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Robust Stability Analysis of Smith Predictor Based Interval fractional-order Control systems:A Case Study in Level Control Process

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IEEE/CAA Journal of Automatica Sinica 2023年第3期10卷 762-780页

作者： Majid Ghorbani Mahsan Tavakoli-Kakhki Aleksei Tepljakov Eduard Petlenkov Department of Computer systems Tallinn University of TechnologyTallinn 12618Estonia Faculty of Electrical Engineering K.N.Toosi University of TechnologyTehran ***Iran IEEE

The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work.Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants.Also,in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative(FOPID)controller.To the best of the authors'knowledge,no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain,time-constants,and time delay.The three primary contributions of this study are as follows:ⅰ)a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system;ⅱ)an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis;andⅲ)two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction.Finally,four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

关键词： Interval uncertainty FOPID controller fractional-order systems robust stability analysis smith predictor

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Optimal Tuning of FOPID-Like Fuzzy Controller for High-Performance fractional-order systems

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Computers, Materials & Continua 2022年第1期70卷 171-180页

作者： Ahmed M.Nassef Hegazy Rezk College of Engineering at Wadi Addawaser Prince Sattam Bin Abdulaziz UniversityAl-Kharj11911Saudi Arabia Department of Computers and Automatic Control Engineering Faculty of EngineeringTanta UniversityTanta31733Egypt Department of Electrical Engineering Faculty of EngineeringMinia UniversityMinia61517Egypt

This paper addresses improvements in fractional order(FO)system performance.Although the classical proportional-integral-derivative(PID)-like fuzzy controller can provide adequate results for both transient and steady-state responses in both linear and nonlinear systems,the FOPID fuzzy controller has been proven to provide better results.This high performance was obtained thanks to the combinative benefits of FO and fuzzy-logic techniques.This paper describes how the optimal gains and FO parameters of the FOPID controller were obtained by the use of a modern optimizer,social spider optimization,in order to improve the response of fractional dynamical systems.This group of systems had usually produced multimodal error surfaces/functions that occasionally had many variant local minima.The integral time of absolute error(ITAE)used in this study was the error function.The results showed that the strategy adopted produced superior performance regarding the lowest ITAE value.It reached a value of 88.22 while the best value obtained in previous work was 98.87.A further comparison between the current work and previous studies concerning transient-analysis factors of the model’s response showed that the strategy proposed was the only one that was able to produce fast rise time,low-percentage overshoot,and very small steady-state error.However,the other strategies were good for one factor,but not for the others.

关键词： Fuzzy-logic control fractional-order systems parameter estimation optimization

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Nonlinear system dynamics of calcium and nitric oxide due to cell memory and superdiffusion in neurons

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Communications in Theoretical Physics 2024年第5期76卷 16-32页

作者： Anand Pawar Kamal Raj Pardasani Department of Mathematics Bioinformatics and Computer ApplicationsMaulana Azad National Institute of TechnologyBhopal-462003Madhya PradeshIndia

The integer-order interdependent calcium([Ca^(2+)])and nitric oxide(NO)systems are unable to shed light on the influences of the superdiffusion and memory in triggering Brownian motion(BM)in neurons.Therefore,a mathematical model is constructed for the fractional-order nonlinear spatiotemporal systems of[Ca^(2+)]and NO incorporating reaction-diffusion equations in neurons.The two-way feedback process between[Ca^(2+)]and NO systems through calcium feedback on NO production and NO feedback on calcium through cyclic guanosine monophosphate(cGMP)with plasmalemmal[Ca^(2+)]-ATPase(PMCA)was incorporated in the model.The Crank–Nicholson scheme(CNS)with Grunwald approximation along spatial derivatives and L1 scheme along temporal derivatives with Gauss–Seidel(GS)iterations were employed.The numerical outcomes were analyzed to get insights into superdiffusion,buffer,and memory exhibiting BM of[Ca^(2+)]and NO systems.The conditions,events and mechanisms leading to dysfunctions in calcium and NO systems and causing different diseases like Parkinson’s were explored in neurons.

关键词： [Ca^(2+)]and nitric oxide signaling reaction-diffusion equations fractional-order systems Grunwald approximation Gauss-Seidel iterations

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On line parameter estimation based on gradient algorithm for fractional order systems

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Journal of Control and Decision 2015年第4期2卷 219-232页

作者： Yiheng Wei Zhenyuan Sun Yangsheng Hu Yong Wang Department of Automation University of Science and Technology of ChinaHefeiP.R.China School of Environmental Science and Optoelectronic Technologies University of Science and Technology of ChinaHefeiP.R.China

This article investigates the problem of on line parameter estimation for fractionalorder linear systems.Based on the theory of fractional-order calculus,the conventional gradient estimator is extended to the fractional-order areas.The stability of the estimator and the convergence are analysed using the continuous frequency distributed model and indirect Lyapunov method.Finally,numerical simulation examples are given to demonstrate the effectiveness of the proposed schemes.

关键词： fractional-order systems gradient estimator indirect Lyapunov method continuous frequency distributed model

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Computation of All Stabilizing First order Controllers for fractional-order systems

Computation of All Stabilizing First Order Controllers for F...

