Non-Fragile Tuning of Fractional-Order PD Controllers for IPD-Modelled Processes

Bahavarnia, MirSaleh; Tavazoei, Mohammad Saleh; Mesbahi, Afshin

doi:10.3182/20130204-3-fr-4032.00094

Cited by 3 publications

(3 citation statements)

References 6 publications

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“…Let K d D 0 for C.s/ given by Equation (31). Suppose D.s/; N.s/, and .K p s C K i / given by Equations (30) and (31) are fractional order polynomials of the same commensurate order˛2 .1; 2/ and K p K i 6 0, then 2. the control system is -stable if…”

Section: Graphical Tuning Of Fopid Controllers For Fractional Order Umentioning

confidence: 99%

“…The problem of selecting the optimal controller from the stabilizing region may become another issue that is studied in References [10][11][12][30][31][32][33][34][35][36]. In fact, the optimal controller can be selected according to different kinds of additional design criteria, such as the value that results in the biggest stabilizing region [10][11][12], satisfies the flat phase condition [30], maintains non-fragile [31], or leads to minimum tracking error [32][33][34][35][36].…”

Section: Comparison With H 1 Optimal Controlmentioning

confidence: 99%

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Graphical tuning method of FOPID controllers for fractional order uncertain system achieving robust ‐stability

Zheng

Tang

Song

2015

Intl J Robust & Nonlinear

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SUMMARYThis paper focuses on the graphical tuning method of fractional order proportional integral derivative (FOPID) controllers for fractional order uncertain system achieving robust D-stability. Firstly, general result is presented to check the robust D-stability of the linear fractional order interval polynomial. Then some alternative algorithms and results are proposed to reduce the computational effort of the general result. Secondly, a general graphical tuning method together with some computational efficient algorithms are proposed to determine the complete set of FOPID controllers that provides D-stability for interval fractional order plant. These methods will combine the results for fractional order parametric robust control with the method of FOPID D-stabilization for a fixed plant. At last, two important extensions will be given to the proposed graphical tuning methods: determine the D-stabilizing region for fractional order systems with two kinds of more general and complex uncertainty structures: multi-linear interval uncertainty and mixed-type uncertainties. Numerical examples are followed to illustrate the effectiveness of the method.

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Section: Graphical Tuning Of Fopid Controllers For Fractional Order Umentioning

confidence: 99%

Section: Comparison With H 1 Optimal Controlmentioning

confidence: 99%

Graphical tuning method of FOPID controllers for fractional order uncertain system achieving robust ‐stability

Zheng

Tang

Song

2015

Intl J Robust & Nonlinear

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“…Thus, the controller tuned based on such a point would be non‐fragile. Utilizing such an approach and generalizing it to three‐parameter controllers, non‐fragile tuning methods have been proposed in References 9 and 10 for fractional‐order PD controllers with a tunable order. In addition to PD and fractional‐order PD controllers, PI and PID controllers have been proposed in References 11 and 12 using the centroid approach and its generalized form.…”

Section: Introductionmentioning

confidence: 99%

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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On the fragility of fractional-order PID controllers for FOPDT processes

Padula

Visioli

2016

ISA Transactions

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Non-Fragile Tuning of Fractional-Order PD Controllers for IPD-Modelled Processes

Cited by 3 publications

References 6 publications

Graphical tuning method of FOPID controllers for fractional order uncertain system achieving robust ‐stability

Graphical tuning method of FOPID controllers for fractional order uncertain system achieving robust ‐stability

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

On the fragility of fractional-order PID controllers for FOPDT processes

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