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Relaxed design conditions using Takagi-Sugeno fuzzy models and Lyapunov-Floquet transformation for controlling time-varying periodic systems

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JOURNAL OF VIBRATION AND CONTROL 2023年第19-20期29卷 4439-4454页

作者： Travassos, Marco A. Cardim, Rodrigo Teixeira, Marcelo Cm Assuncao, Edvaldo Sao Paulo State Univ Dept Elect Engn Ilha Solteira Brazil

This manuscript approaches the Takagi-Sugeno fuzzy control technique, the Lyapunov-Floquet transformation, and their applications for controlling linear time-varying systems. Each of the techniques is applied in the control of a linear time-varying periodic system in order to compare their effectiveness. A hybrid control method involving the Takagi-Sugeno fuzzy control and the Lyapunov-Floquet transformation is proposed. In this method, the stability of the closed-loop system is mathematically guaranteed. In addition, this new procedure can reduce the conservatism of time-varying periodic systems with uncertainties in the input matrix. Finally, an application of the hybrid method is presented in a time-varying periodic system considering a constraint on input and uncertainties on the input matrix.

关键词： fuzzy control Lyapunov-Floquet transformation time-varying periodic system parallel distributed compensation linear matrix inequalities

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IDENTIFICATION AND CONTROL OF A HEAT FLOW SYSTEM BASED ON THE TAKAGI-SUGENO FUZZY MODEL USING THE GREY WOLF OPTIMIZER

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THERMAL SCIENCE 2022年第3期26卷 2275-2286页

作者： Jovanovic, Radisa Z. Zaric, Vladimir R. Univ Belgrade Fac Mech Engn Belgrade Serbia

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.

关键词： temperature control grey wolf optimization algorithm parallel distributed compensation fuzzy control Takagi-Sugeno discrete-time systems

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Disturbance observer supported fuzzy model based controller with application to bilateral teleoperation systems

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022年第2期43卷 1911-1919页

作者： Asad, Muhammad Usman Gu, Jason Farooq, Umar Balas, Marius Chen, Zheng Qureshi, Khurram Karim Abbas, Ghulam Chang, Chunqi Dalhousie Univ Dept Elect & Comp Engn Halifax NS Canada Auriel Vlaicu Univ Arad Dept Informat Arad Romania Intelligent Syst Lab & Automat Facil ISLAF Lahore Pakistan Zhejiang Univ Ocean Coll Hangzhou Zhejiang Peoples R China King Fand Univ Petr & Minerals KFUPM Dept Elect Engn Dhahran Saudi Arabia Univ Lahore Dept Elect Engn Lahore Pakistan Shenzhen Univ Sch Biomed Engn Shenzhen Peoples R China

This paper proposes a disturbance observer supported Takagi-Sugeno (TS) fuzzy model-based control scheme for uncertain systems. The baseline controller is a guaranteed performance fuzzy model based parallel distributed controller (PDC) which is constructed using the nominal system's parameters. The model approximation error and parametric uncertainties are treated as a lumped disturbance and a nonlinear disturbance observer (NDOB) is introduced to counter the lumped disturbance. The applicability of the proposed scheme is demonstrated on the bilateral control of nonlinear teleoperation system in MATLAB/Simulink/QUARC environment through simulations as well as semi-real time experiments.

关键词： TS fuzzy modeling parallel distributed compensation state convergence teleoperation MATLAB/Simulink/QUARC

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Efficient Control of Rotary Inverted Pendulum Systems with T-S Fuzzy Descriptor Models

Efficient Control of Rotary Inverted Pendulum Systems with...

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International Conference on Intelligent Systems and Networks, ICISN 2024

作者： Dao, Quy-Thinh Pham, Duc-Binh Nguyen, Thi-Van-Anh Motion Control and Applied Robotics Laboratory Hanoi University of Science and Technology Hanoi Viet Nam

ISBN: (纸本)9789819755035

This research addresses the challenge of controlling rotary inverted pendulum systems, which are inherently unstable and nonlinear. We propose a control approach that integrates the Takagi-Sugeno (T-S) fuzzy descriptor system with parallel distributed compensation (PDC) and Linear Matrix Inequalities (LMIs). The T-S fuzzy control system offers a flexible and adaptive means of managing complex dynamics by partitioning the system into multiple operating regions using fuzzy sets and linguistic rules. Stability theorems and decay rate analysis ensure robust and rapid convergence to stability performance. PDC facilitates the design of control strategies for systems with multiple subsystems, broadening the applicability of our proposed methodology. This research promises to advance the field of rotary inverted pendulum control, with potential applications in robotics, automation, and mechatronics, where precise and agile control is imperative in the face of inherent instability. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

关键词： decay rate fuzzy control linear matrix inequality parallel distributed compensation Takagi-Sugeno descriptor model

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Dissipative Control for Single Flexible Joint Robotic System via T-S Fuzzy Modelling Approach 7th

Dissipative Control for Single Flexible Joint Robotic System...

