A graphical tuning method of fractional order proportional integral derivative controllers for interval fractional order plant

Zheng, Shiqi; Tang, Xiaoqi; Song, Bao

doi:10.1016/j.jprocont.2014.08.011

Cited by 43 publications

(47 citation statements)

References 23 publications

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“…Hence, when using these results to compute the

scriptD

‐stabilizing region, one can only obtain a sufficient region. Nevertheless, because the computational complexity is reduced considerably, in practical, one can use these results to approximate the complete

scriptD

‐stabilizing region .…”

Section: Main Results For Fractional Order Parametric Controlmentioning

confidence: 99%

“…Yet, the theoretical results in these works lack of strict proofs and the results turn out to be wrong in some certain situations. Therefore, in our previous work [11], general results are given to this problem, and a method is presented to compute the accurate stabilizing region of the interval fractional order system.Nevertheless, the graphical tuning methods mentioned earlier all concentrate on determining the complete set of FOPID controllers achieving Hurwitz stability. In this note, we will focus on computing the complete set of FOPID controllers achieving robust D-stability for fractional order plant with parametric uncertainties.…”

mentioning

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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“…Hence, when using these results to compute the

scriptD

scriptD

‐stabilizing region .…”

Section: Main Results For Fractional Order Parametric Controlmentioning

confidence: 99%

mentioning

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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“…This curve is given by a function f dc ðλÞ as given in (23) and f dc ðλÞ vs λ is also shown in Fig. 13:…”

Section: Design Of Fopi Controllermentioning

confidence: 93%

“…The controllers of the PID family are most common and preferred because of their well-known advantages. Controllers of FOPID family are an advanced extension of PID family having inherent advantages over their integer order counterparts owing to their adjustable non integer orders of integration and derivative which give additional degrees of freedom [19][20][21][22][23]. A controller with three independent parameters is preferable to meet the desired ϕ m , ω gc , and K v .…”

Section: Necessity Of Fractional Order Pi Controlmentioning

confidence: 99%

Dual mode adaptive fractional order PI controller with feedforward controller based on variable parameter model for quadruple tank process

Roy

2016

ISA Transactions

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“…s represents Laplace variable. This motivates us to present the following new FOPI‐type controllers, referred to as (PI μ ) λ (FO[FOPI]) controller:

C ((), s) = {(K_{p} + \frac{K_{i}}{s^{μ}})}^{λ}

where K p , K i , s are defined as equations (1)–(2), λ , μ are fractional orders. It is noted that C ( s ) in equation has more design parameters than C 1 ( s ) and C 2 ( s ), hence, a better control performance may be achieved by C ( s ).…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Modeling And Nonlinear Fractional Order Pi‐Type Control For PMLSM System

Song¹,

Zheng²,

Tang³

et al. 2016

Asian Journal of Control

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In this paper, firstly a fractional order (FO) model is proposed for the speed control of a permanent magnet linear synchronous motor (PMLSM) servo system. To identify the parameters of the FO model, a practical modeling algorithm is presented. The algorithm is based on a pattern search method and its effectiveness is verified by real experimental results. Second, a new fractional order proportional integral type controller, that is, (PIμ)λ or FO[FOPI], is introduced. Then a tuning methodology is presented for the FO[FOPI] controller. In this tuning method, the controller is designed to satisfy four design specifications: stability requirement, specified gain crossover frequency, specified phase margin, flat phase constraint, and minimum integral absolute error. Both set point tracking and load disturbance rejection cases are considered. The advantages of the tuning method are that it fully considers the stability requirement and avoids solving a complex nonlinear optimization problem. Simulations are conducted to verify the effectiveness of the proposed FO[FOPI] controller over classical FOPI and FO[PI] controllers.

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A graphical tuning method of fractional order proportional integral derivative controllers for interval fractional order plant

Cited by 43 publications

References 23 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

Dual mode adaptive fractional order PI controller with feedforward controller based on variable parameter model for quadruple tank process

Fractional Order Modeling And Nonlinear Fractional Order Pi‐Type Control For PMLSM System

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