Controllability of fractional order damped dynamical systems with distributed delays

Arthi, G.; Park, Ju H.; Suganya, K.

doi:10.1016/j.matcom.2019.03.001

Cited by 22 publications

(14 citation statements)

References 28 publications

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“…Despite the promising results achieved by fractional-order controllers in the above papers, the central negative aspect of these control schemes is their design based on the optimization algorithms used to obtain the controllers' parameters increasing the computational complexity [32,33]. A comparative survey has been carried out by [34] between the most efficient optimization algorithms, where ant lion optimizer (ALO), salp swarm algorithm (SSA) and grey wolf optimizer (GWO) are introduced as the most effective alternatives.…”

Section: Introductionmentioning

confidence: 99%

Fractional‐order fuzzy PID controller design on buck converter with antlion optimization algorithm

Ghamari

Narm

Mollaee

2021

IET Control Theory & Appl

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The design of a Fractional-Order fuzzy-based PID (FO-F-PID) control structure is presented for Buck converter in the presence of harmful disturbances. A fractional-order proportional-integral-derivative (FO-PID) control scheme is utilized initially to damp the oscillations and remove the steady-state error. To increase the tendency rate of the error to zero, the FO-PID method is applied to a fuzzy-logic-based compensatory stage. At the same time, the fuzzy part gathers the data based on the error and error derivative. The FO-PID control scheme has the capability to enhance the robustness of the control technique against disturbances and parametric variations. Furthermore, to optimize the control parameters, an efficient algorithm so-called Antlion Optimization (ALO) algorithm, is used. Utilizing the ALO algorithm for tuning the FO-PID gains depicts more accurate responses in solving constrained problems with diverse search spaces. Considering numerous disturbances on DC-DC converters, an FO-F-PID controller can be an appropriate alternative since it is more robust against load variations and noise. Moreover, PSO-PID and FO-PSO-PID controllers are designed to drive a comparison between them. Finally, the merits of the presented controller are validated for various scenarios. It can be seen that the FO-F-ALO-PID method provides much better results with faster dynamics. Matlab-Simulink environment is used for the simulations, and the experimental results are tested by the micro-processor to validate the superiority of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Fractional‐order fuzzy PID controller design on buck converter with antlion optimization algorithm

Ghamari

Narm

Mollaee

2021

IET Control Theory & Appl

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“…In the particles' realistic movement, the resistance to motion is unavoidable, so it is suitable to add the damping character in mathematical models and control systems. Recently, a great deal of meaningful conclusions for the mathematical models with damping influence have been presented by the researchers [11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…It lies in the fact that it is bound up with quadratic optimal control, observer design, and pole assignment. For this reason, the controllability has been actively investigated by many investigators, and an impressive progress has been made in recent years [7][8][9][10][11][12][14][15][16][17][18][19][20]. Controllability of the deterministic systems in infinite dimensional spaces has been broadly investigated.…”

Section: Introductionmentioning

confidence: 99%

Approximate Controllability for a Kind of Fractional Neutral Differential Equations with Damping

Cui

Sun

et al. 2020

Mathematical Problems in Engineering

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This paper gains several meaningful results on the mild solutions and approximate controllability for a kind of fractional neutral differential equations with damping (FNDED) and order belonging to 1,2 in Banach spaces. At first, a new expression for the mild solutions of FNDED via the (p, q)-regularized operator family and the technique of Laplace transform is acquired. Then, we consider the approximate controllability of FNDED by means of the approximate sequence method, and simultaneously, some applicable sufficient conditions are obtained.

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“…However, there is no physical model corresponding to this pure mathematical theoretical research. In this paper, fractional derivative is applied to the damping force term of mass-spring oscillators with the differential order between (0,1] (Arthi et al, 2019; Ramirez and Coimbra, 2007; Tian et al, 2018), which reflects the most basic law of structural vibration, and the optimal displacement control problem of this model is studied theoretically for the first time. Due to each term in the vibration equations with clear physical meaning, the new vibration equations are incommensurate vibration equations.…”

Section: Introductionmentioning

confidence: 99%

The optimal displacement control for fractional incommensurate mass-spring oscillators by Shifted Legendre polynomials

Jin

Zhou

Shi

et al. 2020

Transactions of the Institute of Measurement and Control

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Based on the Riemann–Liouville fractional derivative, an optimal displacement control strategy for fractional incommensurate mass-spring oscillators has been presented. According to the calculus of variations and the Lagrange multiplier technique, the optimality conditions for the given problem are obtained. Using Shifted Legendre polynomials, the problem of solving differential equations is transformed into the problem of solving a set of algebraic equations. The validity, high efficiency and applicability of the proposed method are demonstrated through the simulation results.

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Controllability of fractional order damped dynamical systems with distributed delays

Cited by 22 publications

References 28 publications

Fractional‐order fuzzy PID controller design on buck converter with antlion optimization algorithm

Fractional‐order fuzzy PID controller design on buck converter with antlion optimization algorithm

Approximate Controllability for a Kind of Fractional Neutral Differential Equations with Damping

The optimal displacement control for fractional incommensurate mass-spring oscillators by Shifted Legendre polynomials

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