Sliding-mode boundary control for perturbed time fractional parabolic systems with spatially varying coefficients using backstepping

In this paper, we consider the boundary stabilization of an uncertain time fractional parabolic systems governed by time fractional parabolic partial differential equations (PDEs) with a boundary input disturbance and spatially varying coefficients (nonconstant coefficients) using a fractional-order sliding-mode controller. For this, the backstepping approach is used to transform an original system into a target system with a new manipulable input and perturbation. Then, the fractional-order sliding-mode algorithm is employed to design this new discontinuous boundary input to achieve the asymptotical stabilization of the target system (and, therefore, of the original system as well) by the fractional Lyapunov method. Apart from this, the well-posedness of the fractional parabolic system is analyzed theoretically. Fractional-order numerical simulations are provided to validate the developed technique.     

基于FOPID+ADRC的永磁同步电机低速控制

永磁同步电机(permanent magnet synchronous motor,PMSM)是一个非线性、多变量、强耦合系统,具有不确定的外部干扰。为了提高其低速运行时的控制精度,采用一种改进自抗扰控制(active disturbance rejection control,ADRC)对其进行控制。首先通过插值法构建一个新的非线性函数来代替ADRC中原有的最优控制函数,使其在原点处更平滑和连续。并将此函数应用于扩张观测器(extended state observer,ESO),最后将非线性误差反馈率(nonlinear state error feedback,NLSEF)用分阶数比例积分微分(fractional-order proportion integration differentiation,FOPID)代替以提高其动态性能。经SIMULINK仿真结果表明,该控制算法在PMSM低速控制中比传统ADRC具有更快的响应速度和更好的抗干扰能力。     

周期荷载下岩石分数阶黏弹塑性本构模型研究

为研究周期荷载下岩石疲劳变形特性,基于分数阶微积分构建分数阶黏壶,将分数阶黏壶替换西原模型黏塑性体中的一般黏壶,并在西原模型中串联一个黏性元件,分别建立了可描述周期荷载下岩石变形规律的一维和三维分数阶黏弹塑性本构模型。在高动应力状态下,模型为反映岩石减速、等速、加速3个变形阶段变形规律的岩石分数阶黏弹塑性疲劳本构模型;反之,则为反映岩石减速、加速变形规律的Burgers模型。对既有的岩石疲劳试验结果拟合表明:基于分数阶黏弹塑性模型所建立的岩石疲劳本构方程可较好地描述周期荷载下岩石各种变形特征,拟合系数在0.96以上。研究成果可丰富岩石力学理论,为相关研究提供参考。     

Comparative analysis on Hopf bifurcation of integer-order and fractional-order two-neuron neural networks with delay

This article mainly focuses on the stability and the existence of Hopf bifurcation of integer-order and fractional-order two-neuron neural networks with delay. First of all, we obtain the sufficient criterion to ensure the stability and the existence of Hopf bifurcation of integer-order two-neuron neural networks with delay. Next, we establish the sufficient condition guaranteeing the stability and the existence of Hopf bifurcation of fractional-order two-neuron neural networks with delay. The study reveals that the time delay has a vital effect on the stability and Hopf bifurcation of integer-order and fractional-order two-neuron neural networks with delay. By comparative analysis on Hopf bifurcation for integer-order and fractional-order two-neuron neural networks with delay, we find that under an appropriate parameter conditions, the stability region can be enlarged, and the time of appearance of Hopf bifurcation of the involved two-neuron neural networks can be postponed by using fractional-order case. Finally, computer simulation results are presented to illustrate the theoretical findings. The established results of this article play an important role in designing and controlling networks.     

分数阶RLαCβ电路的多变量域综合方法研究

电路的无源综合方法对电气设备的建模具有重要的应用。针对RLαCβ分数阶元件电路的无源综合问题,文中介绍了其多变量域的综合方法。通过变量代换将频域形式的电路策动点阻抗函数转换到多变量域;进一步推导了其多变量域的Foster综合方法以及Cauer综合方法,并给出与综合方法相对应的电路模型。最后通过实例的仿真与分析,验证了文中所提出的综合方法理论的可行性。所提出的综合方法克服了以往综合方法使用多口变压器的缺点,对于电气设备的分数阶电路建模具有重要的应用价值。     

H∞ filtering for continuous fractional-order 2D Roesser model: The 0<α≤1 case

This paper investigates the $H_{\infty }$ filtering for the continuous fractional-order (FO) two-dimensional (2D) Roesser model with the FO between 0 and 1. Firstly, a sufficient condition to ensure the stability and bounded realness in the sense of $H_{\infty }$-norm for the continuous FO 2D Roesser model is given in the form of linear matrix inequalities (LMIs). Secondly, based on the bounded real lemmas proposed above, the $H_{\infty }$ filtering problem for continuous FO 2D Roesser model is addressed through some congruent transformation and matrix transformation. The results are given in LMI form, and the parameters of the continuous FO 2D filters can be achieved from the LMIs easily. In the end, the effectiveness of the proposed results is verified by two numerical examples.