最优调节器的设计
Design of Optimal Regulators
摘要：
目前的研究建议使用线性二次型性能指标的最优控制的调节器在各种应用。一些例子包括校正火箭和航空器的轨迹、柔性结构的振动抑制和飞机稳定性。在所有这些情况下，重点是快速抑制/减少系统偏差。然而，如果将线性二次调节器（LQR）解决方案与最优解（最小时间）进行比较，可以看出，LQR解决方案在某些情况下比使用最小时间解决方案获得的最优解决方案小小于倍。此外，LQR的解决方案有时是不可接受的，在实践中，由于控制的值超出了允许的限制，因此，设计者必须选择系数的线性二次型，这是未知的。作者提出的方法，允许找到一个准最优的LQR解决方案，有界控制，这是接近最小时间的解决方案。他们还发回了最短时间决定的过程。关键词：最佳调节器，最小时间控制器，线性二次型调节器。--本文被宣布为美国政府的作品，在美国不受版权保护。该手稿作为论文AIAA-2003-6638被2003年9月15-18日在美国加利福尼亚州圣地亚哥举行的第二届AIAA无人驾驶无限系统、技术和操作-航空航天、陆地和See会议和研讨会-展览会接受。
英文摘要：
Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression of flexible structures, and airplane stability. In all these cases, the focus is in suppressing/decreasing system deviations rapidly. However, if one compares the Linear Quadratic Regulator (LQR) solution with optimal solutions (minimum time), it is seen that the LQR solution is less than optimal in some cases indeed (3-6) times that obtained using a minimum time solution. Moreover, the LQR solution is sometimes unacceptable in practice due to the fact that values of control extend beyond admissible limits and thus the designer must choose coefficients in the linear quadratic form, which are unknown. The authors suggest methods which allow finding a quasi-optimal LQR solution with bounded control which is closed to the minimum time solution. They also remand the process of the minimum time decision. Keywords: Optimal regulator, minimum time controller, Linear Quadratic Regulator (LQR). -- This paper is declared a work of the U.S. Government and not subject to copyright protection in the USA. The manuscript is accepted as paper AIAA-2003-6638 by 2nd AIAA Unmanned Unlimited Systems, Technologies, and Operations-Aerospace, Land, and See Conference and Workshop - Exhibit, San Diego, California, USA, 15-18 Sep. 2003.
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