scholarly journals Stabilization of the Fractional-Order Chua Chaotic Circuit via the Caputo Derivative of a Single Input

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Chunde Yang ◽  
Hao Cai ◽  
Ping Zhou
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Caputo Derivative ◽  
Chaotic Attractor ◽  
Chaotic Circuit ◽  
Control Scheme ◽  
Control Schemes ◽  
Gronwall’S Lemma ◽  
Single Input ◽  
Two Parameters

A modified fractional-order Chua chaotic circuit is proposed in this paper, and the chaotic attractor is obtained forq=0.98. Based on the Mittag-Leffler function in two parameters and Gronwall’s Lemma, two control schemes are proposed to stabilize the modified fractional-order Chua chaotic system via the Caputo derivative of a single input. The numerical simulation shows the validity and feasibility of the control scheme.

A computationally efficient adaptive robust control scheme for a quad-rotor transporting cable-suspended payloads

2021 ◽  
pp. 095441002110136
Author(s):  
Nasim Ullah ◽  
Irfan Sami ◽  
Wang Shaoping ◽  
Hamid Mukhtar ◽  
Xingjian Wang ◽  
...  
Keyword(s):  
Robust Control ◽  
Fractional Order ◽  
Sliding Mode ◽  
Adaptive Robust Control ◽  
Computationally Efficient ◽  
Control Scheme ◽  
Control Schemes ◽  
Adaptive Laws ◽  
Unknown Disturbances ◽  
The Stability

This article proposes a computationally efficient adaptive robust control scheme for a quad-rotor with cable-suspended payloads. Motion of payload introduces unknown disturbances that affect the performance of the quad-rotor controlled with conventional schemes, thus novel adaptive robust controllers with both integer- and fractional-order dynamics are proposed for the trajectory tracking of quad-rotor with cable-suspended payload. The disturbances acting on quad-rotor due to the payload motion are estimated by utilizing adaptive laws derived from integer- and fractional-order Lyapunov functions. The stability of the proposed control systems is guaranteed using integer- and fractional-order Lyapunov theorems. Overall, three variants of the control schemes, namely adaptive fractional-order sliding mode (AFSMC), adaptive sliding mode (ASMC), and classical Sliding mode controllers (SMC)s) are tested using processor in the loop experiments, and based on the two performance indicators, namely robustness and computational resource utilization, the best control scheme is evaluated. From the results presented, it is verified that ASMC scheme exhibits comparable robustness as of SMC and AFSMC, while it utilizes less sources as compared to AFSMC.

scholarly journals Theory and applications of new fractional-order chaotic system under Caputo operator

2021 ◽  
Vol 12 (1) ◽  
pp. 20-38
Author(s):  
Ndolane Sene
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Caputo Derivative ◽  
Phase Portraits ◽  
Chaotic Circuit ◽  
Chaotic Model ◽  
The Stability ◽  
The Impact ◽  
Schematic Circuit ◽  
Good Agreement

This paper introduces the properties of a fractional-order chaotic system described by the Caputo derivative. The impact of the fractional-order derivative has been focused on. The phase portraits in different orders are obtained with the aids of the proposed numerical discretization, including the discretization of the Riemann-Liouville fractional integral. The stability analysis has been used to help us to delimit the chaotic region. In other words, the region where the order of the Caputo derivative involves and where the presented system in this paper is chaotic. The nature of the chaos has been established using the Lyapunov exponents in the fractional context. The schematic circuit of the proposed fractional-order chaotic system has been presented and simulated in via Mutltisim. The results obtained via Multisim simulation of the chaotic circuit are in good agreement with the results with Matlab simulations. That provided the fractional operators can be applied in real- worlds applications as modeling electrical circuits. The presence of coexisting attractors for particular values of the parameters of the presented fractional-order chaotic model has been studied.

scholarly journals Fuzzy Fractional-Order PID Controller for Fractional Model of Pneumatic Pressure System

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
M. Al-Dhaifallah ◽  
N. Kanagaraj ◽  
K. S. Nisar
Keyword(s):  
Fractional Order ◽  
Operating Conditions ◽  
Effective Control ◽  
External Disturbances ◽  
Pressure System ◽  
Pneumatic Pressure ◽  
Load Variations ◽  
Control Scheme ◽  
Control Schemes ◽  
Fractional Order Pid

This article presents a fuzzy fractional-order PID (FFOPID) controller scheme for a pneumatic pressure regulating system. The industrial pneumatic pressure systems are having strong dynamic and nonlinearity characteristics; further, these systems come across frequent load variations and external disturbances. Hence, for the smooth and trouble-free operation of the industrial pressure system, an effective control mechanism could be adopted. The objective of this work is to design an intelligent fuzzy-based fractional-order PID control scheme to ensure a robust performance with respect to load variation and external disturbances. A novel model of a pilot pressure regulating system is developed to validate the effectiveness of the proposed control scheme. Simulation studies are carried out in a delayed nonlinear pressure regulating system under different operating conditions using fractional-order PID (FOPID) controller with fuzzy online gain tuning mechanism. The results demonstrate the usefulness of the proposed strategy and confirm the performance improvement for the pneumatic pressure system. To highlight the advantages of the proposed scheme a comparative study with conventional PID and FOPID control schemes is made.

