混合系统的稳定性分析

研究了混合系统的稳定性问题.首先,对于混合系统给出了一种一般的模型,该模型能够描述混合状态的跳变现象.然后,定义了一种辅助函数作为系统能量的一种度量.基于该模型和辅助函数,得到了混合系统稳定性判定的一些新结果.这些结果给出了在离散状态改变时,在由于连续状态的跳变而引起的系统能量增加的情况下,混合系统仍保持稳定的充分条件.最后,给出了一种能量函数的寻找方案,并利用一个仿真实例验证了该方案的有效性.     

STATCOM的系统仿真

本文基于MATLAB中的动态仿真工具SIMULINK,建立了静止无功发生器的仿真模型。以含有静止无功发生器的单机无穷大系统为例,结合多目标控制方法,用S-Function仿真分析了静止无功发生器在系统暂态故障过程中的调节作用。仿真结果验证了本文所设计的多目标控制器的正确性以及本无功发生装置仿真模型的有效性。     

STATCOM的系统仿真

本文基于MATLAB中的动态仿真工具SIMULINK,建立了静止无功发生器的仿真模型.以含有静止无功发生器的单机无穷大系统为例,结合多目标控制方法,用S-Function仿真分析了静止无功发生器在系统暂态故障过程中的调节作用.仿真结果验证了本文所设计的多目标控制器的正确性以及本无功发生装置仿真模型的有效性.     

多目标控制方法的STATCOM系统仿真

为了研究采用多目标控制的静止无功发生器对电力系统的调节作用,建立了基于MATLAB的静止无功发生器的仿真模型。以含有静止无功发生器的单机无穷大系统为例,结合多目标控制方法,用S—Function仿真分析了静止无功发生器在系统暂态故障过程中的调节作用。仿真结果验证了所设计的多目标控制器的正确性以及该无功发生装置仿真模型的有效性。     

随机时滞神经网络的全局指数稳定性

首先对一般随机系统的渐近特性进行了讨论.然后结合神经网络的特点,应用李雅普诺夫第二方法对一类随机时滞神经网络系统的全局指数稳定性进行了分析,给出了易于判定随机时滞神经网络几乎必然指数稳定性新的代数判据,并给出实例进行仿真实验.     

简单电力系统静态稳定性分析及研究

文章以一个单机-无穷大系统为例,分析了影响电力系统静态稳定性的因素,介绍了静态稳定性的分析方法,提出了提高电力系统静态稳定性的措施。通过采取改善电力系统基本元件的特性和参数及采用附加装置等措施,提高了电力系统的静态稳定性。     

带输出误差约束的单机电力系统自适应控制

针对带有静止无功补偿器(SVC)的单机无穷大电力系统,提出了一种自适应动态面与积分滑模控制相结合的控制方案,有效地克服了参数不确定性和外部扰动的影响,确保了系统跟踪误差能够在有限时间内收敛到稳定状态,提高了系统的收敛速度和跟踪精度。通过引入误差转换函数,使得功角的跟踪误差性能指标保持在预定的范围内。采用最小参数学习法在线估计径向基函数神经网络(RBFNN)理想权值向量的范数,避免了神经网络因估计自身权值向量维数增加而引起的“维数灾难”问题,极大减轻了控制器的计算负担。控制算法通过StarSim电力电子实时仿真实验平台进行实验验证,实验结果表明了所提控制方案的有效性。     

基于DSP控制的静止无功发生器控制器的研究

静止无功发生器(SVG)是柔性交流输电系统中的一种重要的控制器.由于以传统的单片机作为控制器的SVG受硬件资源与速度的限制,无法实现对电网的实时动态无功补偿,因此本文提出了一种基于DSP控制新型静止无功发生器的方案,并进行了深入的分析和研究.     

