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Disturbance observer-based Takagi-Sugeno fuzzy control of a delay fractional-order hydraulic turbine governing system with elastic water hammer via frequency distributed model

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INFORMATION SCIENCES 2021年 569卷 766-785页

作者： Ma, Teng Wang, Bin Northwest A&F Univ Coll Water Resources & Architectural Engn Dept Elect Engn Yangling 712100 Shaanxi Peoples R China Northwest A&F Univ Key Lab Agr Soil & Water Engn Arid & Semiarid Are Minist Educ Yangling 712100 Shaanxi Peoples R China

The hydraulic turbine governing system (HTGS) is a core part of a hydropower station, and the dynamic characteristics of its transition process and stability under disturbances have been strong concerns for the stable operations of units. In this paper, a disturbance observer-based Takagi-Sugeno (T-S) fuzzy control (DOBFC) method using the frequency distributed model (FDM) is proposed to improve the anti-interference control performance of a delay fractional-order HTGS. First, a more practical mathematical model of a fractional order HTGS considering both the mechanical time delay and an elastic water hammer is established, and then its fuzzy model is presented on the basis of the generalized T-S fuzzy rules. Second, the disturbance observer is constructed by utilizing the system state and disturbance information, and the output estimated value of the observer is input into the designed fuzzy state feedback controller to compensate for the effect of external disturbances on the system and achieve disturbance suppression. Third, by means of a new FDM transformation and the construction of a novel Lyapunov function, the stability condition and the parameter solving method of the controller are derived using the linear matrix inequality (LMI) technique. Finally, simulation results are given to verify the effectiveness of the proposed algorithm. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Takagi-Sugeno fuzzy control Time delay frequency distributed model Disturbance observer Linear matrix inequality Fractional-order hydraulic turbine governing system

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frequency distributed model of Caputo derivatives and robust stability of a class of multi-variable fractional-order neural networks with uncertainties

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NEUROCOMPUTING 2016年 202卷 91-97页

作者： Gai, Mingjiu Cui, Shiwei Liang, Shu Liu, Xiaolei Naval Aeronaut & Astronaut Univ Inst Syst Sci & Math Yantai 264001 Japan Univ Sci & Technol China Dept Automat Hefei 230027 Peoples R China

This paper addresses the problems of the robust stability of a class of multi-variable fractional order neural networks with linear fractional uncertainties. Firstly, a continuous frequency distributed model of Caputo derivatives which extend the continuous frequency distributed model of the fractional integrator to Caputo derivatives is given. Then, a sufficient condition of robust stability for a class of multi-variable fractional order neural networks with linear fractional uncertainties is presented via the Lyapunov direct method and linear matrix inequality approach. Finally, two numerical examples are provided to demonstrate the effectiveness of the result. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Caputo derivatives frequency distributed model Neural networks Robust stability Linear matrix inequality (LMI)

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Robust finite-time control of fractional-order nonlinear systems via frequency distributed model

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NONLINEAR DYNAMICS 2016年第4期85卷 2133-2142页

作者： Wang, Bin Ding, Junling Wu, Fengjiao Zhu, Delan Northwest A&F Univ Dept Elect Engn Yangling 712100 Shaanxi Peoples R China

This paper studies the application of frequency distributed model for finite-time control of a class of fractional-order nonlinear systems. Firstly, a class of fractional-order nonlinear systems with model uncertainties and external disturbances are introduced, and a new frequency distributed model with theoretical inference is presented. Secondly, a novel fast terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite-time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional-order nonlinear systems. Finally, two typical examples of three-dimensional nonlinear fractional-order Lorenz system and four-dimensional nonlinear fractional-order Chen system are employed to demonstrate the validity of the proposed method.

