非线性控制系统中的相对阶概念在线性系统中的反映
The Reflection of Relative Degree Concept of Nonlinear Control Systems in Linear Systems
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摘要: 相对阶(Relative Degree)概念是非线性系统控制中一个有用的概念,本文探讨了它在 线性系统中的反映.用Markov参数矩阵的方法证明了它与一致秩(Uniform Rank)、级数 指标、系统传递函数阵中元素的分母阶次与分子阶次之差、以及元素的极零点数之差的关系. 证明了线性系统的相对阶对于任意状态反馈常值阵K和任意满秩的前馈常值阵F是一个不变 量.当系统存在相对阶r=[r1,…,rm]r时,可通过K和F进行积分解耦而具有传递矩阵 diag{s-r1,…,s-1m}.Abstract: The relative degree is a useful concept in nonlinear control systems, This paper discusses its reflection in linear systems. By using Markov its parameter matrices, some results are given and relationship with the following has been proved: the uniform rank, the series indices of transfer matrix, degree differences between denominators and numerators of transfer matrix elements, and the pole-zero number differences of transfer matrix elements. The relative degree of linear time-invariant system is invariant under any state feedback K and any full rank feedforward F is also proved. If a linear system has relative degree r=[r1,…,rm]r, this system can be decoupled with the transfer matrix diag {s-r1,…,s-1m}by K and F.
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Key words:
- Nonlinear control systems /
- linear systems /
- relative degree /
- uniform rank /
- decoupling
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