Design, implementation and application of distributed order PI control

Zhou, Fengyu; Zhao, Yang; Li, Yan; Chen, YangQuan

doi:10.1016/j.isatra.2012.12.004

Cited by 41 publications

(12 citation statements)

References 46 publications

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“…Distributed-order system identification is discussed in [12]. In [13], a series of distributed order proportional-integral controller design methods is derived and applied to the robust control of wheeled service robots, which can tolerate more structural and parametric uncertainties than the corresponding fractional-order proportional-integral control. Atanackovic [14] has generalized the multiterm fractional derivative viscoelastic model to a derivative model of distributed order by replacing the finite sums with integrals in the domain of orders.…”

Section: Introductionmentioning

confidence: 99%

Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach

Maleknejad

Rashidinia

Eftekhari

2020

Numerical Methods Partial

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In this paper, a numerical method is presented to obtain and analyze the behavior of numerical solutions of distributed order fractional differential equations of the general form in the time domain with the Caputo fractional derivative. The suggested method is based on the Müntz-Legendre wavelet approximation. We derive a new operational vector for the Riemann-Liouville fractional integral of the Müntz-Legendre wavelets by using the Laplace transform method. Applying this operational vector and collocation method in our approach, the problem can be reduced to a system of linear and nonlinear algebraic equations. The arising system can be solved by the Newton method. Discussion on the error bound and convergence analysis for the proposed method is presented. Finally, seven test problems are considered to compare our results with other well-known methods used for solving these problems. The results in the tabulated tables highlighted that the proposed method is an efficient mathematical tool for analyzing distributed order fractional differential equations of the general form.

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Section: Introductionmentioning

confidence: 99%

Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach

Maleknejad

Rashidinia

Eftekhari

2020

Numerical Methods Partial

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“…Likewise, distributed order calculus, which generalizes fractional calculus, is considered a novel tool in modeling different physical phenomena such as optimal damping [17], rheological behaviors [18] and diffusion processes [19,20]. In addition to modeling some physical processes more accurately, distributed order calculus has also been used in control systems, with the recent emergence of distributed order dynamic systems [21][22][23][24]. However, this prospective field is still quite new and, therefore, requires further study and research.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Conditions for Stability Analysis of Linear Time‐Invariant Distributed Order Dynamic Systems: A Lagrange Inversion Theorem Approach

Taghavian

Tavazoei

2018

Asian Journal of Control

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“…With the motivation of these applications, some attentions have been paid to the fractional partial differential equations (FPDEs) with distributed order [7,16,17]. In [18], a series of distributed-order PI controller design methods are derived and applied to the robust control of wheeled service robots, which can tolerate more structural and parametric uncertain ties than the corresponding fractional-order PI control. In the book [8], two initial applications including distributedorder signal processing and optimal distributed damping are provided as motivating examples to further the investigation in the distributed-order dynamic systems.…”

Section: Introductionmentioning

confidence: 99%

Novel Second-Order Accurate Implicit Numerical Methods for the Riesz Space Distributed-Order Advection-Dispersion Equations

Wang

Liu

Chen

2015

Advances in Mathematical Physics

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We derive and analyze second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations (RSDO-ADE) in one-dimensional (1D) and two-dimensional (2D) cases, respectively. Firstly, we discretize the Riesz space distributed-order advection-dispersion equations into multiterm Riesz space fractional advection-dispersion equations (MT-RSDO-ADE) by using the midpoint quadrature rule. Secondly, we propose a second-order accurate implicit numerical method for the MT-RSDO-ADE. Thirdly, stability and convergence are discussed. We investigate the numerical solution and analysis of the RSDO-ADE in 1D case. Then we discuss the RSDO-ADE in 2D case. For 2D case, we propose a new second-order accurate implicit alternating direction method, and the stability and convergence of this method are proved. Finally, numerical results are presented to support our theoretical analysis.

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Design, implementation and application of distributed order PI control

Cited by 41 publications

References 46 publications

Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach

Numerical solutions of distributed order fractional differential equations in the time domain using the Müntz–Legendre wavelets approach

Algebraic Conditions for Stability Analysis of Linear Time‐Invariant Distributed Order Dynamic Systems: A Lagrange Inversion Theorem Approach

Novel Second-Order Accurate Implicit Numerical Methods for the Riesz Space Distributed-Order Advection-Dispersion Equations

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