Pitfalls of a least-squares-equivalent controller for linear, time-periodic systems
Pitfalls of a least-squares-equivalent controller for linear, time-periodic systems
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线性、时间周期系统的最小二乘等效控制器的缺陷
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. Angeles
中科院分区：
文献类型：
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作者：
P. Montagnier;R. Spiteri;J. Angeles
我们回顾了线性时间周期系统控制器设计的技术。该技术首先由Sinha和Joseph提出，其主要吸引力是使用Floquet-Lypson理论将周期系统转换为可以采用时不变系统经典控制策略的形式。然而，它通常是不可能找到一个完全的时不变控制系统，相当于原来的时变系统：应用的Floquet-Lyapunov变换实际上产生一个时变控制系统，该技术使等效于一个时不变的最小二乘意义上，为了随后合成控制器通过极点配置使用一个恒定的反馈矩阵。然而，经典的控制和Floquet-Lyapunov理论清楚地表明，它是错误的结论，最小二乘等价的，时不变系统的行为总是匹配的原始时间周期系统的行为。使用原始论文中的一个例子，我们提供了一个简单的反例，说明了所提出的策略的失败，并分析了其失败的原因。
We review a technique for the design of controllers for linear, time-periodic systems. A major appeal of the technique, first proposed by Sinha and Joseph, is the use of Floquet-Lyapunov theory to transform the periodic system to a form where classical control strategies for time-invariant systems may be employed. However, it is normally impossible to find a completely time-invariant control system that is equivalent to the original time-varying system: Application of the Floquet-Lyapunov transformation in fact yields a time-varying control system that the technique makes equivalent to a time-invariant one in the least-squares sense, in order to subsequently synthesize the controller via pole placement using a constant feedback matrix. However, classical control and Floquet-Lyapunov theory clearly show that it is erroneous to conclude that the behaviour of the least-squares-equivalent, time-invariant system always matches the behaviour of the original timeperiodic system. Using an example found in the original paper, we provide a simple counter-example that illustrates the failure of the proposed strategy and an analysis of the reasons for its failure.