摘要
为实现振动系统闭环零极点的任意配置同时避免振动系统成为奇异系统,该文提出将积分反馈引入经典动柔度振动控制方法的主动振动控制方法。首先将PID输入反馈引入多自由度线性系统自由振动方程,经拉普拉斯变换,由Sherman-Morrison公式得到闭环系统柔度矩阵。由于此时闭环系统为正定系统,若预设零极点均自共轭且具有负实部,即可由Moore-Penrose广义逆求得PID输入反馈零极点配置理论增益向量解。同时提出系统可配置极点数目、传感器及反馈增益合理配置的概念及其计算方法。最后给出数值实例以验证该理论闭环极点、零点及零极点分配的准确性及有效性。
In order to realize the arbitrary configuration of the closed-loop zeros and poles in vibration system and avoid the vibration system becoming a singular system,an active vibration control method that introduces integral feedback into the classical dynamic compliance vibration control method is proposed.Firstly,the PID input feedback is introduced into the multi-degree-of-freedom linear system free vibration equation.Through the Laplace transform,the closed-loop system flexibility matrix is obtained by the Sherman-Morrison formula.Since the closed-loop system is a positive definite system at this time,if the preset zeros and poles are selfconjugated and have negative real part,the theoretical gain vector solution of the PID input feedback zeros and poles configuration can be obtained from the Moore-Penrose generalized inverse.At the same time,the concept of the system configurable poles number,sensors and feedback gain reasonable configuration and its calculation method are proposed.Finally,numerical examples are given to verify the accuracy and effectiveness of the closed-loop poles,zeros and zeros-poles assignments of this theory.
作者
王见
王作学
张波
WANG Jian;WANG Zuoxue;ZHANG Bo(State Key Laboratory of Mechanical Transmission(Chongqing University),Chongqing 400044,China;Petro China Southwest Oil and Gasfield Company(Chongqing Gas District),Chongqing 401147,China)
出处
《中国测试》
CAS
北大核心
2019年第1期121-127,共7页
China Measurement & Test
基金
国家自然科学基金资助项目面上项目(51675064)
关键词
动柔度法
主动振动控制
积分控制
零极点配置
receptance method
active vibration control
integral control
poles and zeros assignment
