feedback Takagi-Sugeno fuzzy model predictive control through linear matrix inequalities approaches

Output feedback Takagi-Sugeno fuzzy model predictive control through linear matrix inequalities approaches

Output feedback Takagi-Sugeno fuzzy model predictive control through linear matrix inequalities approaches

Output feedback Takagi-Sugeno fuzzy model predictive control through linear matrix inequalities approaches

Development of Fuzzy Observer Gain Design Algorithm for Ship Path Estimation Based on AIS Data

This paper develops a Takagi-Sugeno fuzzy observer gain design algorithm to estimate ship motion based on Automatic Identification System (AIS) data. Nowadays, AIS data is widely applied in the maritime field. To solve the problem of safety, it is necessary to accurately estimate the trajectory of ships. Firstly, a nonlinear ship dynamic system is considered to represent the dynamic behaviors of ships. In the literature, nonlinear observer design methods have been studied to estimate the ship path based on AIS data. However, the nonlinear observer design method is challenging to create directly since some dynamic ship systems are more complex. This paper represents nonlinear ship dynamic systems by the Takagi-Sugeno fuzzy model. Based on the Takagi-Sugeno fuzzy model, a fuzzy observer design method is developed to solve the problem of estimating using AIS data. Moreover, the observer gains of the fuzzy observer can be adjusted systemically by a novel algorithm. Via the proposed algorithm, a more suitable or better observer can be obtained to achieve the objectives of estimation. Corresponding to different AIS data, the better results can also be obtained individually. Finally, the simulation results are presented to show the effectiveness and applicability of the proposed fuzzy observer design method. Some comparisons with the previous nonlinear observer design method are also given in the simulations.

Continuous Stability TS Fuzzy Systems Novel Frame Controlled by a Discrete Approach and Based on SOS Methodology

Generally, the continuous and discrete TS fuzzy systems’ control is studied independently. Unlike the discrete systems, stability results for the continuous systems suffer from conservatism because it is still quite difficult to apply non-quadratic Lyapunov functions, something which is much easier for the discrete systems. In this paper and in order to obtain new results for the continuous case, we proposed to connect the continuous with the discrete cases and then check the stability of the continuous TS fuzzy systems by means of the discrete design approach. To this end, a novel frame was proposed using the sum of square approach (SOS) to check the stability of the continuous Takagi Sugeno (TS) fuzzy models based on the discrete controller. Indeed, the control of the continuous TS fuzzy models is ensured by the discrete gains obtained from the Euler discrete form and based on the non-quadratic Lyapunov function. The simulation examples applied for various models, by modifying the order of the Euler discrete fuzzy system, are presented to show the effectiveness of the proposed methodology.

On Optimal Test Signal Design and Parameter Identification Schemes for Dynamic Takagi-Sugeno Fuzzy Models Using the Fisher Information Matrix

This paper is concerned with the analysis of optimization procedures for optimal experiment design for locally affine Takagi-Sugeno (TS) fuzzy models based on the Fisher Information Matrix (FIM). The FIM is used to estimate the covariance matrix of a parameter estimate. It depends on the model parameters as well as the regression variables. Due to the dependency on the model parameters good initial models are required. Since the FIM is a matrix, a scalar measure of the FIM is optimized. Different measures and optimization goals are investigated in three case studies.