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分数阶控制系统稳定性分析与控制器设计:扩展频率域法 总被引:3,自引:0,他引:3
鉴于整数阶控制系统主要进行正频域分析,本文论述了分数阶控制系统的扩展频域方法.它通过对分数阶系统传递函数的基本分解获得系统频率特性曲线,此过程是唯一和可逆的.本文根据扩展频域分析法扩展了Nyquist稳定性判据,得到能够直观判断任意阶控制系统稳定性的通用判据.另外,扩展频域分析法为分数阶控制器提供了便于设计的直观形式,文章提供了具有新结构的超前滞后补偿器和分数阶P(ID)μ控制器的设计步骤.最后举例用扩展频域法对分数阶系统进行稳定性分析和超前滞后补偿器的综合. 相似文献
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一种线性分数阶系统稳定性的频域判别准则 总被引:1,自引:0,他引:1
在分析了分数阶系统稳定性与传递函数分母相角增量的关系的基础上, 提出了一种线性分数阶系统的频域稳定性判别定理.定义了关于分数阶系统分母各项系数的两个函数,通过分析这两个函数正实数解的大小关系以及解的数目与分母最高阶数的关系,给出了分数阶系统稳定所需满足的条件.将用于在频域上对整数阶系统稳定性判别的Hermite-Biehler定理推广到对分数阶系统稳定性的判定.最后,通过对两个数值算例的分析,说明了提出的稳定性判别准则的正确性. 相似文献
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复杂工作环境中,许多自然现象的个体动力学特性用整数阶方程不能描述,只能用非整数阶(分数阶)动力学来描述个体的运动行为. 本文假设多自主体系统内部连接组成有向加权网络,个体的动态特性应用分数阶动力学方程描述,个体之间数据传输存在通信时延. 应用分数阶系统的Laplace变换和频域理论,研究了离散时间的分数阶多自主体系统的渐近一致性. 应用Hermit-Biehler 定理,研究了具有样本时延的分数阶多自主体系统的运动一致性,得到保证系统稳定的时延的上界阈值. 最后应用一个实例对结论进行了验证. 相似文献
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复杂分数阶多自主体系统的运动一致性 总被引:1,自引:0,他引:1
复杂环境中,许多自然现象的动力学特性不能应用整数阶方程描述,而只能用分数阶(非整数阶)动力学的智能个体合作行为来解释. 本文假设多自主体 系统存在个体差异,采用不同的分数阶动力学特性组成复杂分数混合阶微分方程. 应用分数阶系统的Laplace变换和频域理论,研究了有向网络拓扑下,时延分数混合阶多自主体系统的运动一致性. 由于整数阶系统是分数阶系统的特殊情况,本文的结论可以推广到整数阶与分数阶混合的多自主体系统中. 最后,应用仿真实例对本文结论进行了验证. 相似文献
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采用机理与数据相结合的建模方法对永磁同步电动机进行分数阶时域和频域建模. 在分数阶时域建模方法中, 设计伪随机激励信号, 获取实时实验数据并采用输出误差辨识算法来获取分数阶阶次; 在分数阶频域建模方法中, 由实时实验数据绘制出电动机的对数频率特性曲线. 采用分数阶频域建模中经典Levy 辨识算法, 利用加权函数加以改进, 得到永磁同步电动机分数阶模型辨识结果. 最后通过对两种方法得到的结果进行对比表明了所提出模型的可靠性.
相似文献10.
自抗扰控制器的阶次与参数的选取 总被引:1,自引:0,他引:1
本文就选择不同阶次的自抗扰控制器时,对系统的控制参数选取进行了研究.结果表明:线性时不变系统的线性自抗扰控制,可等效为一个复合控制系统,其等效反馈补偿器为一超前校正单元串联一积分器;其等效前置滤波器为一滞后校正单元串联一微分器.观测器带宽和控制器带宽的比值,决定着反馈补偿器的最大相位超前角,而频带则决定着最大相位超前角的发生位置.同时,随着自抗扰控制器阶次的增加,补偿器的最大超前校正角也增加.通过对开环系统的频域分析,本文给出了利用该补偿器的频域特性进行自抗扰控制器参数设计的一般步骤,可大幅度减少工程师的反复试验过程,方便工程师应用. 相似文献
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Jing Bai Guoguang Wen Ahmed Rahmani Xing Chu 《International journal of systems science》2016,47(1):222-234
This paper investigates consensus of fractional-order multi-agent systems (MASs) with a reference state. First, a consensus control law with a constant reference state is given using graph theory and stability analysis of fractional-order. Then, a general control law and a particular one for consensus of fractional-order MASs with a time-varying reference state are proposed. Next, the above control laws are extended to solve formation tracking problem. Finally, several simulations are presented to verify the effectiveness of the obtained results. 相似文献
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Zhe Gao 《International journal of control》2019,92(5):960-974
This paper presents the fractional-order Kalman filters using Tustin generating function for linear and nonlinear fractional-order systems involving process noise and measurement noise. By using the Tustin generating function, the differential equation model is obtained by discretising the investigated continuous-time fractional-order system. The two kinds of fractional-order Kalman filters are given for the correlated and uncorrelated cases in terms of the process noise and measurement noise for linear fractional-order system, respectively. In addition, based on the first-order Taylor expansion formula, the extended fractional-order Kalman filter using Tustin generating function is proposed to improve the accuracy of state estimation. Finally, three examples are illustrated to verify the effectiveness of the Tustion fractional-order Kalman filters for linear and nonlinear fractional-order systems. 相似文献
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Fractional-order calculus has broad application scenarios in engineering and physics. Unlike integer-order calculus, fractional-order calculus has the ability to analyze nonclassical phenomena in science and engineering. For industrial processes with strong nonlinear characteristics, nonlinear models such as the Wiener model have become research hotspots. This paper studies the parameter identification of the fractional-order Wiener system. In this paper, the forgetting factor extended stochastic gradient (FF-ESG) algorithm and the gradient iterative (GI) algorithm are proposed to identify the parameters of the fractional-order Wiener system. Then, the convergence of the FF-ESG algorithm for the fractional-order Wiener system is analyzed. Both proposed algorithms can obtain exact parameter estimates, which are verified by a numerical example and a case study of a fluid control valve. 相似文献
