A Gain Tuning Method for Active Vibration Control of 1 Degree-of-Freedom Mechanical Systems: A Proportional-Integral-Derivative Control Approach

Abstract

Proportional-integral-derivative (PID) controller is one of the most popular controllers that are used for the active vibration control of mechanical systems. In the most of these studies it can be observed that control gain tuning is the main issue of the active vibration control. An
inappropriate selection of control gains may cause inefficient control performance and be harmful for the controlled system. In PID control it
is possible to select the control gains according to desired transient and steady state specifications when the system model is exactly known but
in general exact knowledge of the system model is not provided. In this study a system model based gain tuning algorithm is proposed for the
active vibration control of 1 degree-of-freedom mechanical systems. To realize this purpose, the transfer function of the system is estimated
from the free vibration response of the system. The estimation process is realized by obtaining damping ration and undamped natural frequency
of the system from the transient state specifications of free vibration response. Then an estimated transfer function based PID control gain
adjustment method is proposed. Performance of the proposed method is demonstrated via numerical simulation studies.