Robust Fractional Order PI Controller Tuning Based on Bode’s Ideal Transfer Function

Azarmi, Roohallah; Tavakoli-Kakhki, Mahsan; Sedigh, Ali Khaki; Fatehi, Alireza

doi:10.1016/j.ifacol.2016.07.519

Cited by 25 publications

(13 citation statements)

References 24 publications

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“…Firstly, consider a fractional-order system whose transfer function is similar to the widely used firstorder system [30]: The reference parameters in (8) and controller parameters in (11) tuned by the proposed algorithm are shown in Table 1. The Bode diagram of 1 ( ) controlled by the proposed controller with reference model parameters = 1, = 90 ∘ is depicted in Figure 10.…”

Section: Simulationmentioning

confidence: 99%

“…These phenomena show that system 1 ( ) controlled by the proposed controller is robust to high amplitude gain variations. The step response comparison of 1 ( ) controlled by the proposed FOPID controller and the FOPID controller used in [30] is shown in Figure 15. The performance of system controlled by the proposed controller outperforms the other one with better robustness, lower overshoot, and smaller settling time.…”

Section: Simulationmentioning

confidence: 99%

“…Bode's ideal transfer function is served as a reference model in the parameter optimization process. Some related fractional-order controller tuning algorithms were discussed in [29][30][31]. However, most of them have a specified controlled system type and cannot be widely applied to different kinds of systems.…”

Section: Introductionmentioning

confidence: 99%

“…However, most of them have a specified controlled system type and cannot be widely applied to different kinds of systems. In [29], a PID controller is proposed based on Bode's ideal transfer function, but it only aims at integer-order controlled plants; a similar work can be found in [30], where a robust fractional-order PI controller is designed; however, according to the derivation process, only one certain type of fractional-order controlled plant has been taken into consideration; moreover, the Bode loop shaping with CRONE compensator is discussed in [31], but it only emphasizes the loop shaping accuracy instead of controller tuning algorithm. The application domain of these studies is quite limited.…”

Section: Introductionmentioning

confidence: 99%

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Robust Fractional‐Order PID Controller Tuning Based on Bode’s Optimal Loop Shaping

Liu

Zhang

2018

Complexity

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This paper presents a novel fractional-order PID controller tuning strategy based on Bode's optimal loop shaping which is commonly used for LTI feedback systems. Firstly, the controller parameters are achieved based on flat phase property and Bode's optimal reference model, so that the controlled system is robust to gain variations and can achieve desirable transient performance according to various control requirements. Then, robustness analysis of the controlled system is carried out to support the results. Furthermore, the parameter setting is analyzed to demonstrate the superiority of the proposed controller. At last, some simulation examples are shown to verify the accuracy and usefulness of the proposed control strategy. The proposed fractional-order PID controller does not have any restriction on the controlled plant, so it can be widely applied on both integer-order and fractionalorder systems.

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Section: Simulationmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Fractional‐Order PID Controller Tuning Based on Bode’s Optimal Loop Shaping

Liu

Zhang

2018

Complexity

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“…In comparison, in [1] one can find the approach dedicated to systems without time delay, and described by first-order transfer functions, based on an analytical tuning method, giving smaller overshoot, shorter settling time, improved noise reduction in comparison to the PI or PID controller, better robustness to plant's gain uncertainty in a low frequency range in comparison to the PI controller. The Matignon's stability theorem is used there to tune the gain of the controller.…”

Section: Introductionmentioning

confidence: 99%

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

Sadalla

Horla

Giernacki

et al. 2017

Archives of Electrical Engineering

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Abstract:The paper aims at presenting the influence of an open-loop time delay on the stability and tracking performance of a second-order open-loop system and continuoustime fractional-order PI controller. The tuning method of this controller is based on Hermite-Biehler and Pontryagin theorems, and the tracking performance is evaluated on the basis of two integral performance indices, namely IAE and ISE. The paper extends the results and methodology presented in previous work of the authors to analysis of the influence of time delay on the closed-loop system taking its destabilizing properties into account, as well as concerning possible application of the presented results and used models.

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Dynamic anti‐windup compensator for fractional‐order system with time‐delay

Sadalla

Horla

Giernacki

et al. 2019

Asian Journal of Control

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This paper describes the results of introducing an additional dynamic element to an anti‐windup compensator from control quality and stability area anslysis viewpoint. The analyzed system consists of a first‐order plant with time delay and a fractional‐order PI controller, to present the discussed approach. The controller is tuned based on Hermite‐Biehler and Pontryagin theorems. In the paper, the stability analysis and tracking performance are presented based on both simulation and experimental results. The experiments have been performed using Inteco Modular Servo System with performance evaluated on the basis of the selected performance criterion, namely the Integral of Absolute Error, to verify the applicability of the proposed method. The results have proven that use of the additional dynamic element provides a wider range of controller parameters to ensure stability of the closed‐loop system and better tracking performance in comparison to the system without anti‐windup compensation or system with a standard anti‐windup compensator. It is actually the first time that this type of analysis for dynamic element compensation in anti‐windup framework has been presented for fractional‐order systems. In addition, all the obtained results are referred to the experimental data.

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Robust Fractional Order PI Controller Tuning Based on Bode’s Ideal Transfer Function

Cited by 25 publications

References 24 publications

Robust Fractional‐Order PID Controller Tuning Based on Bode’s Optimal Loop Shaping

Robust Fractional‐Order PID Controller Tuning Based on Bode’s Optimal Loop Shaping

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

Dynamic anti‐windup compensator for fractional‐order system with time‐delay

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