Synthesis of PI fractional controller for fractional systems with time delay

Gharab, Saddam; Hafsi, Sami; Laabidi, Kaouther

doi:10.1109/codit.2017.8102708

Cited by 5 publications

(9 citation statements)

References 11 publications

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“…Step 2. According to equations (15) and (16) in the ''Procedure analysis'' section, with the range of gain crossing frequency v c ! 0, + ' ½ Þ, draw a cluster of curves in (K p , K i ) plane by specifying different fractional order l 2 (0, 2); the reference stability surface shown in Figure 5(b) will consist of these curves.…”

Section: Generalization Of the Methods With An Examplementioning

confidence: 99%

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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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Section: Generalization Of the Methods With An Examplementioning

confidence: 99%

“…where L(v) and u(v) are gain and phase of open-loop transfer function, respectively; v c is gain crossing frequency; and f m is phase margin. According to equation (14), with fixed v c , f m , and l, K p can be uniquely determined by K i through equation (15)…”

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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“…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%

“…Stability analysis based on an extension of the Hermite-Biehler theorem applied to quasipolynomials is preformed in [31] and [46]. In [46], the mathematical approach analyzes the characteristic equations of fractional order time delayed processes. Also, fractional order PI controllers that stabilize the process are obtained using the aforementioned theorem.…”

Section: Pontryagin and Hermite-biehler Theoremsmentioning

confidence: 99%

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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“…Recently, Hafsi et al has focused on the stabilization of first order with time-delay systems with a fractional controller of the form PI λ [13]. After that, an extension of this work has been developed in [14] for a fractional-order system with delay.…”

Section: Introductionmentioning

confidence: 99%

Generic Noninteger Order Controller for Time-Delay Systems

Hafsi

Ghrab

Laabidi

2021

Mathematical Problems in Engineering

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This paper focuses on the problem of fractional controller P I stabilization for a first-order time-delay systems. For this reason, we utilize the Hermite–Biehler and Pontryagin theorems to compute the complete set of the stabilizing P I λ parameters. The widespread industrial utilization of PID controllers and the potentiality of their noninteger order representation justify a timely interest in P I λ tuning techniques. Step responses are calculated through K p , K i , l a m b d a parameters inside and outside stability region to prove the method efficiency.

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Synthesis of PI fractional controller for fractional systems with time delay

Cited by 5 publications

References 11 publications

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

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

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

Generic Noninteger Order Controller for Time-Delay Systems

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