Novel Fractional Order Controller Design for First Order Systems with Time Delay

Mihaly, Vlad; Dulf, Éva-Henrietta

doi:10.1109/aqtr49680.2020.9129995

Cited by 7 publications

(8 citation statements)

References 12 publications

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“…However, the tunable parameters λ (i,j) and µ (i,j) cannot be used as realp objects, due to exponential operations not supported. As a solution, ORA is used with the tunable parameter being θ λ ≡ √ η from (15). The transfer function ( 14) can be implemented using θ λ as in Algorithm 1.…”

Section: Controller Design Proceduresmentioning

confidence: 99%

“…As such, two generalized versions of Kessler's magnitude methods were presented in [11,12], while a fractional-order internal model controller with event-based implementation was developed in [13]. A fractionalorder integrator was used as a model for the servo problem in [14], while the same structure was used as a speed controller for a DC motor in [15]. In [16] crone control methodologies were presented, along with LMI formulation for the H ∞ fractional-order control problem.…”

Section: Introductionmentioning

confidence: 99%

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μ-Synthesis FO-PID for Twin Rotor Aerodynamic System

2021

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μ-synthesis is a NP-hard optimization problem based on the generalized Robust Control framework which manages to find a controller which fulfills both robust stability and robust performance. In order to solve such problems, nonsmooth optimization techniques are employed to find nearly-optimal parameters values. However, the free parameters available for tuning must be involved only in classical arithmetic operations, which leads to a problem for the fractional-order operator or for its integer-order approximation, exponential operations being involved. The main goal of the current article consists of presenting a possibility to integrate a fixed-structure multiple-input-multiple-output (MIMO) fractional-order proportional-integral-derivative (FO-PID) controller in the μ-synthesis optimization problem. The solution consists in a possibility to find a set of tunable parameters isomorphic with the fractional-order such that the coefficients involved in the approximation of the fractional element, along with the formulation of a fixed-structure mixed-sensitivity loop shaping μ-synthesis control problem. The proposed design procedure is applied to a twin rotor aerodynamic system (TRAS) using both MATLAB numerical simulation and practical experiments on laboratory scale equipment. Moreover, a comparison with the unstructured μ-synthesis is performed, highlighting the advantages of the proposed solution: simpler form and guaranteed robust stability and performance.

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Section: Controller Design Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

μ-Synthesis FO-PID for Twin Rotor Aerodynamic System

2021

Self Cite

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“…That is why a lot of methods and approaches to designing closed-loop control systems are developed [15,16], [17,18], [19,20], [21]. One of them is based on the intellectual control paradigm and allows us to design controllers by intellectual control methods such as neuro and fuzzy control [22,23], [24].…”

Section: Introductionmentioning

confidence: 99%

Information support to solve direct dynamic problem for the previouslydisturbed electromechanicalsystems

Voliansky,

Sadovoi,

Tolochko

et al. 2024

HAIT

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The article is devoted to the creation of methodological foundations for solving a direct problem of dynamics for linear dynamic systems, the motion of which is described by ordinary differential equations with nonzero initial conditions. Consideration of the motions of linear dynamic systems allows to simplify the mathematical apparatus used and to solve motion determination problems by using a known approach based on transfer functions. However, due to the fact that the classical definition of transfer functions does not involve taking into account non-zero initial conditions, which are caused by the presence of initial deviations of the coordinates of the control object from their desired values, in our work we use the Laplace-Carson transformation to find the corresponding images and write the equations of motion in operator form. This approach, in contrast to the generally acceptedone, led to the introduction of information about the initial conditions of motion in the right-hand side of the corresponding operator differential equations and necessitated the generalization of the vector of control signals by including in it components that take into account the initial conditions of motion of the system under consideration. Such transformations made it possible to generalize the concept of a matrix transfer function as a matrix linear dynamic operator, which consists of two components that define disturbed free and controlled forced movements. The use of such an operator makes it possible to study the dynamics of the considered linear system both separately for each of the components of the generalized vector of controlling influences, and in the complex, thus solving the direct problem of the dynamics of linear systems.

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Section: Introductionmentioning

confidence: 99%

“…The design of fractional order controllers for systems with time delays has been mostly studied in [27]- [29]. In [27], a fractional order controller was implemented in the speed control of a DC motor with time delay, and the efficiency of the fractional implementation was reported in the simulations. In [28], a generalised fractional order proportional integral derivative controller was designed according to the obtention of the biggest regional stability area, and it was reported to be useful for systems having time delays.…”

Section: Introductionmentioning

confidence: 99%

On the Tuning of Fractional Order Resonant Controllers for a Voltage Source Converter in a Weak AC Grid Context

et al. 2021

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This paper proposes a method for tuning the fractional exponent of different types of fractional order resonant controllers for a voltage source converter in a weak AC grid context. The main objective is to ensure the stability of the controlled system in a weak AC grid environment and to achieve an adequate dynamic response under disturbances. Therefore, six commonly used integer order proportional resonant (PR) control structures are selected from the literature and compared with each other according to their frequency behaviour. Afterwards, a rational approximation for the fractional order term is selected based on continuous fraction expansion technique. The inclusion of a fractional exponent in each integer order PR structure generates the fractional order proportional resonant (FPR) control transfer functions. Once the FPR controllers have been obtained, their closed-loop responses are tested via eigenvalue trajectory analysis. For each FPR control structure, a range of the fractional exponent that ensures stability is obtained. The conclusions of eigenvalue trajectory analysis are tested by implementing the FPR control structures in an specific application consisting in a modular multi-level converter (MMC) connected to a weak AC grid with adjustable short-circuit ratio. By means of time-domain simulations, not only the previous eigenvalue analyses are validated, but also new tuning criteria are given for the fractional exponent in combination with other control parameters, such as the damping frequency and the inductance of the complementary feedback branch. Moreover, a sensitivity analysis of the tuning criteria is carried out for other sizes of the AC filter inductance.

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Novel Fractional Order Controller Design for First Order Systems with Time Delay

Cited by 7 publications

References 12 publications

μ-Synthesis FO-PID for Twin Rotor Aerodynamic System

μ-Synthesis FO-PID for Twin Rotor Aerodynamic System

Information support to solve direct dynamic problem for the previouslydisturbed electromechanicalsystems

On the Tuning of Fractional Order Resonant Controllers for a Voltage Source Converter in a Weak AC Grid Context

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