A robust fractional-order controller design with gain and phase margin specifications based on delayed Bode’s ideal transfer function

Yumuk, Erhan; Güzelkaya, Müjde; Eksin, İbrahim

doi:10.1016/j.jfranklin.2022.05.033

Cited by 17 publications

(10 citation statements)

References 30 publications

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“…[9][10][11] Moreover, numerous integer-order control strategies are also adapted to their fractional counterparts. [12][13][14][15][16][17] The transfer functions of closed-loop systems that exhibit the desired system dynamics are often called reference models. These models profit from meeting the 1 requirements without causing difficulties in their control system implementations, and therefore, there are many control techniques in which the direct synthesis method is employed.…”

Section: Introductionmentioning

confidence: 99%

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Bi-fractional-order reference model parameters-based control system design

Kececi

Yumuk

Güzelkaya

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part I:

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It is known that analytical manipulation of the time-domain representation of fractional order transfer function is, hitherto, a challenging task. In this study, a controller design methodology based on the direct synthesis design method is proposed using bi-fractional order transfer function as a reference model and certain time-domain criteria. First, an analysis examines the effects of bi-fractional order transfer function parameters, that is, commensurate fractional order, damping ratio and natural frequency, on the system time-domain criteria. This examination has allowed us to set up a relation between damping ratio and commensurate fractional order. Next, a polynomial function fitting is established in order to express the damping ratio in terms of this commensurate order. Bi-fractional-order reference model is regenerated using the above-mentioned relationship. Furthermore, a control design algorithm that utilizes the newly derived bi-fractional order reference model is developed by considering control signal limitations. The proposed fractional order control design method is then compared with globally optimized fractional order proportional-integral-derivative (PID) controllers under the same circumstances and performance index. Finally, the implementation of the proposed controller design algorithm is done on a real-time active suspension system. The results are very satisfactory and incoherent with the simulations.

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Section: Introductionmentioning

confidence: 99%

“…9–11 Moreover, numerous integer-order control strategies are also adapted to their fractional counterparts. 12–17…”

Section: Introductionmentioning

confidence: 99%

Bi-fractional-order reference model parameters-based control system design

Kececi

Yumuk

Güzelkaya

et al. 2023

Proceedings of the Institution of Mechanical Engineers, Part I:

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

“…These methods, which can be considered as the generalized version of integer-order counterpart tuning methods, might be categorized into three types: analytic, numeric, and rule-based methods. [4][5][6][7] Non-integer-order calculation adds three more control system structures to the field of control engineering: fractional-order system (FOS) controlled by FOC, integer-order system (IOS) controlled by FOC, and FOS controlled by IOC. [8][9][10] There exist various application areas in industry where fractional system identification and control methods are employed.…”

Section: Introductionmentioning

confidence: 99%

Reduced inverse integer-order controller design for a class of fractional-order model: Case study on two-tank liquid-level process

Yumuk

Güzelkaya

Eksin

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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In this study, a reduced inverse integer-order controller design methodology for single fractional-order pole model is proposed. First, the higher integer-order equivalent of this model is found using the Oustaloup approximation to fractional operator. Then, the poles and zeros of the higher integer-order model are determined in terms of fractional-order system model parameters employing characteristic equation format and root-locus idea. The order of the higher integer-order model is reduced using dominant pole–zero couples. The proximity of the pole–zero couples to each other as well as their proximity to the origin is key dominance requirement for order reduction. The controller is obtained inverting the reduced order integer system model in terms of fractional-order system model parameters. The proposed controller is compared with integer and fractional proportional–integral–derivative (PID) controllers using the experiments carried out on two-tank liquid-level process. The real-time experiment outcomes demonstrate that the proposed controller has superior performance over integer and fractional proportional–integral–derivative controllers.

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“…Analytical design Fractional order PID controller for fractional order or integer order plant has been studied in (Yumuk et al, 2019). Robust fractional order controller was designed by (Yumuk et al, 2022) using the ideal Bode transfer functions using the fundamental property of fractional order calculus. The fractional order calculus extends its horizon even in the field of electromagnetics.…”

Section: Introductionmentioning

confidence: 99%

Discretization of Fractional Order Operator in Delta Domain

Dolai

Mondal²,

Sarkar

2022

Gazi University Journal of Science Part A: Engineering and Innovation

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The fractional order operator is the backbone of the fractional order system (FOS). The fractional order operator (FOO) is generally represented as s^(±μ) (0<μ<1). Discrete time FOS can be obtained through the discretization of the fractional order operator. The FOO is the general form of either fractional order differentiator (FOD) or integrator (FOI) depending upon the values of μ. Out of the two discretization methods, direct discretization outperforms the method of indirect discretization. The mapping between the continuous time and discrete time domain is done with the development of generating function. Continuous fraction expansion (CFE) is used expand the generating function for the rational approximation of the FOO. There is an inherent problem associated with the discretization of FOO in discrete z-domain particularly at very fast sampling rate. In the other hand, discretization using delta operator parameterization provides the continuous time and discrete time results in hand to hand, when the continuous time systems are sampled at very fast sampling rate and circumventing the problem with shift operator parameterization at fast sampling rate. In this work, a new generating function is proposed to discretize the FOO using the Gauss-Legendre 3-point quadrature rule and generating function is expanded using the CFE to form rational approximation of the FOO in delta domain. The benchmark fractional order systems are considered in this work for the simulation purpose and comparison of results are made to prove the efficacy of the proposed method using MATLAB.

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A robust fractional-order controller design with gain and phase margin specifications based on delayed Bode’s ideal transfer function

Cited by 17 publications

References 30 publications

Bi-fractional-order reference model parameters-based control system design

Bi-fractional-order reference model parameters-based control system design

Reduced inverse integer-order controller design for a class of fractional-order model: Case study on two-tank liquid-level process

Discretization of Fractional Order Operator in Delta Domain

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