A New Fractional-order Control Method for Robust Synchronization Between Fractional-order Uncertain Permanent Magnet Synchronous Motors

This paper presents a new fractional-order sliding mode controller (FOSMC) for disturbance rejection and stabilization of a class of fractional-order systems with mismatched disturbances. To design this control strategy, firstly, a fractional-order extended disturbance observer (FOEDO) is proposed to estimate the matched and mismatched disturbances and their derivatives. Then, according to the design procedure of the sliding mode controller and based on the designed FOEDO, a proper sliding mode surface is proposed. Subsequently, the proposed FOSMC is designed to guarantee that the system states reach the sliding surface and stay on it forever. The stability of the controlled fractional-order systems is proved via fractional-order Lyapunov stability theory. The numerical examples are used to illustrate the effectiveness of the proposed fractional-order controller. The simulation results of the proposed FOSMC are compared with the results of some other researchers’ works to show the superiority of the proposed control method. The new approach displays some attractive features such as fast response, the chattering reduction, robust stability, less disturbance estimation error, the mismatched disturbance, noise rejection, and better control performance.

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“…Based on the mentioned Lemma 2 ( I 1 − α ( | S | ) ≥ L ) in Pashaei and Hashemzadeh (2019), one can write…”

Section: The Proposed Control Methodsmentioning

confidence: 99%

“…Moreover, based on Lemma 3 ( I 1 − α ( − sgn ( | S | ) ) ≤ | I 1 − α false( − sgn false( | S | false) false) | ≤ N ) of Pashaei and Hashemzadeh (2019), one can write…”

Section: The Proposed Control Methodsmentioning

confidence: 99%

Control of a class of fractional-order systems with mismatched disturbances via fractional-order sliding mode controller

Pashaei

Badamchizadeh

2020

Transactions of the Institute of Measurement and Control

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“…Note that the intermediate signal between the two subsystems has been written as an algebraic operation, and substituting (26) into (13)…”

Section: Parameter Identification Of the Fractional Hammerstein Systementioning

confidence: 99%

“…On the contrary, fractional-order (FO) representations have been seen to improve robustness in control designs [10] and have the ability to model complex systems with a reduced number of parameters [11] due to fractional calculus' non-locality and the mathematical emphasis of long memory. FO systems have found wide applications in physics and control [12][13][14]. It has been demonstrated that a singular function can represent the conceptual models of nonlinear physical phenomena accurately [15] and can be extended to processes related with natural phenomena, such as epidemiology [16].…”

Section: Introductionmentioning

confidence: 99%

Parametric Identification of Nonlinear Fractional Hammerstein Models

2019

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In this paper, a system identification method for continuous fractional-order Hammerstein models is proposed. A block structured nonlinear system constituting a static nonlinear block followed by a fractional-order linear dynamic system is considered. The fractional differential operator is represented through the generalized operational matrix of block pulse functions to reduce computational complexity. A special test signal is developed to isolate the identification of the nonlinear static function from that of the fractional-order linear dynamic system. The merit of the proposed technique is indicated by concurrent identification of the fractional order with linear system coefficients, algebraic representation of the immeasurable nonlinear static function output, and permitting use of non-iterative procedures for identification of the nonlinearity. The efficacy of the proposed method is exhibited through simulation at various signal-to-noise ratios.

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“…There are other authors, such as [33] [34], that have focused the design of fractional order controllers on stability considerations, as proposed in the present paper. In [33], the fractional-order control strategy was based on fractionalorder Lyapunov stability theory and its effectiveness was checked via numerical simulations. In [34], the authors designed the fractional order controller based on the quatitative feedback theory.…”

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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A New Fractional-order Control Method for Robust Synchronization Between Fractional-order Uncertain Permanent Magnet Synchronous Motors

Cited by 5 publications

References 10 publications

Control of a class of fractional-order systems with mismatched disturbances via fractional-order sliding mode controller

Control of a class of fractional-order systems with mismatched disturbances via fractional-order sliding mode controller

Parametric Identification of Nonlinear Fractional Hammerstein Models

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

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