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When using H ∞ techniques to design decentralized controllers for large systems,the whole system is divided into subsystems, which are analysed using H ∞ control theory before being recombined. An analogy was established with substructural analysis in structural mechanics, in which H∞ decentralized control theory corresponds to substructural modal synthesis theory so that the optimal H∞ norm of the whole system corresponds to the fundamental vibration frequency of the whole structure. Hence, modal synthesis methodology and the extended Wittrick-Williams algorithm were transplanted from structural mechanics to compute the optimal H ∞ norm of the control system. The orthogonality and the expansion theorem of eigenfunctions of the subsystems H∞ control are presented in part ( Ⅰ ) of the paper. The modal synthesis method for computation of the optimal H∞ norm of decentralized control systems and numerical examples are presented in part ( Ⅱ ). 相似文献
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The nonstationary probability densities of system response of a single-degree-of -freedom system with lightly nonlinear damping and strongly nonlinear stiffness subject to modulated white noise excitation are studied.Using the stochastic averaging method based on the generalized harmonic functions,the averaged Fokker-Planck-Kolmogorov equation governing the nonstationary probability density of the amplitude is derived. The solution of the equation is approximated by the series expansion in terms of a set... 相似文献
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梁以德 《非线性动力学学报》1993,1(1):36-44
本文对增量谐波平衡法做了下列改进:(i)为求分叉解颠倒了增量和线性化的顺序:(ii)用快速傅里叶变换计算解增量和富劳魁特矩阵;(iii)用改进的弧长方法求出子分叉之后的二次分叉曲线,采取了一个用线性弹簧联接的两个Duffing振子组成的系统作为数值计算的例子,详细研究了联接弹簧刚度变化时解的定性变化行为。 相似文献
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H∞分散控制系统范数计算的模态综合法(Ⅰ) 总被引:1,自引:1,他引:0
在大系统控制中,H∞分散控制方法将整个系统划分成一系列子系统分别研究,然后综合设计大系统的分散控制器。这与结构力学中的子结构分析技术类似.本着这一思想建立了分散H∞。控制与子结构振动分析的模拟关系、分散控制系统的最优H∞范数与整体结构一阶本征值之间的对应关系,进而利用结构力学中的模态综合法和扩展Wittrick-Williams算法计算这一参数.论的第(Ⅰ)部分主要介绍系统H∞控制及其本征函数的正交性和展开定理;第(Ⅱ)部分介绍分散控制系统最优H∞范数计算的模态综合法及数值算例。 相似文献
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一类非自治滞后-自激系统的主共振与锁模现象 总被引:6,自引:0,他引:6
研究一类受外激励作用的滞后-自激系统(van der Pol系统)的振动。对于主共振情况,用平均法求出了稳态响应方程,揭示了响应与系统参数的关系。结果表明,外激励的影响占主导地位,滞后因素对非线性共振频率有影响,而自激因素使得周期解在偏离非线性共振频率后发生Hopf分岔,转变为概周期运动。通过用映射法求得旋转数,揭示了主共振前、后的概周期运动中存在的锁模现象,其阶数分布符合Farey树规律。研究表明,锁模振动因滞后非线性因素而产生。随着滞后参数值(代表滞后程度)增大,各阶共振特别是亚谐振动的存在能力增强,对系统结构会带来较大影响。 相似文献
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China's first interest rate hike during the last decade, aiming to cool down the seemingly overheated real estate market, had aroused more caution on housing market. This paper aims to analyze the housing price dynamics after an unanticipated economic shock, which was believed to have similar properties with the back ward- looking expectation models. The analysis of the housing price dynamics is based on the cobweb model with a simple user cost affected demand and a stock-flow supply assumption. Several nth-order delay rational difference equations are set up to illustrate the properties of housing dynamics phenomena, such as the equilibrium or oscillations, overshoot or undershoot and convergent or divergent, for a kind of heterogeneous backward-looking expectation models. The results show that demand elasticity is less than supply elasticity is not a necessary condition for the occurrence of oscillation. The housing price dynamics will vary substantially with the heterogeneous backward-looking expectation assumption and some other endogenous factors. 相似文献
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