Optimal fractional‐order controller design using direct synthesis method

Yumuk, Erhan; Güzelkaya, Müjde; Eksin, İbrahim

doi:10.1049/iet-cta.2020.0596

Cited by 15 publications

(13 citation statements)

References 36 publications

(41 reference statements)

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“…On the basis of the research conducted in [10,11], [12,13], it is shown that fractional order (FO) controllers have advantages over classical ones, in particular, in the case of their use for the optimization of two-mass EMSs.…”

Section: Literature Reviewmentioning

confidence: 99%

The genetic algorithm fortransition from high to fractional order controllers of a two-mass positional electromechanical system

Kopchak,

Kushnir,

Kushka

2024

AAIT

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A new original approach to the synthesis of the loops of automatic control systems of two-mass positional electromechanical systems is proposed in the article based on the application of the generalized characteristic polynomial at the first stage and the intelligent optimization method at the second.In practice, the skyliftingmechanism of a fire truck is a complex control object.Imperfect manufacturing of mechanical components and their connections, elastic deformations of the boom during operation and supply of fire-extinguishing substance cause rescue cageoscillations.The use of an automatic control system makes it possible to damp the elastic boom vibrations.The synthesized automatic control system, which controls the movement of the boom, must meet the following requirements: the necessary speed, static and dynamic accuracy of the rescue cage movement, the absence of significant adjustments in transient modes, etc. To meet these requirements, an analysis of various automatic control systems and methods of their synthesis was carried out.As a result of the analysis, a two-mass positional three-loop system of subordinate regulationbythe rescue cage rotation mechanism, taking into account the elastic properties of the boom was created using the generalized characteristic polynomial method.The synthesized system of subordinate regulationallows damping of elastic oscillations, providing the desired transitionprocesses of the rescue cage rotation mechanism and low sensitivity in the stable mode to the action of disturbances.The transfer functions of the angular speedcontrollersof the motorand rescue cage obtained in the process of synthesis are high order and turned out to be quite complexfrom the point of view of practical implementation.It is proposed to replace these controllerswith more compact fractional order controllers.The conducted research using mathematical modellingconfirmed the effectiveness of replacing high-order controllersof the angular speed of the motorand rescue cage with fractionalorder controllers. The transfer functions of these controllers are determined by approximating the transfer functions of the controllersusing a genetic algorithm.

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Section: Literature Reviewmentioning

confidence: 99%

The genetic algorithm fortransition from high to fractional order controllers of a two-mass positional electromechanical system

Kopchak,

Kushnir,

Kushka

2024

AAIT

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“…It should be noted that simulations and real-time implementations may differ from each other. The initial controller in equation (20) and the final controller in equation ( 21) are implemented on the plant, respectively. The real-time responses for initial and final controllers on the real system are given in Figure 15.…”

Section: Real-time Implementationmentioning

confidence: 99%

“…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. [18][19][20][21] Direct synthesis is also the most preferred control method developed for nonminimum phase systems. In this method, a reference model is employed as the closed-loop transfer function, and therefore, pole-zero cancelation is required for the open-loop transfer function.…”

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:

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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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“…Using the DS method, an optimal fractional-order controller is proposed for a fractional-order model. Utilising a genetic algorithm, the parameters of the fractional-order closedloop reference transfer function are specified based on the integral square error performance index within the required stability range [18]. Pawan et al [19] presented the PI 𝜆 -D strategy for second-order integrating systems.…”

Section: Introductionmentioning

confidence: 99%

Direct synthesis approach to design PDμ${\text{PD}}^\mu$ based smith predictor for integrating plants: Studied on a quadrotor UAV

Ranjan,

Mehta,

Prakash

et al. 2024

The Journal of Engineering

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This article presents a simple yet novel method of designing a fractional‐order proportional derivative (namely, ) controller for all types of integrating plants. Considering the importance of the direct synthesis approach, the method obtains robust closed‐loop performance. The setpoint parameter is obtained using the multi‐optimization Pareto solution, considering the optimal values in control efforts and performance index together. The numerical investigations have shown improved servo and regulatory responses compared to recently published strategies with fractional orders. It is also known that classical PIDs cannot accurately follow a ramp setpoint. A real‐world situation also demands that the reference inputs become an acceleration ramp type. The proposed technique can handle rising ramp setpoints with plant uncertainty and measurement noise. Hardware verification is also performed on a quadrotor minidrone to check for real‐time issues.

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Optimal fractional‐order controller design using direct synthesis method

Cited by 15 publications

References 36 publications

The genetic algorithm fortransition from high to fractional order controllers of a two-mass positional electromechanical system

The genetic algorithm fortransition from high to fractional order controllers of a two-mass positional electromechanical system

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

Direct synthesis approach to design PDμ${\text{PD}}^\mu$ based smith predictor for integrating plants: Studied on a quadrotor UAV

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