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7th International Conference on Advances in Control and Optimization of Dynamical Systems (ACODS)

作者： Datta, Rupak Dey, Rajeeb Adhikari, Nabanita Natl Inst Technol Silchar Dept Elect Engn Silchar 788010 India

The dissipativity analysis for single flexible joint robotic system via Takagi-Sugeno (T-S) fuzzy modelling technique is the main focus of this paper. Our aim is to design a delayed state feedback controller by using parallel distributed compensation (PDC) so that the considered system is asymptotically stable with a phi(2), phi(3)) -gamma- dissipativity condition is derived in terms of linear matrix inequality (LMI) framework by constructing an appropriate Lyapunov Krasovskii functional (LKF) and using higher order polynomial based integral inequality (HOPBII) to estimate its derivative. Finally, numerical simulation result is given to show the effectiveness of the proposed theoretical method. Copyright (C) 2022 The Authors.

关键词： Dissipativity analysis Takagi-Sugeno fuzzy modelling parallel distributed compensation linear matrix inequality Lyapunov-Krasovskii functional

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Design of a Decoupling Fuzzy Control Scheme for Omnidirectional Inverted Pendulum Real-World Control

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IEEE ACCESS 2021年 9卷 26083-26092页

作者： Chiu, Chih-Hui Hung, Yao-Ting Peng, Ya-Fu Natl Taiwan Ocean Univ Dept Commun Nav & Control Engn Keelung 20224 Taiwan Chien Hsin Univ Dept Elect Engn Taoyuan 320 Taiwan

In this study, an omnidirectional inverted pendulum (ODIP) is controlled based on a dual Takagi-Sugeno (TS) fuzzy control scheme. The ODIP is a handmade system. It contains two subsystems. The lower mechanism system includes a brushless rim motor, a system platform, batteries, and an encoder. The upper mechanism system is mainly composed of a circuit system, a motor fixed platform, a motor, and a flywheel. The proposed controller combines two fuzzy control approaches for ODIP system control with disturbances and uncertainties. The core of the ODIP operating system is an embedded controller, which executes real-world control processes. Moreover, to address the coupling problem, the shafts of the two motors are oriented in orthogonal directions. Then, the two fuzzy controllers can be designed independently without coupling. In the proposed controller, the Takagi-Sugeno fuzzy model is adopted for fuzzy modeling of the ODIP. The conception of parallel distributed compensation (PDC) is utilized to develop fuzzy control from TS fuzzy models. The format of linear matrix inequalities (LMIs) can formulate sufficient conditions. The main contributions of this study are (1) the implementation of an ODIP and (2) the application of the proposed dual Takagi-Sugeno (TS) fuzzy control scheme for real-time control of the ODIP. Finally, the efficiency of the proposed control scheme is illustrated by the experimental results presented in this study.

关键词： Fuzzy control Control systems Acceleration Mathematical model Couplings Linear matrix inequalities Wheels Omnidirectional inverted pendulum TS~fuzzy control scheme parallel distributed compensation linear matrix inequality Lyapunov function embedded controller

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Improved stabilization criteria for Takagi-Sugeno fuzzy systems with variable delays

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INFORMATION SCIENCES 2021年 579卷 591-606页

作者： Datta, Rupak Saravanakumar, Ramasamy Dey, Rajeeb Bhattacharya, Baby Ahn, Choon Ki Natl Inst Technol Agartala Dept Math Agartala 799046 India Hiroshima Univ Grad Sch Adv Sci & Engn 1-4-1 Kagamiyama Higashihiroshima 7398527 Japan Natl Inst Technol Silchar Dept Elect Engn Silchar 788010 India Korea Univ Sch Elect Engn Anam Dong 5 Ga Seoul 136701 South Korea

