Best tracking and regulation performance under control energy constraint
Best tracking and regulation performance under control energy constraint
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DOI：
10.1109/tac.2003.815012
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发表时间：
2003-08
期刊：
影响因子：
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通讯作者：
Jie Chen;S. Hara;Gang Chen
中科院分区：
文献类型：
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作者：
Jie Chen;S. Hara;Gang Chen
本文研究了最优跟踪和调节控制问题，其中目标函数的跟踪误差和调节响应，定义的积分平方措施，是最小化共同的控制努力，后者是衡量的植物输入能量。在这项工作中，我们的主要目标是寻找基本的设计限制超出那些已知的非最小相位零点，不稳定极点，和时间延迟。为了这个目的，我们明确地解决问题，推导出的最佳可实现的性能的解析表达式。它被发现，这种性能限制不仅取决于植物的非最小相位零点，时间延迟，和不稳定的极点-一个已知的事实，但也在整个频率范围内的植物增益。因此，结果揭示和量化的另一个来源的基本性能限制超出了那些已经知道的，这是不存在的，当只有传统的性能目标，如跟踪和调节，而不考虑控制能量约束。除其他外，他们展示了如何轻阻尼极点，反谐振零点，以及带宽的植物可能会影响性能。
This paper studies optimal tracking and regulation control problems, in which objective functions of tracking error and regulated response, defined by integral square measures, are to be minimized jointly with the control effort, where the latter is measured by the plant input energy. Our primary objective in this work is to search for fundamental design limitations beyond those known to be imposed by nonminimum phase zeros, unstable poles, and time delays. For this purpose, we solve the problems explicitly by deriving analytical expressions for the best achievable performance. It is found that this performance limit depends not only on the plant nonminimum phase zeros, time delays, and unstable poles-a fact known previously-but also on the plant gain in the entire frequency range. The results thus reveal and quantify another source of fundamental performance limitations beyond those already known, which are nonexistent when only conventional performance objectives such as tracking and regulation are addressed without taking into account the control energy constraint. Among other things, they exhibit how the lightly damped poles, the anti-resonant zeros, as well as the bandwidth of the plant may affect the performance.