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This paper is concerned with the problem of global power-rate synchronization of fractional-order nonautonomous neural networks with heterogeneous proportional delays. By utilizing the Leibniz rule for fractional differentiation and an extended comparison technique, delay-dependent conditions are derived to ensure that the considered fractional-order neural network model is globally synchronous with a power decaying rate. Two examples with numerical simulations are given to demonstrate the effectiveness of the obtained results. 相似文献
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The study of feedback fractional-order systems has been receiving considerable attention due to the facts that many physical systems are well characterized by fractional-order models, and that fractional-order controllers are used in feedback systems with the intention of breaking through the performance limitation of integer-order controllers. Owing to the lack of effective analytic methods for the time-domain analysis and simulation of linear feedback fractional-order systems, we suggest in this paper two reliable and accurate numerical methods for inverting fractional-order Laplace transforms. One is based on computing Bromwich's integral with a numerical integration scheme capable of accuracy control, and the other is based on expanding the time response function in a B-spline series. In order to demonstrate the superiority in solution accuracy and computational complexity of these two numerical methods over the Grunwald-Letniknov approximation method and Podlubny's analytic formulas, which are in a form of double infinite series, the time-domain simulations of the feedback control of a fractional-order process with a PDμ-controller and a fractional-order band-limited lead compensator are worked out. The simulation results indicate that a convergence problem indeed occurs in using Podlubny's infinite series expressions, and that the problem could not be overcome by a series acceleration scheme 相似文献
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By viewing the anti-windup problem as a decoupled set of subsystems and relating this configuration to a general static anti-windup set-up, LMI conditions are established which guarantee stability and performance of the resulting closed-loop system. The approach taken, and the mapping used for the performance index, are logical and intuitive–-and, it is argued, central to the ‘true’ anti-windup objective. The approach enables one to construct static anti-windup compensators in a systematic and numerically tractable manner. The idea is extended to allow low-order anti-windup compensators to be synthesized, which, while being sub-optimal, can improve transient performance and possess several desired properties (such as low computational overhead and sensible closed-loop pole locations). In addition, low-order anti-windup synthesis is often feasible when the corresponding static synthesis is not. 相似文献
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Joachim Deutscher 《国际强度与非线性控制杂志
》2014,24(1):110-122
》2014,24(1):110-122
In this article, the concept of dual observer‐based compensators is extended from linear to nonlinear systems. It is shown that a dual observer‐based compensator achieves stabilization by rendering an invariant manifold attractive in which desired dynamics can be assigned. The design of these compensators for nonlinear systems is considerably simple if a flat output of the system to be controlled is known which is illustrated by means of a simple example. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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Characterization of PID and lead/lag compensators satisfying given H/sub /spl infin// specifications
Blanchini F. Lepschy A. Miani S. Viaro U. 《Automatic Control, IEEE Transactions on》2004,49(5):736-740
This note deals with the problem of characterizing a class of second-order three-parameter controllers [including proportional-integral-derivative (PID) and lead/lag compensators] satisfying given H/sub /spl infin// closed-loop specifications. Design characterizations of similar form as in the recent work on PID control, are derived for a larger class of compensators using simple geometric considerations. Specifically it is shown that, given the value of one parameter: i) the region of the plane defined by the other two parameters where the considered H/sub /spl infin// constraint is satisfied, consists of the union of disjoint convex sets whose number can be bounded by means of the pancake-cutting formula, and ii) the closed-loop pole distribution can be related to them. An example illustrates how the method can be applied to design a PID controller in the case of bounded sensitivity. 相似文献