Dynamics and Synchronization of the Fractional-Order Sprott E System

2013 ◽  
Vol 850-851 ◽  
pp. 876-879
Author(s):  
Hong Gang Dang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractor ◽  
Fractional Order Systems ◽  
The Stability

In this paper, dynamics and synchronization of the fractional-order Sprott E system are investigated. Firstly, the chaotic attractor of the system is got by means of numerical simulation. Then based on the stability theory of fractional-order systems, the synchronization of the system is realized. Numerical simulations are carried out to demonstrate the effectiveness of the controllers.

scholarly journals Anti-Synchronization of Fractional-Order Chaotic Circuit with Memristor via Periodic Intermittent Control

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Fanqi Meng ◽  
Xiaoqin Zeng ◽  
Zuolei Wang ◽  
Xinjun Wang
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Intermittent Control ◽  
Chaotic Circuit ◽  
Control Scheme

In this paper, the anti-synchronization of fractional-order chaotic circuit with memristor (FCCM) is investigated via a periodic intermittent control scheme. Based on the principle of periodic intermittent control and the Lyapunov stability theory, a novel criterion is adopted to realize the anti-synchronization of FCCM. Finally, some examples of numerical simulations are exploited to verify the feasibility of theoretical analysis.

Synchronization of a Fractional-Order System with Unknown Parameters

2013 ◽  
Vol 850-851 ◽  
pp. 796-799
Author(s):  
Xiao Ya Yang
Keyword(s):  
Numerical Simulation ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Stability Theory ◽  
Chaotic Attractor ◽  
Fractional Order System ◽  
Order System ◽  
Fractional Order Systems ◽  
Unknown Parameters ◽  
The Stability

In this paper, synchronization of a fractional-order system with unknown parameters is studied. The chaotic attractor of the system is got by means of numerical simulation. Then based on the stability theory of fractional-order systems, suitable synchronization controllers and parameter identification rules for the unknown parameters are designed. Numerical simulations are used to demonstrate the effectiveness of the controllers.

Cluster synchronization in fractional-order network with nondelay and delay coupling

2021 ◽  
pp. 2250006
Author(s):  
Yi Wang ◽  
Zhaoyan Wu
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Cluster Synchronization ◽  
Sufficient Condition ◽  
Fractional Order Systems ◽  
Adaptive Controllers ◽  
Control Scheme ◽  
Control Schemes ◽  
The Stability ◽  
Adaptive Control Scheme

In this paper, cluster synchronization for fractional-order complex network with nondelay and delay coupling is investigated. Based on the stability theory of fractional-order systems and the properties of fractional derivative, both static and adaptive control schemes are adopted to design effective controllers. Sufficient condition for achieving cluster synchronization about static controllers is provided. From the condition, the needed feedback gains can be estimated by simple calculations. Further, adaptive control scheme is introduced to design unified controllers. Noticeably, in the adaptive controllers, the feedback gains need not be calculated in advance and can adjust themselves to the needed values according to updating laws. Finally, numerical simulations are given to demonstrate the correctness of the obtained results.

scholarly journals A Proposed High-Gain Observer for a Class of Nonlinear Fractional-Order Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Dorsaf Etlili ◽  
Atef Khedher ◽  
Ayachi Errachdi
Keyword(s):  
Numerical Simulation ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Caputo Derivative ◽  
High Gain ◽  
Estimation Problem ◽  
Fractional Order Systems ◽  
High Gain Observer ◽  
Fractional System ◽  
Fractional Orders

This paper proposes a high-gain observer for a class of nonlinear fractional-order systems. Indeed, this approach is based on Caputo derivative to solve the estimation problem for nonlinear systems. The proposed high-gain observer is used to estimate the unknown states of a nonlinear fractional system. The use of Lyapunov convergence functions to establish stability of system is detailed. The influence of different fractional orders on the estimation is presented. Ultimately, numerical simulation examples demonstrate the efficiency of the proposed approach.

scholarly journals Complexity and Chimera States in a Network of Fractional-Order Laser Systems

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 341
Author(s):  
Shaobo He ◽  
Hayder Natiq ◽  
Santo Banerjee ◽  
Kehui Sun
Keyword(s):  
Numerical Simulation ◽  
Numerical Solution ◽  
Bifurcation Diagram ◽  
Fractional Order ◽  
Dynamical Model ◽  
Chimera States ◽  
Laser Systems ◽  
Complexity Algorithm ◽  
Derivative Order

By applying the Adams-Bashforth-Moulton method (ABM), this paper explores the complexity and synchronization of a fractional-order laser dynamical model. The dynamics under the variance of derivative order q and parameters of the system have examined using the multiscale complexity algorithm and the bifurcation diagram. Numerical simulation outcomes demonstrate that the system generates chaos with the decreasing of q. Moreover, this paper designs the coupled fractional-order network of laser systems and subsequently obtains its numerical solution using ABM. These solutions have demonstrated chimera states of the proposed fractional-order laser network.

scholarly journals Nonlinear Current-Mode Control of SCIG Wind Turbines

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 55
Author(s):  
Nicholas Hawkins ◽  
Bhagyashri Bhagwat ◽  
Michael L. McIntyre
Keyword(s):  
Current Mode ◽  
Nonlinear Controller ◽  
Flux Observer ◽  
Current Mode Control ◽  
Mode Control ◽  
Squirrel Cage ◽  
Control Scheme ◽  
Control Schemes ◽  
Rotor Flux ◽  
Squirrel Cage Induction Generator

In this paper, a nonlinear controller is proposed to manage the rotational speed of a full-variable Squirrel Cage Induction Generator wind turbine. This control scheme improves upon tractional vector controllers by removing the need for a rotor flux observer. Additionally, the proposed controller manages the performance through turbulent wind conditions by accounting for unmeasurable wind torque dynamics. This model-based approach utilizes a current-based control in place of traditional voltage-mode control and is validated using a Lyapunov-based stability analysis. The proposed scheme is compared to a linear vector controller through simulation results. These results demonstrate that the proposed controller is far more robust to wind turbulence than traditional control schemes.

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