Discrete-Time Fractional, Variable-Order PID Controller for a Plant with Delay

Oziablo, Piotr; Mozyrska, Dorota; Wyrwas, Małgorzata

doi:10.3390/e22070771

Cited by 11 publications

(8 citation statements)

References 21 publications

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“…However, the application of fractional-variable or-der is not unique and exists various solutions to this problem [24], [25]. Therefore, various variable-order FOPID controller implementations can be found in the literature [26]- [29].…”

Section: Introductionmentioning

confidence: 99%

“…It results that for t → ∞, implementations of fractional-order integrator have no longer the integration property. In [6], [44] it is shown that using various optimization techniques reduces the steady-state error. Another way to eliminate steady-state error is proposed in [45], [46], where integer-order integration combined with fractional-order derivative is used to model the fractional-order integrator.…”

Section: Introductionmentioning

confidence: 99%

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A New Reduced-Order Implementation of Discrete-Time Fractional-Order PID Controller

Stanisławski

Rydel

2022

IEEE Access

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This paper presents a new method for computationally effective implementation of a discretetime fractional-order proportional-integral-derivative (FOPID) controller. The proposed method is based on a unique representation of the FOPID controller, where fractional properties are modeled by a specific finite impulse response (FIR) filter. The balanced truncation model order reduction method is applied in the proposed approach to obtain an effective, low-order model of the FOPID controller. The time-invariant FOPID controller implementation is presented first, and then the methodology is extended to the controller with time-varying gains. A comparative analysis shows that the proposed methodology leads to the effective modeling of discrete-time FOPID controllers. In addition to simulation runs, the effectiveness of the introduced methodology is confirmed in a real-life experiment involving the control of the DC motor servo system. The paper concludes with the implementation tools developed in the Matlab/Simulink environment.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Reduced-Order Implementation of Discrete-Time Fractional-Order PID Controller

Stanisławski

Rydel

2022

IEEE Access

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“…Unlike integer-order operators, the intrinsic multiscale nature of fractional operators enabled a very unique and effective approach to model historically challenging physical processes involving, as an example, nonlocality or memory effects. Indeed, many of the early applications of FC to physical modeling included viscoelastic effects [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ], nonlocal behavior [ 8 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ], anomalous and hybrid transport [ 9 , 10 , 11 , 24 , 25 , 26 , 27 , 28 , 29 , 30 ], fractal media [ 12 , 31 , 32 , 33 , 34 , 35 ], and even control theory [ 36 , 37 , 38 , 39 ]. The interested reader is referred to the work in [ 40 ] for a detailed account of the birth and evolution of fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Applications of Distributed-Order Fractional Operators: A Review

Ding

Patnaik

Sidhardh

et al. 2021

Entropy

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Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader area of fractional calculus that has important and far-reaching applications for the modeling of complex systems. DOFC generalizes the intrinsic multiscale nature of constant and variable-order fractional operators opening significant opportunities to model systems whose behavior stems from the complex interplay and superposition of nonlocal and memory effects occurring over a multitude of scales. In recent years, a significant amount of studies focusing on mathematical aspects and real-world applications of DOFC have been produced. However, a systematic review of the available literature and of the state-of-the-art of DOFC as it pertains, specifically, to real-world applications is still lacking. This review article is intended to provide the reader a road map to understand the early development of DOFC and the progressive evolution and application to the modeling of complex real-world problems. The review starts by offering a brief introduction to the mathematics of DOFC, including analytical and numerical methods, and it continues providing an extensive overview of the applications of DOFC to fields like viscoelasticity, transport processes, and control theory that have seen most of the research activity to date.

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“…In the paper a novelty variable, the fractional-order PID (VFOPID) [6,28,[33][34][35][36][37][38][39][40][41] controller synthesis is proposed. It consists of dividing the closed-loop system discrete-transient time division into the finite time intervals over which are defined fractional orders summation and differentiation functions.…”

Section: Introductionmentioning

confidence: 99%

Variable, Fractional-Order PID Controller Synthesis Novelty Method

Ostalczyk¹,

Duch²

2021

Control Based on PID Framework - The Mutual Promotion of Control and Identification for Complex Systems

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The novelty method of the discrete variable, fractional order PID controller is proposed. The PID controllers are known for years. Many tuning continuous time PID controller methods are invented. Due to different performance criteria there are optimized three parameters: proportional, integral and differentiation gains. In the fractional order PID controllers there are two additional parameters: fractional order integration and differentiation. In the variable, fractional order PID controller fractional orders are generalized to functions. Nowadays all PID controllers are realized by microcontrollers in a discrete time version. Hence, the order functions are discrete variable bounded ones. Such controllers offer better transient characteristics of the closed loop systems. The choice of the order functions is still the open problem. In this Section a novelty intuitive idea is proposed. As the order functions one applies two spline functions with bounded functions defined for every time subinterval. The main idea is that in the final time interval the variable, fractional order PID controller transforms itself to the classical one preserving the stability conditions and zero steady-state error signal. This means that in the last time interval the discrete integration order is −1 and differentiation is 1.

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Discrete-Time Fractional, Variable-Order PID Controller for a Plant with Delay

Cited by 11 publications

References 21 publications

A New Reduced-Order Implementation of Discrete-Time Fractional-Order PID Controller

A New Reduced-Order Implementation of Discrete-Time Fractional-Order PID Controller

Applications of Distributed-Order Fractional Operators: A Review

Variable, Fractional-Order PID Controller Synthesis Novelty Method

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