离散系统的环形区域极点配置及约束方差综合控制

RING POLE ASSIGNMENT AND VARIANCE CONSTRAINED SYNTHETICAL-CONTROL FOR DISCRETE SYSTEM

  • 摘要: 利用广义逆理论和奇异值分解理论,研究离散型线性随机系统的综合控制设计问题.旨在设计期望的控制器,使闭环系统的特征集合定位在单位圆内的一个环形区域之中,且每一个稳态状态方差都符合即定的约束.本文提供一种综合设计方法,使这一类应用广泛的工程控制系统同时具备良好的稳定特性和动态性能.通过研究一个修正的代数Lyapunov矩阵方程,导出控制器存在的充分条件和解集合的表达式,并提供了一个算例.本方法所得的结果具有形式简洁,易于工程实现,设计保守性少的特点.

     

    Abstract: This paper discusses the synthetical control designing problem for discrete linear stochastic systems with generalized inverse theory and the singular value decomposition theory. The designed controller maked the eigenvalues of the closed-loop system located in a ring of the unit circle, and the variance of each steady state composes to the given constraint. A synthetical designing method is proposed which makes this kind of engineering control system applied generally achieve good dynamic and steady characteristics. This paper derives the existing sufficient and necessary conditions and the expression of solution by a modified algebraic Lyapunov matrix equation, and provides an example. The result is simple, easy for realizing and the designing method has little conservation.

     

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