Fractional-order exponential switching technique to enhance sliding mode control

Yin, Chun; Huang, Xuegang; Chen, YangQuan; Dadras, Sara; Zhong, Shouming; Cheng, Yuhua

doi:10.1016/j.apm.2017.02.034

Cited by 128 publications

(59 citation statements)

References 28 publications

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“…Remark A fractional‐order reaching law has also been proposed in the work of Yin et al,() which can shorten the reaching time and attenuate the chattering phenomenon in control input compared with the conventional reaching law. It can be expressed as

\overset{s}{true} = - {k 𝒟}^{α} sgn false(s false), k > 0, 0 < α < \leq 1,

whose reaching time is

{((), \frac{normalΓ ((), 2 - α) (||, s false(0 false))}{k})}^{\frac{1}{1 - α}}

.…”

Section: Resultsmentioning

confidence: 99%

“…In the work of Yin et al, an improved fractional‐order reaching law

\overset{s}{true} = - k false| s |^{α} 𝒟^{β} sgn false(s false), k > 0, 0 < α < 1, 0 < β < 1

was proposed to control a class of 3‐dimensional nonlinear fractional‐order systems. Another improved fractional‐order reaching law containing additional attenuation item − ϵ s was then proposed in the work of Yin et al, and a faster convergence rate was derived. We have to declare here that the reaching time of the mentioned reaching laws is sensitive to initial conditions, where the reaching time is varying for different s 0 with fixed controller parameters.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On 2 types of robust reaching laws

Chen

Wei

Wang

2018

Intl J Robust & Nonlinear

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Summary The reaching law is an important part of a sliding‐mode controller, which guarantees the existence of sliding motion in finite time. Fast access to sliding motion with a weak chattering phenomenon in control input is always desired. In this paper, 2 different types of reaching laws are proposed, which guarantee finite‐time convergence to the sliding manifold. Moreover, the reaching time is robust to initial conditions and can be designed by the user. Some useful discussions on the design of parameters are also presented to weaken the chattering phenomenon. A careful simulation study is finally provided to verify the effectiveness and efficiency of the proposed methods.

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\overset{s}{true} = - {k 𝒟}^{α} sgn false(s false), k > 0, 0 < α < \leq 1,

whose reaching time is

{((), \frac{normalΓ ((), 2 - α) (||, s false(0 false))}{k})}^{\frac{1}{1 - α}}

.…”

Section: Resultsmentioning

confidence: 99%

“…In the work of Yin et al, an improved fractional‐order reaching law

\overset{s}{true} = - k false| s |^{α} 𝒟^{β} sgn false(s false), k > 0, 0 < α < 1, 0 < β < 1

Section: Introductionmentioning

confidence: 99%

On 2 types of robust reaching laws

Chen

Wei

Wang

2018

Intl J Robust & Nonlinear

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“…There are some computational complexities in calculating the state function (19) and computing the control function from the system dynamics. To overcome this issue, the fractional derivative is approximated via an operational matrix.…”

Section: Solution Of the 2d-foocpmentioning

confidence: 99%

“…In [18], the parametric optimization method is employed to solve fixed final time FOCPs. Sliding mode control with the aid of fractional order control in [19,20] is employed for nonlinear systems as well as 3D fractional order nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

The Use of the Ritz Method and Laplace Transform for Solving 2D Fractional‐Order Optimal Control Problems Described by the Roesser Model

Nemati

Mamehrashi

2018

Asian Journal of Control

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In this article a numerical solution is presented for a class of two-dimensional fractional-order optimal control problems (2D-FOOCPs) with one input and two outputs. To implement the numerical method, the Legendre polynomial basis is used with the aid of the Ritz method and the Laplace transform. By taking the Ritz method as a basic scheme into account and applying a new constructed fractional operational matrix to estimate the fractional and integer order derivatives of the basis, the given 2D-FOOCP is reduced to a system of algebraic equations. One of the advantages of the proposed method is that it provides greater flexibility in which the given initial and boundary conditions of the problem are imposed. Moreover, satisfactory results are obtained in just a small number of polynomials order. The convergence of the method is extensively investigated and finally two illustrative examples are included to show the validity and applicability of the novel proposed technique in the current work.

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“…11 The applications of fractional-order calculus in many research fields have been widely explored and verified effectively. [12][13][14][15][16][17][18] Therefore, efficient control algorithms aiming at delayed fractional-order systems, both stable and unstable systems, are needed. In this paper, we focus on robust stability analysis based on the FFSA algorithm, which can be used on both fractional-order and integer-order systems.…”

mentioning

confidence: 99%

Robust stability analysis for fractional‐order systems with time delay based on finite spectrum assignment

Liu

Zhang

Xue

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, the robust stability of a fractional‐order time‐delay system is analyzed in the frequency domain based on finite spectrum assignment (FSA). The FSA algorithm is essentially an extension of the traditional pole assignment method, which can change the undesirable system characteristic equation into a desirable one. Therefore, the presented analysis scheme can also be used as an alternative time‐delay compensation method. However, it is superior to other time‐delay compensation schemes because it can be applied to open‐loop poorly damped or unstable systems. The FSA algorithm is extended to a fractional‐order version for time‐delay systems at first. Then, the robustness of the proposed algorithm for a fractional‐order delay system is analyzed, and the stability conditions are given. Finally, a simulation example is presented to show the superior robustness and delay compensation performance of the proposed algorithm. Moreover, the robust stability conditions and the time‐delay compensation scheme presented can be applied on both integer‐order and fractional‐order systems.

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Fractional-order exponential switching technique to enhance sliding mode control

Cited by 128 publications

References 28 publications

On 2 types of robust reaching laws

On 2 types of robust reaching laws

The Use of the Ritz Method and Laplace Transform for Solving 2D Fractional‐Order Optimal Control Problems Described by the Roesser Model

Robust stability analysis for fractional‐order systems with time delay based on finite spectrum assignment

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