scholarly journals Automatic voltage regulator performance enhancement using a fractional order model predictive controller

2021 ◽  
Vol 10 (5) ◽  
pp. 2424-2432
Author(s):  
Imen Deghboudj ◽  
Samir Ladaci
Keyword(s):  
Fractional Order ◽  
Performance Enhancement ◽  
Linear Time ◽  
Design Method ◽  
Order System ◽  
Voltage Regulator ◽  
Order Model ◽  
Linear Time Invariant ◽  
Fractional Order Model ◽  
Automatic Voltage Regulator

In this paper, a new design method for fractional order model predictive control (FO-MPC) is introduced. The proposed FO-MPC is synthesized for the class of linear time invariant system and applied for the control of an automatic voltage regulator (AVR). The main contribution is to use a fractional order system as prediction model, whereas the plant model is considered as an integer order one. The fractional order model is implemented using the singularity function approach. A comparative study is given with the classical MPC scheme. Numerical simulation results on the controlled AVR performances show the efficiency and the superiority of the fractional order MPC.

Switched Fractional Order Model Reference Adaptive Control for an Automatic Voltage Regulator

2021 ◽  
Author(s):  
Norelys Aguila-Camacho ◽  
Jorge E. García-Bustos ◽  
Eduardo I. Castillo-López
Keyword(s):  
Fractional Order ◽  
Adaptive Controller ◽  
System Response ◽  
Voltage Regulator ◽  
Order Model ◽  
Model Reference ◽  
Fractional Order Model ◽  
Automatic Voltage Regulator ◽  
Adaptive Laws ◽  
Model Reference Adaptive

Abstract This paper presents the design and implementation of a Switched Fractional Order Model Reference Adaptive Controller (SFOMRAC) for an Automatic Voltage Regulator (AVR). The fractional orders, adaptive gains and switching times of the controller adaptive laws are tuned offline, using Particle Swarm Optimization (PSO). The functional to be optimized contains not only parameters of the AVR response but also the control energy. The obtained controllers are compared to non switched Integer Order Model Reference Adaptive Controller (IOMRAC) and non switched Fractional Order Model Reference Adaptive Controller (FOMRAC) proposed previously for this process, showing that the SFOMRAC can improve both, the system response and the control energy used.

Multistability and Coexisting Attractors in a New Circulant Chaotic System

2019 ◽  
Vol 29 (13) ◽  
pp. 1950174 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
Fawaz E. Alsaadi ◽  
Fahimeh Nazarimehr ◽  
...  
Keyword(s):  
Fractional Order ◽  
Order System ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Coexisting Attractors ◽  
Circuit Realization ◽  
Chaotic Flow ◽  
Fractional Order Model ◽  
Dynamical Properties ◽  
Fractional Orders

In this paper, a new four-dimensional chaotic flow is proposed. The system has a cyclic symmetry in its structure and shows a complicated, chaotic attractor. The dynamical properties of the system are investigated. The system shows multistability in an interval of its parameter. Fractional order model of the proposed system is discussed in various fractional orders. Bifurcation analysis of the fractional order system shows that it has a kind of multistability like the integer order system, which is a very rare phenomenon. Circuit realization of the proposed system is also carried out to show that it is usable for engineering applications.

scholarly journals Fractional-Order Model of Two-Prey One-Predator System

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mohammed Fathy Elettreby ◽  
Ahlam Abdullah Al-Raezah ◽  
Tamer Nabil
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Equilibrium Solution ◽  
Order System ◽  
Asymptotically Stable ◽  
Equilibrium Solutions ◽  
Order Model ◽  
Local Asymptotic Stability ◽  
Fractional Order Model ◽  
Predator System

We propose a fractional-order model of the interaction within two-prey and one-predator system. We prove the existence and the uniqueness of the solutions of this model. We investigate in detail the local asymptotic stability of the equilibrium solutions of this model. Also, we illustrate the analytical results by some numerical simulations. Finally, we give an example of an equilibrium solution that is centre for the integer order system, while it is locally asymptotically stable for its fractional-order counterpart.

scholarly journals The hunting cooperation of a predator under two prey's competition and fear-effect in the prey-predator fractional-order model

2022 ◽  
Vol 7 (4) ◽  
pp. 5463-5479
Author(s):  
Ali Yousef ◽  
◽  
Ashraf Adnan Thirthar ◽  
Abdesslem Larmani Alaoui ◽  
Prabir Panja ◽  
...  
Keyword(s):  
Fractional Order ◽  
Equation System ◽  
Order System ◽  
Differential Equation System ◽  
Order Model ◽  
Predator Prey ◽  
Fear Effect ◽  
Fractional Order Model ◽  
Prey Interaction ◽  
The Stability

<abstract><p>This paper investigates a fractional-order mathematical model of predator-prey interaction in the ecology considering the fear of the prey, which is generated in addition by competition of two prey species, to the predator that is in cooperation with its species to hunt the preys. At first, we show that the system has non-negative solutions. The existence and uniqueness of the established fractional-order differential equation system were proven using the Lipschitz Criteria. In applying the theory of Routh-Hurwitz Criteria, we determine the stability of the equilibria based on specific conditions. The discretization of the fractional-order system provides us information to show that the system undergoes Neimark-Sacker Bifurcation. In the end, a series of numerical simulations are conducted to verify the theoretical part of the study and authenticate the effect of fear and fractional order on our model's behavior.</p></abstract>

Evaluation of fractional order of the discrete integrator. Part II

2020 ◽  
Vol 23 (2) ◽  
pp. 408-426
Author(s):  
Piotr Ostalczyk ◽  
Marcin Bąkała ◽  
Jacek Nowakowski ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Output Signal ◽  
Linear Time ◽  
Mathematical Problem ◽  
Simple Method ◽  
Linear Time Invariant ◽  
Input And Output ◽  
Order Difference Equation ◽  
Time Invariant ◽  
Discrete Integrator

AbstractThis is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

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