关键词： Fractional-order nonlinear systems frequency distributed model Robust finite-time control Terminal sliding mode Uncertainty

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Stabilization of Fractional-Order T-S Fuzzy Systems with Time Delays via an H∞Performance model

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2024年第4期26卷 1300-1312页

作者： Liu, Yiyu Zhang, Xiulan Guangxi Minzu Univ Sch Math & Phys Nanning 530006 Peoples R China Nanjing Univ Aeronaut & Astronaut Sch Aerosp Engn Nanjing 210016 Peoples R China

Takagi-Sugeno (T-S) fuzzy model is an effective technology for describing complex nonlinear industrial processes and dynamic systems with un measurable parameters. However, to stabilize this type of system, feedback linearization techniques and complex adaptive schemes usually need to be adopted. This paper focuses on the stabilization of uncertain fractional-order (FO) systems with unmeasurable states, external disturbances, and time delays, where certain ''IF-THEN'' rules based on an FO T-S model are proposed to describe FO systems. A new FOH(infinity)performance model is established to provide stabilization sufficient conditions. A fuzzy observer is implemented to reconstruct system states, and a feedback controller is established to stabilize the integrated system. Benefiting from a continuous frequency distribution model,the stabilization can be discussed through integer-orderstabilization theories, and several stabilization conditionsare obtained. Moreover, the proposed control approachavoids the usage of feedback linearization techniques,which effectively reduces the computational *** from theoretical analysis, through a numericalexperiment, the feasibility of derived results is verified.

关键词： Fractional-order system Takagi-Sugeno fuzzy model frequency distributed model Time delay Fuzzy observer

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Adaptive iterative learning control for a class of parameterized fractional-order systems subjected to backlash-like hysteresis

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING 2024年第3期238卷 410-424页

作者： Wang, Hong Wei, Jianming Wang, Zhe Naval Aviat Univ Yantai Peoples R China Naval Univ Engn Wuhan Peoples R China Naval Univ Engn Wuhan 430033 Peoples R China

In this article, a fractional-order adaptive iterative learning control scheme is proposed for a class of parameterized fractional-order systems with unknown control gain and backlash-like hysteresis nonlinearity under disturbance. Based on the sufficient condition for the stability of linear fractional-order systems, a sliding mode surface of tracking errors is constructed to facilitate the controller design and stability analysis. A new boundary layer function is designed by using Mittag-Leffler function to relax the restriction of the identical initial condition of iterative learning control design. The fractional-order differential-type adaptive laws and difference-type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. To deal with the influence of backlash-like hysteresis nonlinearity reminder term and unknown bounded external disturbance, a robust control term is designed by employing the hyperbolic tangent function with a convergent series sequence which can guarantee the learning convergence along iteration axis. By constructing Lyapunov-like composite energy function, the stability analysis is presented to prove the convergence of the system output to a small neighborhood of the desired trajectory and the boundedness of all the closed-loop signals. Finally, a simulation example of second-order nonlinear fractional-order system is presented, which demonstrates the effectiveness of the proposed fractional-order adaptive iterative learning control scheme.

关键词： Adaptive iterative learning control parameterized fractional-order systems backlash-like hysteresis Mittag-Leffler function boundary layer function frequency distributed model

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Adaptive fuzzy event-triggered cooperative control for fractional-order delayed multi-agent systems with unknown control direction

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MATHEMATICS AND COMPUTERS IN SIMULATION 2024年 220卷 552-566页

作者： Zhang, Xiulan Shi, Jiangteng Liu, Heng Chen, Fangqi Nanjing Univ Aeronaut & Astronaut Coll Aerosp Engn Nanjing 210016 Peoples R China Guangxi Minzu Univ Ctr Appl Math Guangxi Sch Math & Phys Nanning 530006 Peoples R China Nanjing Univ Aeronaut & Astronaut Dept Math Nanjing 210016 Peoples R China

In this paper, the cooperative control of fractional -order multi -agent systems with time delay and unknown control direction is studied by combining frequency distributed model and eventtriggered mechanism. The Nussbaum function is employed to address the unmeasured control direction. Then, through the event -triggered mechanism, a corresponding controller is designed, which can guarantee that all signals are bounded while saving resources. The proposed theme is convenient for analyzing the stability of fractional -order systems based on a transformation of frequency distributed model. In particular, in order to enhance the universality of the proposed scheme in the fractional -order system stability analysis, a generalized fractional -order generalized lemma with respect to the Nussbaum function is given. Finally, the availability of the proposed method is confirmed by a simulation example.

