Reduction of Rotor Vibration Amplitude Using PID Tuning Methods

Rotating machines present some common inherent operational problems, such as the critical amplitude of motion that the machine may experience when passing through one or more of its natural frequencies. High vibration levels can be harmful to the machine and its attenuation is important to maintain the system working healthily. In this context, the paper proposes a proportional-integral-derivative (PID) controller acting with two pairs of electromagnetic actuators to reduce the vibration amplitude of a flexible rotor, supported by hydrodynamic journal bearings, crossing its first resonance. The oil film behavior of the hydrodynamic bearings is modeled both through linear equivalent stiffness and damping coefficients and by the complete solution of the Reynolds equation applied to short bearings. Next, the relay feedback test (a frequency response method) is applied to estimate the ultimate gain and ultimate period of the respective PID controllers. Finally, five different tuning methods are proposed to adjust the PID: the Ziegler-Nichols traditional method, three Ziegler-Nichols modifications to obtain less aggressive controllers, and a fifth method, the Tyreus-Luyben method, whose objective is to improve the robustness of the controller.