Robust non-fragile fractional order PID controller for linear time invariant fractional delay systems

Mesbahi, Afshin; Haeri, ءMohammad

doi:10.1016/j.jprocont.2014.07.001

Cited by 18 publications

(19 citation statements)

References 28 publications

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“…By using the D‐partition method to carry out the stabilizing region, the expression of k i and k d with respect to ω cannot be separately obtained. In this example, the stabilizing region in the case λ + μ = 2 is determined.…”

Section: Simulation Examplesmentioning

confidence: 99%

“…However, for the fractional‐order system with time delay, the stabilization problem of the PI λ D μ controllers has not been well resolved. Recently, several D‐decomposition methods were used to construct the stabilizing regions of the PI λ D μ controller . In the work of Moornani and Haeri, the D‐decomposition method was used to get the stabilizing region for the first‐order system with time delay.…”

Section: Introductionmentioning

confidence: 99%

“…In the work of Moornani and Haeri, the D‐decomposition method was used to get the stabilizing region for the first‐order system with time delay. The D‐decomposition method was also used to choose the stabilizing set for the fractional systems with multiple commensurate delays . However, for these methods, a point in each region divided by the boundaries with respect to the singular frequencies has to be chosen to test the system stability in terms of the Nyquist criterion.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, several D-decomposition methods were used to construct the stabilizing regions of the PI λ D μ controller. [15][16][17][18][19][20][21][22] In the work of Moornani and Haeri, 20 the D-decomposition method was used to get the stabilizing region for the first-order system with time delay. The D-decomposition method was also used to choose the stabilizing set for the fractional systems with multiple commensurate delays.…”

mentioning

confidence: 99%

“…The D-decomposition method was also used to choose the stabilizing set for the fractional systems with multiple commensurate delays. 21 However, for these methods, a point in each region divided by the boundaries with respect to the singular frequencies has to be chosen to test the system stability in terms of the Nyquist criterion. If the number of the divided regions is very large, the procedure of determining the stabilizing region will become redundant.…”

mentioning

confidence: 99%

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General stabilization method of fractional‐order PI^λD^μ controllers for fractional‐order systems with time delay

Yang

Liu

et al. 2018

Intl J Robust & Nonlinear

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Summary In this paper, an effective method is proposed to get the stabilizing regions of fractional‐order PIλDμ controllers for an arbitrarily given fractional‐order system with time delay. For each known proportional gain (kp), integral gain (ki), or derivative gain (kd) in the PIλDμ controllers, the stabilizing region with respect to the other two control gains is derived respectively. The boundaries of the stabilizing regions are firstly obtained based on singular frequencies. Then, the main results are presented to directly determine the stabilizing region from an analytical viewpoint. The results avoid the time‐consuming stability test since the stabilizing region is usually determined by manually choosing lots of test points from all the divided regions by the resultant boundaries. Besides, the stabilizing (ki, kd) regions of the PIλDμ controllers for λ + μ = 2 can be determined and the linear programming characteristic of the stabilizing (ki, kd) region for the case λ + μ = 2 is obtained. Furthermore, the robust stabilizing region is analyzed. The results in this paper provide the basis for both the tuning of the PIλDμ controller in practice and the design of the PIλDμ controller satisfying different performance criteria. Numerical examples and an application example are presented to check the validity of the proposed method.

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Section: Simulation Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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General stabilization method of fractional‐order PI^λD^μ controllers for fractional‐order systems with time delay

Yang

Liu

et al. 2018

Intl J Robust & Nonlinear

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A probabilistic framework to achieve robust non‐fragile tuning methods: PD control of IPD‐modeled processes

Bahavarnia

Tavazoei

2021

Intl J Robust & Nonlinear

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We introduce a novel probabilistic framework to achieve robust non-fragile tuning methods in control of processes with parametric uncertainties. We consider probability distributions to model the process parameters' uncertainties.First, we propose the tuning framework in a general setting. Then, as an illustration, we apply it to PD control of IPD-modeled processes. It is noteworthy that the proposed tuning method is robust against the considered parametric uncertainties. Also, to empower the proposed robust tuning method in the viewpoint of non-fragility, we utilize a centroid approach. Selecting the form of the probabilistic framework, we empirically observe some of the popular tuning methods are special cases of the proposed novel framework. Moreover, we theoretically/empirically make a comparison among the tuning methods in the literature based on non-fragility and robustness via such a probabilistic framework.

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Design and implementation of fractional differentiators, Part I: System based methods

Wei

Gao

Chen

et al. 2019

Control Engineering Practice

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Robust non-fragile fractional order PID controller for linear time invariant fractional delay systems

Cited by 18 publications

References 28 publications

General stabilization method of fractional‐order PI^λD^μ controllers for fractional‐order systems with time delay

General stabilization method of fractional‐order PI^λD^μ controllers for fractional‐order systems with time delay

A probabilistic framework to achieve robust non‐fragile tuning methods: PD control of IPD‐modeled processes

Design and implementation of fractional differentiators, Part I: System based methods

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Robust non-fragile fractional order PID controller for linear time invariant fractional delay systems

Cited by 18 publications

References 28 publications

General stabilization method of fractional‐order PIλDμ controllers for fractional‐order systems with time delay

General stabilization method of fractional‐order PIλDμ controllers for fractional‐order systems with time delay

A probabilistic framework to achieve robust non‐fragile tuning methods: PD control of IPD‐modeled processes

Design and implementation of fractional differentiators, Part I: System based methods

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Product

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General stabilization method of fractional‐order PI^λD^μ controllers for fractional‐order systems with time delay

General stabilization method of fractional‐order PI^λD^μ controllers for fractional‐order systems with time delay