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1.
郭昊 《中国矿业》2021,30(S1):463-466
Riemann-Liouville分数阶微积分算子是一类带有一个函数的分数阶微积分算子的特殊情形,以Riemann-Liouville分数阶微积分算子的积分中值定理和微分中值定理为基础,我们得到了一类带有一个函数的分数阶微积分算子的积分中值定理和微分中值定理,并给出其在计算方面的一些应用。  相似文献   
2.
In this article, we develop proportional, fractional-integral, and derivative () controllers for the regulation and tracking problems of nonlinear systems. The analytic results are obtained by extending the passivity-based approach to include fractional operators. Robustness under parametric uncertainty is dealt with by a combination with an adaptive scheme. It is also shown their robustness under additive noise and their robustness under uncertainty in the derivation order. The advantages in the controlled system performance and in the control energy consumption in comparison to classic PI and proportional integral derivative controllers are illustrated for the quadratic boost converter and a benchmark system in the literature.  相似文献   
3.
In this paper, a new tuning method of variable-order fractional fuzzy PID controller (VOFFLC) is proposed for a class of fractional-order and integer-order control plants. Fuzzy logic control (FLC) could easily deal with parameter variations of control system, but the fractional-order parameters are unable to change through this way and it has confined the effectiveness of FLC. Therefore, an attempt is made in this paper to allow all the five parameters of fractional-order PID controller vary along with the transformation of system structure as the outputs of FLC, and the influence of fractional orders λ and μ on control systems has been investigated to make the fuzzy rules for VOFFLC. Four simulation results of different plants are shown to verify the availability of the proposed control strategy.  相似文献   
4.
李志农  王海峰  肖尧先 《兵工学报》2015,36(9):1790-1798
在考虑非线性涡动的情况下,建立了分数阶阻尼裂纹转子系统的非线性动力学模型,并用龙格-库塔法和连分式Euler法对其进行了数值仿真。讨论了分数阶阶次、转子转速和裂纹深度对分数阶阻尼裂纹转子系统非线性动力学特性的影响。研究结果表明:对于具有分数阶特性的转子系统,采用分数阶来建立裂纹转子系统模型,能更好地揭示系统的非线性动力学特性;在相同的裂纹深度和相同的分数阶阶次下,随着转速比的增加,转子系统依次经历混沌、倍周期和周期运动;在相同的转速比和相同的分数阶阶次下,裂纹深度比较小时,引起的转子刚度变化量不大,一般不会出现复杂的分叉与混沌现象;随着裂纹深度的加深,转子的刚度减小,转子系统呈现复杂的振动特性,裂纹故障特征越来越明显,转子系统由单周期运动变换到倍周期运动,二倍频分量占主导地位,同时其他倍频分量也相继出现。这些有价值的结论对转子裂纹的故障诊断提供了参考。  相似文献   
5.
It is eminent that partial differential equations are extensively meaningful in physics, mathematics and engineering. Natural phenomena are formulated with partial differential equations and are solved analytically or numerically to interrogate the system’s dynamical behavior. In the present research, mathematical modeling is extended and the modeling solutions Helmholtz equations are discussed in the fractional view of derivatives. First, the Helmholtz equations are presented in Caputo’s fractional derivative. Then Natural transformation, along with the decomposition method, is used to attain the series form solutions of the suggested problems. For justification of the proposed technique, it is applied to several numerical examples. The graphical representation of the solutions shows that the suggested technique is an accurate and effective technique with a high convergence rate than other methods. The less calculation and higher rate of convergence have confirmed the present technique’s reliability and applicability to solve partial differential equations and their systems in a fractional framework.  相似文献   
6.
为进一步揭示超磁致伸缩致动器(Giant magnetostrictive actuator, GMA)系统非线性运动过程中的内在机理和动力学特征,基于分数阶微积分理论,将GMA动力学系统模型拓展至分数阶,建立含有分数阶阻尼的非线性GMA系统动力学方程,基于平均法分析系统主共振,得到系统的幅频响应方程;使用幂级数方法求解系统的数值解,通过Matlab数值模拟分析不同激励幅值和阻尼阶次对GMA系统的影响机理,从定性和定量的角度研究系统的分岔和混沌运动现象。结果表明:激励幅值和阻尼阶次对系统的幅频特性有显著影响;阻尼阶次对系统的分岔和混沌行为影响较大;不同阻尼阶次下由激励幅值变化引起系统的动力学行为相似但混沌区域不同。该研究有助于更好地了解GMA系统动力学特性,对工程实践中控制GMA系统稳定运行提供新的视角。  相似文献   
7.
The optimization of a fixed-structure controller is in general computationally intractable, posing a challenge to control system engineers. This paper introduces a novel technique for designing such control techniques by formulating it as a nonlinear non-convex constrained problem. A novel PSO algorithm, namely the Augmented Lagrangian Particle Swarm Optimization with Fractional Order Velocity (ALPSOFV), is proposed for improving the convergence rate. The structure of the controller is selectable and, therefore, the Fractional Order Proportional Integral Derivative (FOPID) algorithm is chosen in the scope of the study. The results for three test examples show the good performance of the ALPSOFV.  相似文献   
8.
As the risk access control model can not match rules dynamically and the risk values are insensitive to access requests, a cloud platform dynamic risk access control model(CDRAC) is proposed. First, the attribute based access control(ABCA) is improved with the event calculus(EC), and the dynamic rule matching module is constructed in the CDRAC. Then, the dynamic risk evaluation index weight distribution sub-module is designed, and the risk assessment module with high sensitivity to access requests is constructed. Experimental results show that the CDRAC has good effectiveness and feasibility, and that it has a better real-time performance and adaptability than other existing models.  相似文献   
9.
李文军  王潇楠  郑永军 《兵工学报》2018,39(9):1820-1828
为了研究热电偶动态特性,用分数阶模型进行建模和模型辨识。测量瞬态温度时,温度响应存在延迟,该测量过程属于物理上的延迟过程或者叫做遗传过程。热电偶与被测介质接触时,测量接点和偶丝都产生热量传递。测量接点的温度分布取决于介质与测量接点的换热以及测量接点与偶丝之间的导热。根据分数阶微积分理论,引入时间分数阶微积分建立了热电偶半无限固体导热模型。模型描述了露端式热电偶测量接点与被测介质之间的换热过程,包括测量接点与偶丝的热量传递。通过分数阶拉普拉斯变换得到一种阶次呈比例的分数阶传递函数结构,这种结构的传递函数描述了测量接点热惯性的延迟和热电偶偶丝热扩散的单相延迟。建立了热电偶测量固体表面温度的实验系统,采集热电偶在温度激励下的输入和输出。根据输入和输出数据,用改进Luus-Jaakola算法对分数阶传递函数的参数和阶次进行了估计。实验和计算结果表明,变阶次分数阶传递函数的拟合结果优于固定阶次分数阶传递函数。  相似文献   
10.
In this paper, we estimate the parameter values of a fractional-order model of supercapacitors involving fractional derivatives of Liouville-Caputo, Caputo-Fabrizio, and Atangana-Baleanu and fractional conformable derivative in the Liouville-Caputo sense. We present the exact solution of the considered model using the properties of the Laplace transform operator together with the convolution theorem. They developed numerical simulations using each one of the fractional derivatives; the results were compared graphically with experimental data obtained from different supercapacitors using standard laboratory equipment. The nonlocal parameters involved in the equivalent electrical circuit for the supercapacitor model are recalculated for each fractional derivative using a particle swarm optimization algorithm for generating optimal solutions.  相似文献   
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