Inaccuracies Revealed During the Analysis of Propagation of Measurement Uncertainty Through a Closed-Loop Fractional-Order Control System

2019 ◽  
pp. 213-226 ◽  
Author(s):  
Józef Wiora ◽  
Alicja Wiora
Keyword(s):  
Control System ◽  
Measurement Uncertainty ◽  
Fractional Order ◽  
Closed Loop ◽  
Fractional Order Control

Adaptive synchronization of uncertain fractional-order chaotic systems using sliding mode control techniques

2019 ◽  
Vol 234 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Bahram Yaghooti ◽  
Ali Siahi Shadbad ◽  
Kaveh Safavi ◽  
Hassan Salarieh
Keyword(s):  
Control System ◽  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Sliding Mode ◽  
Closed Loop Control ◽  
Loop Control ◽  
Closed Loop Control System ◽  
Loop Control System

In this article, an adaptive nonlinear controller is designed to synchronize two uncertain fractional-order chaotic systems using fractional-order sliding mode control. The controller structure and adaptation laws are chosen such that asymptotic stability of the closed-loop control system is guaranteed. The adaptation laws are being calculated from a proper sliding surface using the Lyapunov stability theory. This method guarantees the closed-loop control system robustness against the system uncertainties and external disturbances. Eventually, the presented method is used to synchronize two fractional-order gyro and Duffing systems, and the numerical simulation results demonstrate the effectiveness of this method.

scholarly journals A Closed-Loop Brain Stimulation Control System Design Based on Brain-Machine Interface for Epilepsy

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Moshu Qian ◽  
Guanghua Zhong ◽  
Xinggang Yan ◽  
Heyuan Wang ◽  
Yang Cui
Keyword(s):  
Control System ◽  
Fractional Order ◽  
Brain Stimulation ◽  
Closed Loop ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Brain Machine Interface ◽  
Machine Interface ◽  
Electromagnetic Disturbances ◽  
Stimulation Control

In this study, a closed-loop brain stimulation control system scheme for epilepsy seizure abatement is designed by brain-machine interface (BMI) technique. In the controller design process, the practical parametric uncertainties involving cerebral blood flow, glucose metabolism, blood oxygen level dependence, and electromagnetic disturbances in signal control are considered. An appropriate transformation is introduced to express the system in regular form for design and analysis. Then, sufficient conditions are developed such that the sliding motion is asymptotically stable. Combining Caputo fractional order definition and neural network (NN), a finite time fractional order sliding mode (FFOSM) controller is designed to guarantee reachability of the sliding mode. The stability and reachability analysis of the closed-loop tracking control system gives the guideline of parameter selection, and simulation results based on comprehensive comparisons are carried out to demonstrate the effectiveness of proposed approach.

scholarly journals Lead and lag controller design in fractional-order control systems

2019 ◽  
Vol 52 (7-8) ◽  
pp. 1017-1028
Author(s):  
Tufan Dogruer ◽  
Nusret Tan
Keyword(s):  
Control System ◽  
Control Systems ◽  
Fractional Order ◽  
Fourth Order ◽  
Controller Design ◽  
Design Method ◽  
Performance Criteria ◽  
Order System ◽  
Fractional Order Control ◽  
Minimum Error

This paper presents a controller design method using lead and lag controllers for fractional-order control systems. In the presented method, it is aimed to minimize the error in the control system and to obtain controller parameters parametrically. The error occurring in the system can be minimized by integral performance criteria. The lead and lag controllers have three parameters that need to be calculated. These parameters can be determined by the simulation model created in the Matlab environment. In this study, the fractional-order system in the model was performed using Matsuda’s fourth-order integer approximation. In the optimization model, the error is minimized by using the integral performance criteria, and the controller parameters are obtained for the minimum error values. The results show that the presented method gives good step responses for lead and lag controllers.

Review of Fractional Order Control

2014 ◽  
Vol 1049-1050 ◽  
pp. 983-986 ◽  
Author(s):  
Bo Yang Leng ◽  
Zhi Dong Qi ◽  
Liang Shan ◽  
Hui Juan Bian
Keyword(s):  
Control System ◽  
Control Systems ◽  
Fractional Order ◽  
Mathematical Theory ◽  
Fractional Order Control ◽  
Fractional Order Controller ◽  
Theory System

With the development of mathematical theory of fractional order, fractional order control system is more widely studied and discussed. In order to make the theory system of fractional order control systems perfect,this paper give out the review of fractional order control systems.The fractional order controller is divided into five categories to be described.

Extended feedback and simulation strategies for a delayed fractional-order control system

2020 ◽  
Vol 545 ◽  
pp. 123127 ◽  
Author(s):  
Chengdai Huang ◽  
Heng Liu ◽  
Xiaoping Chen ◽  
Jinde Cao ◽  
Ahmed Alsaedi
Keyword(s):  
Control System ◽  
Fractional Order ◽  
Fractional Order Control

scholarly journals Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 735 ◽  
Author(s):  
Dumitru Baleanu ◽  
Vladimir E. Fedorov ◽  
Dmitriy M. Gordievskikh ◽  
Kenan Taş
Keyword(s):  
Control System ◽  
Fractional Order ◽  
Approximate Controllability ◽  
Homogeneous Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Degenerate Equation ◽  
Fractional Order Control ◽  
Infinite Dimensional ◽  
Initial Boundary Value

We consider a class of linear inhomogeneous equations in a Banach space not solvable with respect to the fractional Caputo derivative. Such equations are called degenerate. We study the case of the existence of a resolving operators family for the respective homogeneous equation, which is an analytic in a sector. The existence of a unique solution of the Cauchy problem and of the Showalter—Sidorov problem to the inhomogeneous degenerate equation is proved. We also derive the form of the solution. The approximate controllability of infinite-dimensional control systems, described by the equations of the considered class, is researched. An approximate controllability criterion for the degenerate fractional order control system is obtained. The criterion is illustrated by the application to a system, which is described by an initial-boundary value problem for a partial differential equation, not solvable with respect to the time-fractional derivative. As a corollary of general results, an approximate controllability criterion is obtained for the degenerate fractional order control system with a finite-dimensional input.

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