时域鲁棒设计的新方法--σ[P]和σ[V]·σ[V-1]的极小化
A new Approach to Robust Design in Time Domain-on Minimizing σ[P] and σ[V]σ[V-1]
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摘要: 本文讨论在极点配置的约束下,使σ[P]和σ[V]·σ[V-1](条件数)极小化的问题,其 中P是(A+BF)'P+P(A+BF)=-21n的正定解,V是A+BF的特征向量矩阵.两 种指标都反映了系统鲁棒稳定的程度.通过定义一矩阵函数并引入新的自由变量U,可放松 极点配置的约束,并能系统的推导σ2[P]/U及(σ2[V]·σ2[V-1])/U,从而将鲁棒设计 转化为无约束的梯度法寻优,实例说明,本文设计方法的效果很好.
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关键词:
- 鲁棒设计 /
- 条件数 /
- Lyapunov方法 /
- 极点配置 /
- 梯度方法
Abstract: This paper suggest a method to minimize σ[P] and σ[V]σ[V-1] under the constraint of pole assignment, where P is the selution to (A+BF)'P+P(A+BF)= -2In, and V is the eigenvector matrix of A+BF. These two indices reflect the robustness of a system. By defining a matrix function and introducing a free matrix U, the pole assignment constraint is relaxed, and the gradient σ2[P]/U and σ2 [V]σ2[V-1]/U are obtained. Thus robust design can be achieved by gradient method. Examples show that this method is very effective.-
Key words:
- Robust design /
- condition number /
- Lyapunov criterion /
- pole assignment /
- gradient method
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