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191.
将求解整数阶系统最优控制的方法和步骤拓展到分数阶系统的最优控制中,对由Caputo定义的分数阶微分方程描述的分数阶系统提出了求解性能指标函数在始端固定的条件下,终端时间固定而终端状态自由和始端固定、终端时间固定而终端状态受函数约束的最优控制的状态方程、伴随方程、控制方程、横截条件和终端约束方程,并给予了证明. 相似文献
192.
提出一种分数阶线性系统稳定性证明方法。首先分析了双参数Mittag-Leffler函数估值定理中的限制条件, 通过证明得出了该定理收敛域有误, 因此改进了双参数Mittag-Leffler函数估值定理, 并将它的参数由实数推广到矩阵。然后提出了可适用于分数阶线性系统的稳定性理论, 并利用改进的双参数Mittag-Leffler函数估值定理进行了证明。仿真结果验证了理论的正确性。 相似文献
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为了克服在过热蒸汽温度控制中对象参数变化对控制效果的影响,将分数阶PID(FOPID)控制与广义预测控制(GPC)算法相结合,构成了分数阶PID型FOPID广义预测控制(FOPID-GPC)算法。该算法的参数设置与传统的整数阶PID广义预测控制算法的参数设置具有一定的相似性,并增加了积分阶数和微分阶数2个可调参数,该参数的取值对控制系统的性能具有很大的影响。仿真结果表明,FOPID-GPC算法使控制系统具有超调量小、调节时间短、能够快速跟踪系统变化的特点,提高了控制系统动态性能,能够较好地将蒸汽温度控制在设定值附近。 相似文献
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Design and Robust Performance Evaluation of a Fractional Order PID Controller Applied to a DC Motor
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This paper proposes a methodology for the quantitative robustness evaluation of PID controllers employed in a DC motor. The robustness analysis is performed employing a 23 factorial experimental design for a fractional order proportional integral and derivative controller (FOPID), integer order proportional integral and derivative controller (IOPID) and the Skogestad internal model control controller (SIMC). The factors assumed in experiment are the presence of random noise, external disturbances in the system input and variable load. As output variables, the experimental design employs the system step response and the controller action. Practical implementation of FOPID and IOPID controllers uses the MATLAB stateflow toolbox and a NI data acquisition system. Results of the robustness analysis show that the FOPID controller has a better performance and robust stability against the experiment factors. 相似文献
199.
Local Bifurcation Analysis of a Delayed Fractional-order Dynamic Model of Dual Congestion Control Algorithms
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Min Xiao Guoping Jiang Jinde Cao Weixing Zheng 《IEEE/CAA Journal of Automatica Sinica》2017,4(2):361-369
In this paper, we propose a delayed fractional-order congestion control model which is more accurate than the original integer-order model when depicting the dual congestion control algorithms. The presence of fractional orders requires the use of suitable criteria which usually make the analytical work so harder. Based on the stability theorems on delayed fractionalorder differential equations, we study the issue of the stability and bifurcations for such a model by choosing the communication delay as the bifurcation parameter. By analyzing the associated characteristic equation, some explicit conditions for the local stability of the equilibrium are given for the delayed fractionalorder model of congestion control algorithms. Moreover, the Hopf bifurcation conditions for general delayed fractional-order systems are proposed. The existence of Hopf bifurcations at the equilibrium is established. The critical values of the delay are identified, where the Hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium. Same as the delay, the fractional order normally plays an important role in the dynamics of delayed fractional-order systems. It is found that the critical value of Hopf bifurcations is crucially dependent on the fractional order. Finally, numerical simulations are carried out to illustrate the main results. 相似文献
200.
Distributed Adaptive Cooperative Tracking of Uncertain Nonlinear Fractional-order Multi-agent Systems
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In this paper, the leader-following tracking problem of fractional-order multi-agent systems is addressed. The dynamics of each agent may be heterogeneous and has unknown nonlinearities. By assumptions that the interaction topology is undirected and connected and the unknown nonlinear uncertain dynamics can be parameterized by a neural network, an adaptive learning law is proposed to deal with unknown nonlinear dynamics, based on which a kind of cooperative tracking protocols are constructed. The feedback gain matrix is obtained to solve an algebraic Riccati equation. To construct the fully distributed cooperative tracking protocols, the adaptive law is also adopted to adjust the coupling weight. With the developed control laws, we can prove that all signals in the closed-loop systems are guaranteed to be uniformly ultimately bounded. Finally, a simple simulation example is provided to illustrate the established result. 相似文献