State space approximation for general fractional order dynamic systems

Liang, Shu; Cheng, Peng; Zeng, Lingzao; Wang, Yong

doi:10.1080/00207721.2013.766773

Cited by 54 publications

(20 citation statements)

References 23 publications

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“…The modified Oustaloup method achieves high accuracy in the whole frequency range, while the frequency range must be symmetric, and otherwise the method tends to be ineffective. The so-called fixed-pole approximate method for FOSs has been studied in the co-authors' recent work [14]. The true state variables of fractional integrator and the integer order state space system representation for FOSs can be found in [16].…”

Section: Introductionmentioning

confidence: 99%

A rational approximate method to fractional order systems

Wei

Gao

Cheng

et al. 2014

Int. J. Control Autom. Syst.

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This paper presents an approximate method for general fractional order dynamic systems. Firstly, a novel piecewise approximate method is proposed for fractional order integrator based on its frequency distributed mode. Based on the above method, an integer order approximation system is constructed to approximate a fractional order system. Theoretical analysis results show that the proposed method can achieve much better performance than the existing schemes for a given order in an interested frequency range. The advantage of the proposed method lies in that the resulting system are standard integer order system, which facilitates systematic stability analysis and controller synthesis in view of the well-developed linear or nonlinear system theory. Numerical simulations are presented to illustrate the effectiveness of the proposed approach in the end.

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Section: Introductionmentioning

confidence: 99%

A rational approximate method to fractional order systems

Wei

Gao

Cheng

et al. 2014

Int. J. Control Autom. Syst.

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“…Fundamentally speaking, the core task of numerical approximation is to approximate the fractional calculus operators. Following this idea, many valuable results have been produced in the solution of continuous time fractional order systems [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Modelling and simulation of nabla fractional dynamic systems with nonzero initial conditions

Wei

Wang

Tse

et al. 2019

Asian Journal of Control

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The paper focuses on the numerical approximation of nabla fractional order systems with the conditions of nonzero initial instant and nonzero initial state. First, the inverse nabla Laplace transform is developed and the equivalent infinite dimensional frequency distributed models of discrete fractional order system are introduced. Then, resorting the nabla Laplace transform, the rationality of the finite dimensional frequency distributed model approaching the infinite one is illuminated. Based on this, an original algorithm to estimate the parameters of the approximate model is proposed with the help of vector fitting method. Additionally, the applicable object is extended from a sum operator to a general system. Three numerical examples are performed to illustrate the applicability and flexibility of the introduced methodology.

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“…Subsequently, to reduce the order of approximation, Liang et al (2014) proposed a fixed-pole approximation technique.…”

Section: Introductionmentioning

confidence: 99%

Frequency Response Based Curve Fitting Approximation of Fractional–Order PID Controllers

Bingi

Ibrahim

Karsiti

et al. 2019

International Journal of Applied Mathematics and Computer Science

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Fractional-order PID (FOPID) controllers have been used extensively in many control applications to achieve robust control performance. To implement these controllers, curve fitting approximation techniques are widely employed to obtain integer-order approximation of FOPID. The most popular and widely used approximation techniques include the Oustaloup, Matsuda and Cheraff approaches. However, these methods are unable to achieve the best approximation due to the limitation in the desired frequency range. Thus, this paper proposes a simple curve fitting based integer-order approximation method for a fractional-order integrator/differentiator using frequency response. The advantage of this technique is that it is simple and can fit the entire desired frequency range. Simulation results in the frequency domain show that the proposed approach produces better parameter approximation for the desired frequency range compared with the Oustaloup, refined Oustaloup and Matsuda techniques. Furthermore, time domain and stability analyses also validate the frequency domain results. stable performance, especially for higher-order systems. Moreover, the controller can easily attain the iso-damping property (Monje et al., 2010; Shah and Agashe, 2016). It should be noted that seven different configurations can be achieved with the PI λ D μ controller (i.e., P, PI, PI λ , PD, PD μ , PID and PI λ D μ ) (Xue et al., 2007;Xue, 2017;Monje et al., 2010;Kishore et al., 2018; Shah and Agashe, 2016). However, a key issue with the practical realization or equivalent circuit implementation of such controllers in a finite-dimensional integer-order system is the approximation of the fractional-order parameters. This has generated a lot of interest among researchers recently.For effective approximation of a fractional-order integrator and differentiator in the PI λ D μ controller,

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State space approximation for general fractional order dynamic systems

Cited by 54 publications

References 23 publications

A rational approximate method to fractional order systems

A rational approximate method to fractional order systems

Modelling and simulation of nabla fractional dynamic systems with nonzero initial conditions

Frequency Response Based Curve Fitting Approximation of Fractional–Order PID Controllers

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