带有时变时滞和同步切换的忆阻神经网络的全局指数稳定性

本文建立并研究了一类具有时变时滞和不同切换机制的忆阻神经网络.利用李雅普诺夫稳定性理论,得到了该神经网络平衡点一致稳定性的充分条件,该充分条件直接有效地反映了时变时滞对稳定性的影响.数值模拟结果验证了理论结果的有效性.     

基于T-S模型的体操机器人系统模糊变结构控制

针对体操机器人（Acrobot）这类非线性系统,给出一种基于T—S模型的模糊变结构控制律设计．首先采用T—S模型建模,得到Acrobot的全局模糊模型;然后基于Lyapunov理论设计出保证Acrobot全局渐近稳定的模糊变结构平衡控制器．仿真结果表明,所设计的模糊变结构控制器与普通变结构控制器相比．可使Acrobot系统在垂直向上平衡点附近具有更大的吸引域和更强的鲁棒性．     

一类互联电力系统的鲁棒联结稳定性分析

研究一类互联电力系统在不确定结构扰动下的鲁棒联结稳定问题．基于系统中互联矩阵的不确定性给出了鲁棒联结稳定的定义,利用向量Lyapunov函数方法及范数、特征值的性质推导了此类系统鲁棒联结稳定的两个充分条件．对系统在不确定结构扰动下联结稳定的鲁棒程度进行分析,得到了不确定参数的鲁棒界．两区域互联电力系统的仿真实例说明了所推导条件的有效性．     

发电机和静止无功补偿器鲁棒非线性协调控制

采用Hamilton函数方法研究发电机励磁和静止无功补偿器(SVC)的鲁棒协调控制问题。首先建立系统的不确定非线性微分代数系统控制数学模型;然后通过预置状态反馈完成系统的耗散Hamilton实现,并基于耗散实现设计鲁棒非线性协调控制器。仿真结果表明,该控制器能有效提高电力系统的暂态稳定性。     

Characterization of uniform attractors for control systems

This paper is devoted to the characterisation of uniform attractors for control systems by means of Lyapunov functions. We consider a uniform attractor that is compact and positively invariant by the system. We present the relationship between the concept of uniform attractor and the Conley concept of attractor.     

LMI stability conditions for uncertain rational nonlinear systems

This paper presents LMI conditions for local, regional, and global robust asymptotic stability of rational uncertain nonlinear systems. The uncertainties are modeled as real time varying parameters with magnitude and rate of variation bounded by given polytopes and the system vector field is a rational function of the states and uncertain parameters. Sufficient LMI conditions for asymptotic stability of the origin are given through a rational Lyapunov function of the states and uncertain parameters. The case where the time derivative of the Lyapunov function is negative semidefinite is also considered and connections with the well known LaSalle's invariance conditions are established. In regional stability problems, an algorithm to maximize the estimate of the region of attraction is proposed. The algorithm consists of maximizing the estimate for a given target region of initial states. The size and shape of the target region are recursively modified in the directions where the estimate can be enlarged. The target region can be taken as a polytope (convex set) or union of polytopes (non‐convex set). The estimates of the region of attraction are robust with respect to the uncertain parameters and their rate of change. The case of global and orthant stability problems are also considered. Connections with some results found in sum of squares based methods and other related methods found in the literature are established. The LMIs in this paper are obtained by using the Finsler's Lemma and the notion of annihilators. The LMIs are characterized by affine functions of the state and uncertain parameters, and they are tested at the vertices of a polytopic region. It is also shown that, with some additional conservatism, the use of the vertices can be avoided by modifying the LMIs with the S‐Procedure. Several numerical examples found in the literature are used to compare the results and illustrate the advantages of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Hybrid adaptive robust control of static var compensator in power systems

