A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Design and Implementation of Takagi-Sugeno Fuzzy Tracking Control for a DC-DC Buck Converter

This paper presents the design and implementation of a Takagi-Sugeno (T-S) fuzzy controller for a DC-DC buck converter using Arduino board. The proposed fuzzy controller is able to pilot the states of the buck converter to track a reference model. The T-S fuzzy model is employed, firstly, to represent exactly the dynamics of the nonlinear buck converter system, and then the considered controller is designed on the basis of a concept called Virtual Desired Variables (VDVs). In this case, a two-stage design procedure is developed: i) determine the reference model according to the desired output voltage, ii) determine the fuzzy controller gains by solving a set of Linear Matrix Inequalities (LMIs). A digital implementation of the proposed T-S fuzzy controller is carried out using the ATmega328P-based Microcontroller of the Arduino Uno board. Simulations and experimental results demonstrate the validity and effectiveness of the proposed control scheme

A layered fuzzy logic controller for nonholonomic car-like robot

A system for real time navigation of a nonholonomic car-like robot in a dynamic environment consists of two layers is described: a Sugeno-type fuzzy motion planner; and a modified proportional navigation based fuzzy controller. The system philosophy is inspired by human routing when moving between obstacles based on visual information including right and left views to identify the next step to the goal. A Sugeno-type fuzzy motion planner of four inputs one output is introduced to give a clear direction to the robot controller. The second stage is a modified proportional navigation based fuzzy controller based on the proportional navigation guidance law and able to optimize the robot's behavior in real time, i.e. to avoid stationary and moving obstacles in its local environment obeying kinematics constraints. The system has an intelligent combination of two behaviors to cope with obstacle avoidance as well as approaching a target using a proportional navigation path. The system was simulated and tested on different environments with various obstacle distributions. The simulation reveals that the system gives good results for various simple environments

Comparative Study of Takagi-Sugeno-Kang and Madani Algorithms in Type-1 and Interval Type-2 Fuzzy Control for Self-Balancing Wheelchairs

This study examines the effectiveness of four different fuzzy logic controllers in self-balancing wheelchairs. The controllers under consideration are Type-1 Takagi-Sugeno-Kang (TSK) FLC, Interval Type-2 TSK FLC, Type-1 Mamdani FLC, and Interval Type-2 Mamdani FLC. A MATLAB-based simulation environment serves for the evaluation, focusing on key performance indicators like percentage overshoot, rise time, settling time, and displacement. Two testing methodologies were designed to simulate both ideal conditions and real-world hardware limitations. The simulations reveal distinct advantages for each controller type. For example, Type-1 TSK excels in minimizing overshoot but requires higher force. Interval Type-2 TSK shows the quickest settling times but needs the most force. Type-1 Mamdani has the fastest rise time with the lowest force requirement but experiences a higher percentage of overshoot. Interval Type-2 Mamdani offers balanced performance across all metrics. When a 2.7 N control input cap is imposed, Type-2 controllers prove notably more efficient in minimizing overshoot. These results offer valuable insights for future design and real-world application of self-balancing wheelchairs. Further studies are recommended for the empirical testing and refinement of these controllers, especially since the initial findings were limited to four-wheeled self-balancing robotic wheelchairs

PSO BASED TAKAGI-SUGENO FUZZY PID CONTROLLER DESIGN FOR SPEED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTOR

A permanent magnet synchronous motor (PMSM) is one kind of popular motor. They are utilized in industrial applications because their abilities included operation at a constant speed, no need for an excitation current, no rotor losses, and small size. In the following paper, a fuzzy evolutionary algorithm is combined with a proportional-integral-derivative (PID) controller to control the speed of a PMSM. In this structure, to overcome the PMSM challenges, including nonlinear nature, cross-coupling, air gap flux, and cogging torque in operation, a Takagi-Sugeno fuzzy logic-PID (TSFL-PID) controller is designed. Additionally, the particle swarm optimization (PSO) algorithm is developed to optimize the membership functions' parameters and rule bases of the fuzzy logic PID controller. For evaluating the proposed controller's performance, the genetic algorithm (GA), as another evolutionary algorithm, is incorporated into the fuzzy PID controller. The results of the speed control of PMSM are compared. The obtained results demonstrate that although both controllers have excellent performance; however, the PSO based TSFL-PID controller indicates more superiority

Variable structure control with chattering reduction of a generalized T-S model

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) is presented. The main objective is to obtain an improved performance of highly non-linear unstable systems. New functions for chattering reduction and error convergence without sacrificing invariant properties are proposed. The main feature of the proposed method is that the switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules; together with the state variables. In this work, a tuning of the well known weighting parameters approach is proposed to optimize local and global approximation and modelling capability of the Takagi-Sugeno (T-S) fuzzy model to improve the choice of the performance index and minimize it. The main problem encountered is that the T-S identification method can not be applied when the membership functions are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. The approach developed here can be considered as a generalized version of the T-S method. An inverted pendulum mounted on a cart is chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of the proposed estimation approach in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the estimation method and the robustness of the chattering reduction algorithm. In this paper, we prove that the proposed estimation algorithm converge the very fast, thereby making it very practical to use. The application of the proposed FLC-VSC shows that both alleviation of chattering and robust performance are achieved

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

Variable structure control with chattering elimination and guaranteed stability for a generalized T-S model

In this paper, a fuzzy based Variable Structure Control (VSC) with guaranteed stability is presented. The main objective is to obtain an improved performance of highly non-linear unstable systems. The main contribution of this work is that, firstly, new functions for chattering reduction and error convergence without sacrificing invariant properties are proposed, which is considered the main drawback of the VSC control. Secondly, the global stability of the controlled system is guaranteed.The well known weighting parameters approach, is used in this paper to optimize local and global approximation and modeling capability of T-S fuzzy model.A one link robot is chosen as a nonlinear unstable system to evaluate the robustness, effectiveness and remarkable performance of optimization approach and the high accuracy obtained in approximating nonlinear systems in comparison with the original T-S model. Simulation results indicate the potential and generality of the algorithm. The application of the proposed FLC-VSC shows that both alleviation of chattering and robust performance are achieved with the proposed FLC-VSC controller. The effectiveness of the proposed controller is proven in front of disturbances and noise effects