作者：王见¹, 王作学¹, 张波²

作者单位：1. 机械传动国家重点实验室(重庆大学), 重庆 400044;
2. 中国石油西南油气田分公司(重庆气矿工艺研究所), 重庆 401147

关键词：动柔度法;主动振动控制;积分控制;零极点配置

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。

PID poles and zeros assignment theory in vibration system
WANG Jian¹, WANG Zuoxue¹, ZHANG Bo²
1. State Key Laboratory of Mechanical Transmission (Chongqing University), Chongqing 400044, China;
2. Petro China Southwest Oil and Gasfield Company (Chongqing Gas District), Chongqing 401147, China
Abstract: 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 self-conjugated 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.
Keywords: receptance method;active vibration control;integral control;poles and zeros assignment
2019, 45(1):121-127  收稿日期: 2018-03-09;收到修改稿日期: 2018-04-16
基金项目: 国家自然科学基金资助项目面上项目（51675064）
作者简介: 王见(1975-),男,副教授,硕士生导师,主要研究方向为测试仪器与信号处理、机电一体化技术及智能控制与计算机协同监控
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