群时延引起的受控小车二级摆失稳及其抑制
刘博，胡海岩
摘要:以受控小车一二级摆为对象,通过理论和实验方法讨论了数字滤波器群时延引起的系统失稳问题,并采用时滞LQ方法实现了对这类失稳的抑制.首先,建立小车-二级摆系统的动力学模型,测试其自由衰减振动后指出对其进行主动控制的必要性.然后,讨论了数字滤波器对受控系统稳定性的影响,其中低通滤波器用于去除控制输人信号中的强高频噪声.研究发现,滤波器指标设置过高时会因群时延量过大而引起系统失稳.由于滤波器群时延量仅与滤波器相频特性相关,可以事先得到,故含滤波器的系统适合于基于状态变换的时滞控制.最后介绍了一种离散的时滞LQ控制,并用其成功实现了对群时延造成的系统失稳的抑制.
关键词：时滞；二级摆；滤波器群时延；实验；状态变换
Group delay induced instability and its suppression for a controlled-double pendulum
Bo Liu, Haiyan Hu
Abstract：The group delay of digital filters induced instability of a controlled-double pendulum was discussed, and then a discrete delayed linear quadratic controller was used to suppress the instability. First, the dynamic model of the double-pendulum on a moving cart was established and the free-decaying vibration of the system was measured. It was found that the settling time of the free system was very long, and hence, an active control was needed to shorten the settling time. Then, the effects of digital filters on the stability of the system under the linear quadratic control were discussed, where the Butterworth low pass digital filters were used to remove the heavy noise embedded in the control input signal. The conclusion of this research is that if the filter parameters are properly selected, the digital filters can not only enhance the performance of control system, but also reduce the cost of energy. However, when the specifications of the filters are set too high, the group delay will exceed the critical value and cause the instability of the closed loop system. The delay controls based on state transform are suitable for the dynamic systems involving digital filters because the group delay of a digital filter can be completely determined by its frequency response of phase and can be estimated accurately beforehand. At the last section of the paper, therefore, a newly proposed discrete delayed linear quadratic controller is represented to suppress the group delay induced instability of the double pendulum.
Keyword：time delay double pendulum; group delay of digital filters; experiment; state transformation
原文链接：http://d.wanfangdata.com.cn/periodical/zdgcxb200905001
