A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control

Tai, Yongpeng; Chen, Ning; Wang, Lijin; Feng, Zaiyong; Xu, Jun

doi:10.3390/math8071134

Cited by 5 publications

(4 citation statements)

References 22 publications

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“…Compared with these index reduction methods, our method is able to address a fairly wide class of large-dimension systems of DAEs precisely and efficiently. In the future, the proposed approach will also be applied to exploit some large-scale fractional DAEs [28] or partial DAEs.…”

Section: Discussionmentioning

confidence: 99%

A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations

Tang

Rao

2020

Mathematics

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A new generation of universal tools and languages for modeling and simulation multi-physical domain applications has emerged and became widely accepted; they generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAE systems with large dimensions, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on the Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameters has been presented. It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples, and preliminary numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

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Section: Discussionmentioning

confidence: 99%

A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations

Tang

Rao

2020

Mathematics

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Section: Discussionmentioning

confidence: 99%

A New Block Structural Index Reduction Approach for Large-scale Differential Algebraic Equations

Tang¹,

Rao²

2020

Preprint

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A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameter has been presented.It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples. And numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

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“…First, the vibration equation is transformed into a fractional state equation, and then the control rate is designed based on this equation. Finally, the method in (Tai et al, 2020) is adopted to solve the fractional state equation and obtain the corresponding time-domain response.…”

Section: Control Algorithm Design Based On the Linear Quadratic Regulator Methodsmentioning

confidence: 99%

“…LQR method. Based on the method in (Tai et al, 2020), equation ( 27) can be transformed to the following form:…”

Section: State Space Equation Of the Beammentioning

confidence: 99%

New control strategy for suppressing the local vibration of sandwich beams based on the wave propagation method

Chen

Tai

et al. 2021

Journal of Intelligent Material Systems and Structures

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The general vibration control strategy of beam structures is a global vibration control method based on the principle of modal superposition. However, the vibration wave control of beams can achieve local control of the vibration energy. This paper presents a wave control method for the local vibration control of fractional viscoelastic composite beams based on the operating principle of a piezoelectric sheet. To obtain better control performance, a particle swarm optimization algorithm was adopted to optimize the parameters of the piezoelectric sheet. A linear quadratic regulator control algorithm was designed to verify the validity of the proposed method. In addition, the effects of the piezoelectric sheet number and fractional order on the amplitude response and optimization parameters were investigated. We observed that the proposed method has a good control effect on the local area vibration, and it can control the flow direction of the vibration power. The proposed method can be used to directly design the voltage and phase of a piezoelectric sheet without real-time feedback computation. This method is suitable for reducing local vibration under single repetitive operating conditions in engineering and can provide a theoretical basis for a follow-up study on the acoustic black hole phenomenon.

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A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control

Cited by 5 publications

References 22 publications

A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations

A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations

A New Block Structural Index Reduction Approach for Large-scale Differential Algebraic Equations

New control strategy for suppressing the local vibration of sandwich beams based on the wave propagation method

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