Influence of time delay on fractional-order PI-controlled system for a second-order oscillatory plant model with time delay

Sadalla, Talar; Horla, Dariusz; Giernacki, Wojciech; Kozierski, Piotr

doi:10.1515/aee-2017-0052

Cited by 7 publications

(8 citation statements)

References 13 publications

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“…Classical tuning algorithms are used in the design of fractional order controllers, such as the Ziegler-Nichols rules [27], Hermite-Biehler and Pontryagin theorems [28]- [31] linear programming formulation [32], F-MIGO optimization [16], [33]. Other tuning methods based on optimizing a certain performance index were developed [8], [13], [34], [35].…”

Section: Tuning Methods For Fractional Order Controllers (Foc) Fomentioning

confidence: 99%

“…Pontryagin and Hermite-Biehler theorems are used to determine the fractional controllers for delayed plants in [28], [30], [31], and [46]. As stated in the quoted literature, the Hermite-Biehler theorem is described by the following equation…”

Section: Pontryagin and Hermite-biehler Theoremsmentioning

confidence: 99%

“…The paper presents thoroughly the influence of the proportional gain, k p , and the integral gain, k i on the closed loop system's stability. The same tuning procedure is found in [28] which uses the two theorems to design a fractional order PI controller for a process characterized by a second order plus time delay model. Performance indexes such as IAE and ISE are used to asses the tracking performance of the closed loop system as well as the influence of time delay and destabilizing factors.…”

Section: Pontryagin and Hermite-biehler Theoremsmentioning

confidence: 99%

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A Survey of Recent Advances in Fractional Order Control for Time Delay Systems

et al. 2019

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Several papers reviewing fractional order calculus in control applications have been published recently. These papers focus on general tuning procedures, especially for the fractional order proportional integral derivative controller. However, not all these tuning procedures are applicable to all kinds of processes, such as the delicate time delay systems. This motivates the need for synthesizing fractional order control applications, problems, and advances completely dedicated to time delay processes. The purpose of this paper is to provide a state of the art that can be easily used as a basis to familiarize oneself with fractional order tuning strategies targeted for time delayed processes. Solely, the most recent advances, dating from the last decade, are included in this review.

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Section: Tuning Methods For Fractional Order Controllers (Foc) Fomentioning

confidence: 99%

Section: Pontryagin and Hermite-biehler Theoremsmentioning

confidence: 99%

Section: Pontryagin and Hermite-biehler Theoremsmentioning

confidence: 99%

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A Survey of Recent Advances in Fractional Order Control for Time Delay Systems

et al. 2019

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“…Then, by following two specifications, gain crossing frequency and phase margin, equations (13) and (14) can be described…”

Section: Determine Optimal Solution By Frequency-domain Specificationsmentioning

confidence: 99%

Design of fractional order proportional integral controller using stability and robustness criteria in time delay system

Chen

Huang

2019

Measurement and Control

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In this paper, a tuning procedure of the parameters of fractional order proportional integral controller is presented for time delay system with arbitrary order. On the basis of obtaining stable solution space by utilizing some stability-domain boundaries which include real-root boundary and σ-stability boundary, the optimal solution can be achieved by applying specific frequency-domain specifications which include gain crossing frequency, phase margin, and robustness constraint. Using the same synthesis by traversing phase angle and phase margin in a given interval, the complete solution space of gain crossing frequency can be obtained and visualized, which is equivalent to demonstrate the complete solution space of optimal parameters of fractional order proportional integral controllers. As a comparison, the tuning procedure of the parameters of integral order proportional integral derivative controller is also discussed. At last, the proposed algorithm is validated by numerical simulation and experimental illustrations. The results show the robustness and advantage of the proposed fractional order proportional integral controller over other controllers.

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“…Authors of references [14][15][16] designed a first-order inertia model with pure time delay, which can be approximated by the second-order inertial model. In [24] the second-order inertial plant model with time delay was developed. In [12] a fuzzy model of coaxial propulsion unit (first-order inertial element with the varying time constant) was defined.…”

Section: Model Of Propulsion Unitmentioning

confidence: 99%