To improve the transient response of an electric power transmission system, a hybrid adaptive robust control method is proposed in this paper for the static var compensator by incorporating the immersion and invariance adaptive (I&I adaptive) and L₂‐gain control. In contrast to the standard I&I adaptive control algorithm, establishing a target system is not required in constructing the robust control law with the proposed method. Thus, the procedure of solving PDEs to satisfy the immersion condition can be avoided. In addition, both parametric and non‐parametric uncertainties, which commonly exist in electric power transmission systems, are considered. The parametric uncertainty induced by the damping coefficient of the system is estimated by the designed adaptive law, which is constructed by ensuring the estimation error converges to zero. The non‐parametric uncertainty is caused by external disturbances and approximation errors in modeling the uncertain structure. By assuming that the L₂‐gain of the system to the non‐parametric uncertainties satisfies a dissipation inequality, we found that the robustness of the controller can be guaranteed. It is proved that all the system states are globally bounded and converge to a new stable equilibrium. Simulation results are also presented to show the effectiveness of the proposed control method in improving the transient response of the system and the convergence speed of the system states. Copyright © 2013 John Wiley & Sons, Ltd.     

感应耦合电能传输系统稳定域的分析

感应耦合电能传输(inductive coupled power transfer,ICPT)技术是目前应用最为广泛的无线电能传输技术.应用软开关技术能提高ICPT系统的效率,但同时也带来了多软开关工作点(频率分叉)问题,使系统呈现复杂的动态特性.通过求解极限环的稳定域(region of stability,RoS)可以对其背后的原理进行很好的解释.本文以串联谐振型ICPT系统为例,首先对其建立了分段线性模型与碰撞映射模型,并利用ICPT系统的对称特性将碰撞映射模型进行了简化.通过理论分析,推导出基于二次型李雅普诺夫函数的稳定性判据.设计算法,以稳定性判据为约束条件,RoS体积为目标函数,通过遗传算法实现了RoS的求解.最后通过实例对此方法进行了验证.相比于现有方法,本方法求得的RoS体积更大,从而更好地解释了软开关ICPT系统的动态特性.本文所提出的方法也可用于求解其他分段线性系统的极限环RoS,为这类系统的研究与设计提供了一定的参考.     

Lyapunov stability analysis for nonlinear delay systems

Sufficient conditions ensuring that a nonlinear system with disturbances having a delay is globally asymptotically stable independent of delay are given. The proof carried out relies extensively on a characterization of the stability property in terms of Lyapunov function. The result is applied to some biological systems and neural networks. A stabilizing memoryless controller for a second-order system with state-delay is also proposed.     

Estimating the domain of attraction for non-polynomial systems via LMI optimizations

This paper proposes a strategy for estimating the domain of attraction (DA) for non-polynomial systems via Lyapunov functions (LFs). The idea consists of converting the non-polynomial optimization arising for a chosen LF in a polynomial one, which can be solved via LMI optimizations. This is achieved by constructing an uncertain polynomial linearly affected by parameters constrained in a polytope which allows us to take into account the worst-case remainders in truncated Taylor expansions. Moreover, a condition is provided for ensuring asymptotical convergence to the largest estimate achievable with the chosen LF, and another condition is provided for establishing whether such an estimate has been found. The proposed strategy can readily be exploited with variable LFs in order to search for optimal estimates. Lastly, it is worth remarking that no other method is available to estimate the DA for non-polynomial systems via LMIs.     

Input-to-state stability of switched nonlinear systems

The input-to-state stability （ISS） problem is studied for switched systems with infinite subsystems. By using multiple Lyapunov function method, a sufficient ISS condition is given based on a quantitative relation of the control and the values of the Lyapunov functions of the subsystems before and after the switching instants. In terms of the average dwell-time of the switching laws, some sufficient ISS conditions are obtained for switched nonlinear systems and switched linear systems, respectively.     

Effect of embedded voltage source converter on power system oscillation damping

This paper presents the damping torque analysis of power system oscillation stability as affected by the dynamic and control functions of an embedded voltage source converter(VSC).The objective of the study is to explain why and how the dynamic and basic control functions of the embedded VSC,ac and dc voltage regulation,provide damping to power system oscillations.The most important conclusion obtained in the paper is that both the dynamics and the dc voltage control of the VSC contribute a variable damping...