基于PID反馈的两级超低频隔振系统理论分析及仿真

Analysis and Simulation of Two-Stage Ultra-Low Frequency Vibration Isolation System Based on PID Feedback

建立两级隔振系统的运动模型,推导系统的闭环传递函数并对传递函数进行分析。结果表明:1)系统采用PID反馈较当前超长弹簧中采用的PD反馈具有更好的等效阻尼系数调节功能。2)系统的等效固有周期主要受反馈比例系数k p影响,k p越大,等效固有周期越长,隔振效果越好;k p选定后,积分系数k i和微分系数k d共同影响系统的阻尼,且k i占主导地位,决定系统的稳定性。通过仿真验证了闭环传递函数分析结果的准确性,且仿真结果表明,系统在1 Hz处的隔振效果可达-70 dB。

In this paper,we establish the motion model of the two-stage vibration isolation system,then derive and analyze the closed-loop transfer function of the system.The analysis results show that when PID feedback is adopted,the equivalent damping coefficient of the system can be adjusted more conveniently than the PD feedback used in the current ultra-long spring(superspring).The equivalent natural period of the system is mainly affected by the feedback proportional coefficient k p;the larger the k p is,the longer the equivalent natural period,and the system will have better vibration isolation performance.After k p is selected,the integral coefficient k i together with the differential coefficient k d will affect the damping of the system,and k i is dominant,which determines the stability of the system.The accuracy of the closed-loop transfer function analysis results are verified by simulation,which show that the vibration isolation effect of the system can reach-70 dB at 1 Hz.