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第二十七届中国控制会议

作者： Hamamci S.E. Kanthabhabha P. Vaithiyanathan K. Electrical-Electronics Engineering Department Inonu University Department of Chemical Engineering Annamalai University

ISBN: (纸本)9787900719706

This paper presents an effective solution to the problem of stabilizing a given but arbitrary fractional-order system using a first order controller 1 2 3 C（s） =（x s +x） /（s +x） .The problem is solved by determining the global stability region in the controller parameter space[x1,x2,x3]using D-decomposition technique.Analytical expressions are derived for the purpose of obtaining the stability boundaries of this region which are described by real root boundary,infinite root boundary and complex root boundary.Thus,the complete set of stabilizing first order controller parameters is obtained.The algorithm has a simple and reliable result which is illustrated by several examples,and hence is practically useful in the analysis and design of fractional-order control systems.

关键词： Stabilization fractional-order systems First order Controllers

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Control and Synchronization of Nonlinear fractional-order systems by Comparison Pricinple

Control and Synchronization of Nonlinear Fractional-order Sy...

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第三十届中国控制会议

作者： WANG Zhiliang~1,MA Tiedong~2,WANG Yinchun~1 1.School of Information Science and Engineering,Northeastern University,Shenyang 110004,P.R.China 2.College of Automation,Chongqing University,Chongqing 400044,P.R.China

＜正＞To overcome the difficulties in the stability analysis and stabilization for nonlinear fractional systems,the comparison principle for fractional-order systems with Caputo fractional derivatives is constructed,which can simplify the processes of stability analysis and stabilization controller design in a great degree.To verify the feasibility of the proposed method,the problem of stabilizing the fractional-order Chen hyperchaotic system is studied.The effective linear controller is designed,and computer simulation verifies the theory result.

关键词： Comparison Principle fractional-order systems Nonlinear Hyperchaotic

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Tracking control for fractional-order uncertain systems based on the indirect Lyapunov method

Tracking control for fractional-order uncertain systems base...

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第40届中国控制会议

作者： Ruijuan Liu Zhiqiang Qin Zhuoyun Nie School of Applied Mathematics Xiamen University of Technology School of Electrical Engineering and Automation Xiamen University of Technology School of Information Science and Engineering National Huaqiao University

Aiming at a class of uncertain fractional-order systems, the idea of equivalent-input-disturbance is applied to design the tracking control of the system. Firstly, the state space model of the system is established, and then the indirect Lyapunov method is used to analyze the stability of the system and design the parameters. Sufficient conditions for stability are given in the form of linear matrix inequalities. Finally, numerical examples show that the method has good tracking control and disturbance suppression performance.

关键词： fractional-order systems uncertainty tracking control Lyapunov method equivalent-input-disturbance

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fractional-order PID Controllers for Stabilization of fractional-order Time Delay systems Based on Region Stability

Fractional-Order PID Controllers for Stabilization of Fracti...

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第30届中国控制与决策会议

作者： YUAN Tangqing ZHENG Min ZHANG Ke HUANG Tao College of Mechatronic Engineering and Automation Shanghai University Shanghai Key Laboratory of Power Station Automation Technology

Stability is essential to the power system.But a practical system should not only has good steady-state performance,but also need to have good transient performance,such as adjusting the time,overshoot and so on.The transient performance of the system is usually determined by the exact position of the pole.Therefore,the study of regional stability(δ-stability) has more extensive,complex and theoretical and engineering significance.The paper proposed an algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers.This method can be used to find the set of stabilizing controllers that guarantees the biggest δ-stability region needed by the control system.It is based on determining a set of global stability regions in the(k,k,k)-space corresponding to the fractional orders λ and μ in the range of(0,2) and then choosing the biggest δ-stability region in this set.The algorithm has reliable result which is illustrated by an example,and,hence is practically useful in the analysis and design of feedback control for fractional-order systems having times delays.

关键词： fractional-order PID controller fractional-order systems Region Stability stabilization time delay

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Synchronization Control for a Class of Nonlinear fractional-order systems Subject to Input Saturation

Synchronization Control for a Class of Nonlinear Fractional-...

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第16届中国系统仿真技术及其应用学术会议

作者： Shao Shu-yi Chen Mou College of Automation Engineering Nanjing University of Aeronautics and Astronautics Jiangsu Key Laboratory of Internet of Things and Control Technologies(Nanjing University of Aeronautics and Astronautics)

This paper develops a synchronization control scheme for a class of nonlinear fractional-order systems with input saturation.On the basis of a memoryless nonlinearity function,the saturation constraint is tackled.By means of the generalized Gronwall inequality,the Laplace transform and the Mittag-Leffler function,a sufficient condition is given for the synchronization control of nonlinear fractional-order systems with input saturation with order 1 ＜ α ＜ 2.Finally,the numerical simulation results illustrate the effectiveness of the proposed synchronization control method.

关键词： fractional-order systems Synchronization Control Input Saturation

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Observer-based controller design for uncertain singular fractional-order systems via LMI approach

Observer-based controller design for uncertain singular frac...

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第37届中国控制会议

作者： Xuefeng Zhang Yuanwei Lv Linghui Long School of Sciences Northeastern University School of Mechanical Engineering and Automation Northeastern University

This paper considers singular fractional-order systems with order 0 ＜ α ＜ 1. Necessary and sufficient condition of designing an observer-based controller for the closed-loop systems to be admissible is obtained. The approach is derived via linear matrix inequalities（LMIs） and two cases for certain and uncertain system are discussed respectively. Meanwhile, we can design a state feedback controller which keeps the system admissible through this approach.Furthermore, two examples for certain and uncertain singular system are given to demonstrate the effectiveness of the results respectively. And the state figures are obtained through simulink toolbox to verify the feasibility of the designed observer-based controller.

关键词： Observer-based control fractional-order systems Singular systems Admissible Linear matrix inequalities

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