Application of Backstepping Control Technique to Fractional Order Dynamic Systems

2011 ◽  
pp. 33-47 ◽  
Author(s):  
Mehmet Önder Efe
Keyword(s):  
Fractional Order ◽  
Dynamic Systems ◽  
Backstepping Control ◽  
Control Technique

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy
Keyword(s):  
Permanent Magnet ◽  
Fractional Order ◽  
Dynamic Properties ◽  
Synchronous Generator ◽  
Adaptive Controller ◽  
Control Technique ◽  
Order Model ◽  
Permanent Magnet Synchronous Generator ◽  
Chaos Suppression ◽  
Fractional Order Model

AbstractIn this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

scholarly journals A novel self-tuning fractional order PID control based on optimal model reference adaptive system

2019 ◽  
Vol 10 (1) ◽  
pp. 230
Author(s):  
Mohamed Abdelbar Shamseldin ◽  
Mohamed Sallam ◽  
Abdel Halim Bassiuny ◽  
A. M. Abdel Ghany
Keyword(s):  
Fractional Order ◽  
Load Frequency Control ◽  
The Other ◽  
Control Technique ◽  
Order System ◽  
Optimal Model ◽  
Model Reference ◽  
Self Tuning ◽  
Fractional Order Pid ◽  
Model Reference Adaptive

<span>This paper presents a novel self-tuning fractional order PID (FOPID) control based on optimal Model Reference Adaptive Control (MRAC). The proposed control technique has subjected to a third order system case study (power system load frequency control). The model reference describes the requirements of designer. It can be first or second order system. The parameters of MRAC have obtained using the harmony search (HS) optimization technique to achieve the optimal performance. Sometimes, the tuning of the five parameters of FOPID control online at same moment consumes more calculation time and more processing. So, this study proposes three methods for self-tuning FOPID control. The first method has been implemented to tune the two integral and derivative parameters only and the rest of parameters are fixed. The second method has been designed to adjust the proportional, integral derivative parameters while the other fractional parameters are constant. The last method has developed to adjust the five parameters of FOPID control simultaneously. The simulation results illustrate that the third method of self-tuning FOPID control can accommodate the sudden disturbance compared to other techniques. Also, it can absorb the system uncertainty better than the other control techniques.</span>

scholarly journals The Microcontroller Implementation of the Basic Fractional-Order Element

2020 ◽  
Vol 24 (4) ◽  
pp. 19-26
Author(s):  
Krzysztof Oprzędkiewicz ◽  
Maciej Rosół ◽  
Jakub Żegleń-Włodarczyk
Keyword(s):  
Control Systems ◽  
Real Time ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Broad Class ◽  
Fractional Order Control ◽  
Linear And Nonlinear ◽  
Hard Real Time ◽  
Order Element ◽  
Accuracy Of Approximation

The paper presents the implementation of the basic fractional order element sγ on the STM32 microcontroller platform. The implementation employs the typical CFE and FOBD approximations, the accuracy of approximation as well as duration of calculations are experimentally tested. Microcontroller implementation of fractional order elements is known; however, real-time tests of such implementations have been not presented yet. Results of experiments show that both methods can be implemented at the considered platform. The FOBD approximation is more accurate, but the CFE one is faster. The presented experimental results prove that the STM32F7 family processor could be used to develop the embedded fractional-order control systems for a broad class of linear and nonlinear dynamic systems. This is crucial during the implementation of the fractional-order control in the hard real-time or embedded systems.

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