关键词： Event-triggered mechanism frequency distributed model Lyapunov-Krasovskii function Nussbaum function

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distributed solving Sylvester equations with fractional order dynamics

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Control Theory and Technology 2021年第2期19卷 249-259页

作者： Songsong Cheng Shu Liang Yuan Fan Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education School of Electrical Engineering and AutomationAnhui UniversityHefei230601AnhuiChina Key Laboratory of Knowledge Automation for Industrial Processes of Ministry of Education School of Automation and Electrical EngineeringUniversity of Science and Technology BeijingBeijing100083China

This paper addresses distributed computation Sylvester equations of the form AX+XB=C with fractional order *** partitioning parameter matrices A,B and C,we transfer the problem of distributed solving Sylvester equations as two distributed optimization models and design two fractional order continuous-time algorithms,which have more design freedom and have potential to obtain better convergence performance than that of existing first order ***,rewriting distributed algorithms as corresponding frequency distributed models,we design Lyapunov functions and prove that proposed algorithms asymptotically converge to an exact or least squares ***,we validate the effectiveness of proposed algorithms by providing a numerical example.

关键词： Fractional order calculus distributed optimization Sylvester equation frequency distributed model Convergence

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modelling and simulation of nabla fractional dynamic systems with nonzero initial conditions

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ASIAN JOURNAL OF CONTROL 2021年第1期23卷 525-535页

作者： Wei, Yiheng Wang, Jiachang Tse, Peter W. Wang, Yong Univ Sci & Technol China Dept Automat Hefei 230026 Anhui Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China

The paper focuses on the numerical approximation of discrete fractional order systems with the conditions of nonzero initial instant and nonzero initial state. First, the inverse nabla Laplace transform is developed and the equivalent infinite dimensional frequency distributed model of discrete fractional order system is introduced. Then, resorting the nabla discrete Laplace transform, the rationality of the finite dimensional frequency distributed model approaching the infinite one is illuminated. Based on this, an original algorithm to estimate the parameters of the approximate model is proposed with the help of vector fitting method. Additionally, the applicable object is extended from a sum operator to a general system. Three numerical examples are performed to illustrate the applicability and flexibility of the introduced methodology.

关键词： discrete fractional calculus frequency distributed model nabla laplace transform nonzero initial conditions

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Adaptive neural network H∞ tracking control for a class of nonlinear fractional order systems 40

Adaptive neural network H∞ tracking control for a class of ...

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40th Chinese Control Conference (CCC)

作者： Wu, Yu Li, Xiaohua Li, Ping Univ Sci & Technol Liaoning Sch Elect & Informat Engn Anshan 114051 Peoples R China

ISBN: (纸本)9789881563804

The H infinity tracking control problem is investigated for a class of incommensurate fractional order strict feedback nonlinear systems with unknown nonlinear functions and external disturbances in this paper. The adaptive neural network H infinity tracking controller of the system is designed by combining backstepping technique, adaptive neural network technique with H infinity control theory and utilizing the frequency distributed model to construct Lyapunov functions. The H infinity tracking controller proposed in this paper can guarantee that the tracking error and all the signals in the closed-loop system are bounded, and the system has an H infinity performance for external disturbances. Finally, the simulation results verify the feasibility and effectiveness of the proposed control method.

关键词： Incommensurate fractional order systems backstepping technique frequency distributed model H infinity tracking control adaptive neural network

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A non-integer sliding mode controller to stabilize fractional-order nonlinear systems

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ADVANCES IN DIFFERENCE EQUATIONS 2020年第1期2020卷 1-19页

作者： Haghighi, Ahmadreza Ziaratban, Roveida Tech & Vocat Univ Dept Math Tehran Iran Payame Noor Univ Tehran Dept Math Tehran Iran

In this study, we examine the stabilization of fractional-order chaotic nonlinear dynamical systems with model uncertainties and external disturbances. We used the sliding mode controller by a new approach for controlling and stabilization of these systems. In this research, we replaced a continuous function with the sign function in the controller design and the sliding surface to suppress chattering and undesirable vibration effects. The advantages of the proposed control method are rapid convergence to the equilibrium point, the absence of chattering and unwanted oscillations, high resistance to uncertainties, and the possibility of applying this method to most fractional order chaotic systems. We applied the direct method of Lyapunov stability theory and the frequency distributed model to prove the stability of the slip surface and closed loop system. Finally, we simulated this method on two commonly used and practical chaotic systems and presented the results.

关键词： Fractional-order system Uncertainty Chattering Lyapunov theory Sliding mode control frequency distributed model

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