In the present research, the stability analysis and stabilization of nonlinear processes characterized by the Takagi-Sugeno (T-S) fuzzy model with variable time delays have been investigated. The state's delay is presumed to belong to a given interval, ensuring that the delay lower limit is not constrained to zero. First, a new and improved integral inequality (II) lemma is proposed to deal with the cross-product terms in the derivative of the constructed delay-product-type (DPT) augmented Lyapunov-Krasovskii functional (LKF). Second, a novel delay-range-dependent (DRD) stability condition and parallel distributed compensation (PDC) technique-based stabilization condition is then achieved in terms of linear matrix inequalities (LMIs). Finally, to illustrate the superiority of the proposed stability criterion and controller design approach over existing ones, three numerical examples are given. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Takagi-Sugeno fuzzy model delay-product-type Lyapunov-Krasovskii functional integral inequality delay-range-dependent parallel distributed compensation

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Improved stabilization condition of delayed T-S fuzzy systems via an extended quadratic function negative-determination lemma

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CHAOS SOLITONS & FRACTALS 2023年第Part2期175卷

作者： Yang, Tianqing Zou, Runmin Liu, Fang Liu, Cai Sidorov, Denis Cent South Univ Sch Automat Changsha 410083 Hunan Peoples R China Irkutsk Natl Res Tech Univ Ind Math Lab Baikal Sch BRICS Lermontov Str 83 Irkutsk 664074 Russia

This paper focuses on the stability and stabilization problems of continuous-time T-S fuzzy systems (TSFS) with variable delay. A new augmented Lyapunov-Krasovskii functional (LKF) is established by combining the negative quadratic term with the alterable delay-product-integral term. To further improve the results, an extended quadratic function negative-determination (QFND) lemma is proposed to deal with delta(t)-related quadratic function in the LKF derivative. Subsequently, based on the parallel distributed compensation (PDC) technique, a bounded delay correlation stabilization criterion is derived. Finally, the proposed methods are applied to a numerical example and an inverted pendulum system to verify their effectiveness and superiority.

关键词： Stability and stabilization Quadratic function negative-determination lemma T-S fuzzy systems Variable delay parallel distributed compensation

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H∞Control for T-S Fuzzy System via Delayed State Feedback: Application to Two-Link Robotic System 7th

H∞Control for T-S Fuzzy System via Delayed State Feedback: ...

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7th International Conference on Advances in Control and Optimization of Dynamical Systems, ACODS 2022

作者： Datta, Rupak Dey, Rajeeb Adhikari, Nabanita Gu, Jason Farooq, Umar Asad, Muhammad Usman Department of Electrical Engineering National Institute of Technology Silchar788010 India Department of Electrical and Computer Engineering Dalhousie University Halifax Canada

This paper introduces a fuzzy control design method for nonlinear systems with H∞performance index. First, the Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear system. Next, based on the fuzzy model, a parallel distributed compensation (PDC) based delayed fuzzy controller is developed. The advantage of the proposed control design is that only a simple fuzzy controller is used in our approach without the feedback linearization technique. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the Wirtinger-based inequality method, the proposed fuzzy control problem is designed in terms of linear matrix inequality (LMI) problem. Finally, the simulation result is presented to show the effectiveness of the proposed condition. © 2022 Elsevier B.V.. All rights reserved.

关键词： Fuzzy control Linear matrix inequality Lyapunov-Krasovskii functional parallel distributed compensation Takagi-Sugeno fuzzy model

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Controller design and stability analysis for spinning missiles via tensor product

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AEROSPACE SCIENCE AND TECHNOLOGY 2022年第0期130卷

作者： Zhou, Zhiming Liu, Zhen Pan, Yi Yi, Jianqiang Chinese Acad Sci Inst Automat Beijing 100190 Peoples R China

In this paper, the controller design and stability analysis for the parameters time-varying model of spinning missiles are investigated. A mathematical model for the spinning missile considering the flight parameters varying with time is proposed. Based on tensor product (TP) model transformation for the spinning missile, the parallel distributed compensation (PDC) state feedback controller is designed, and the stability of the controlled system is analyzed with the tool of linear matrix inequalities (LMIs). Numerical simulations with time-varying parameters are conducted to demonstrate the effectiveness of the proposed controller. The given controller can not only guarantee the steady performance but also the decoupling performance between pitch and yaw channels when used in the flight parameters time -varying spinning missiles.(c) 2022 Elsevier Masson SAS. All rights reserved.

关键词： Spinning missile Tensor product model transformation parallel distributed compensation Model filtering Stability analysis

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