The Effect of Proportional, Proportional-Integral, and Proportional-Integral-Derivative Controllers on Improving the Performance of Torsional Vibrations on a Dynamical System

Abstract

The primary goal of this research is to lessen the high vibration that the model causes by using an appropriate vibration control. Thus, we begin by implementing various controller types to investigate their impact on the system’s reaction and evaluate each control’s outcomes. The controller types are presented as proportional (P), proportional-integral (PI), and proportional-integral-derivative (PID) controllers. We employed PID control to regulate the torsional vibration behavior on a dynamical system. The PID controller aims to increase system stability after seeing the impact of P and PI control. This kind of control ensures that there are no unstable components in the system. By using the multiple time scale perturbation (MTSP) technique, a first-order approximate solution has been obtained. Using the frequency response function approach, the stability and steady-state response of the system at the primary resonance scenario (Ω1≅ω1,Ω2≅ω2) are considered as the worst resonance and addressed. Additionally examined are the nonlinear dynamical system’s chaotic response and the numerical solution for various parameter values. The MATLAB programs are utilized to attain simulation outcomes.