Dynamical system design from a control perspective: finite frequency positive-realness approach
Dynamical system design from a control perspective: finite frequency positive-realness approach
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DOI：
10.1109/tac.2003.815013
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发表时间：
2003-08
期刊：
影响因子：
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通讯作者：
T. Iwasaki;S. Hara;H. Yamauchi
中科院分区：
文献类型：
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作者：
T. Iwasaki;S. Hara;H. Yamauchi
众所周知，当控制增益被允许为任意高时，非最小相位零点限制了可实现的最佳控制性能。另一方面，当不允许使用高增益控制器时，相位交叉似乎是性能的限制因素。特别是，在有限的频率范围内的正实性似乎至关重要的控制约束的存在下，实现良好的性能。本文将首先给出多个理由来支持这一猜想，然后开发一个系统的方法来设计机械系统，以实现有限频率正实（FFPR）属性。具体来说，我们提出了一个状态空间表征的FFPR属性通过推广著名的卡尔曼-Yakubovich-Popov引理处理一类频域不等式，需要在有限的频率间隔内举行。结果进一步扩展到不确定系统，给出了满足鲁棒FFPR属性的充分条件。（标称）FFPR结果在时域中根据输入/输出信号进行解释。最后，我们表明，某些传感器/执行器的放置问题，以实现FFPR属性可以减少到有限维凸问题，涉及线性矩阵不等式。该方法应用于磁存储器件摆臂的形状设计，其目标是在有限的驱动功率下最大化可实现的控制带宽。
Nonminimum phase zeros are well known to limit the best achievable control performance when the control gain is allowed to be arbitrarily high. On the other hand, the phase crossover appears to be a limiting factor for performance when high-gain controllers are not allowed. In particular, the positive-realness in a finite frequency range seems crucial for achieving good performance in the presence of control constraints. This paper will first give multiple reasons to support this conjecture, and then develop a systematic method for designing mechanical systems to achieve the finite frequency positive-real (FFPR) property. Specifically, we present a state-space characterization of the FFPR property by generalizing the well known Kalman-Yakubovich-Popov lemma to deal with a class of frequency domain inequalities that are required to hold within a finite frequency interval. The result is further extended for uncertain systems to give a sufficient condition for satisfaction of a robust FFPR property. The (nominal) FFPR result is interpreted in the time-domain in terms of input/output signals. Finally, we show that certain sensor/actuator placement problems to achieve the FFPR property can be reduced to finite dimensional convex problems involving linear matrix inequalities. The method is applied to the shape design of a swing-arm for magnetic storage devices with the objective of maximizing the control bandwidth achievable with a limited actuator power.