Experimental Studies of the Fractional PID and TID Controllers for Industrial Process

Koszewnik, Andrzej; Pawłuszewicz, Ewa; Ostaszewski, Michal

doi:10.1007/s12555-020-0123-4

Cited by 14 publications

(4 citation statements)

References 26 publications

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“…However, due to the lack of a well-defined physical sense, it has not received sufficient attention from researchers. With the deepening of research, an increasing number of valuable results have been achieved in the field of control systems and differential equations in recent years (Feng and Sutton, 2021; Koszewnik et al, 2021). Fractional calculus, as a generalization of integer-order differential and integral operators, has attracted more and more attention from experts and scholars due to its attractive properties in many fields such as physics and engineering.…”

Section: Introductionmentioning

confidence: 99%

Fixed-time convergence of second-order nonlinear systems based on nonsingular fractional sliding mode

Lei,

Lan,

Sun

et al. 2024

Transactions of the Institute of Measurement and Control

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In this paper, a fixed-time convergence scheme for fractional sliding modes is proposed for nonlinear second-order systems. Firstly, a fixed-time fractional-order sliding mode surface is designed by combining the fixed-time theory with fractional-order sliding mode control, which has a faster convergence rate and less chattering. Secondly, the proposed sliding mode controller is applied to a class of second-order nonlinear systems subject to uncertainties and external perturbations to ensure that the system is globally robust fixed-time stable. Then, a continuous fractional order approach law is designed and the proposed sliding mode controller is shown to converge in fixed time by Lyapunov function and the convergence time is related to the choice of controller parameters. Finally, the fixed-time fractional-order sliding mode control strategy is applied to a second-order nonlinear magnetic levitation system system, and the simulation results verify the effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Fixed-time convergence of second-order nonlinear systems based on nonsingular fractional sliding mode

Lei,

Lan,

Sun

et al. 2024

Transactions of the Institute of Measurement and Control

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“…After this first development, the use of the FOPID controller to regulate different types of systems increased. Examples of the applications in engineering systems that are regulated by FOPIDs are: smart reactors [17], electronic power converters [18][19][20], rehabilitation systems [21]; automatic voltage regulators [22,23], industrial process models [24,25], robotic systems [26], power systems using synchronous generators [27], and wind turbines [28].…”

Section: Introductionmentioning

confidence: 99%

Experimental Validation of Fractional PID Controllers Applied to a Two-Tank System

et al. 2023

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An experimental validation of fractional-order PID (FOPID) controllers, which were applied to a two coupled tanks system, is presented in this article. Two FOPID controllers, a continuous FOPID (cFOPID) and a discrete FOPID (dFOPID), were implemented in real-time. The gains tuning process was accomplished by applying genetic algorithms while considering the cost function with respect to the tracking error and control effort. The gains optimization process was performed directly to the two-tanks non-linear model. The real-time implementation used a National Instruments PCIe-6321 card as a data acquisition system; for the interface, we used a Simulink Matlab and Simulink Desktop Real-Time Toolbox. The performance of the fractional controllers was compared with the performance of classical PID controllers.

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“…This derives from the fact that fractional-order equations are more adequate for modeling physical processes than differential equations with an integer order and provides} some explanation of discontinuity and singularity formations in nature, see [9,11]. One can find many applications of fractional calculus and control in viscoelasticity, electrochemistry, electromagnetism, ecnophysics, and others, see for example [1,12,13,23,26]. It cannot be ignore that many modeled systems contain non-local dynamics, which can be better described using integro-differential operators with a fractional order, [9,10,20,21].…”

Section: Introductionmentioning

confidence: 99%

Avoidence Strategies for Fractional Order Systems with Caputo Derivative

Pawłuszewicz

2023

Acta Mechanica Et Automatica

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A control strategy is derived for fractional-order dynamic systems with Caputo derivative to guarantee collision-free trajectories for two agents. To guarantee that one agent keeps the state of the system out of a given set regardless of the other agent’s actions a Lyapunov-based approach is adopted. As a special case showing that the given approach to choosing proposed strategy is constructive for a fractional-order system with the Caputo derivative, a linear system as an example is discussed. Obtained results extend to the fractional order case the avoidance problem Leitman’s and Skowronski’s approach.

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Experimental Studies of the Fractional PID and TID Controllers for Industrial Process

Cited by 14 publications

References 26 publications

Fixed-time convergence of second-order nonlinear systems based on nonsingular fractional sliding mode

Fixed-time convergence of second-order nonlinear systems based on nonsingular fractional sliding mode

Experimental Validation of Fractional PID Controllers Applied to a Two-Tank System

Avoidence Strategies for Fractional Order Systems with Caputo Derivative

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