Simply structured controllers for vibration suppression in long rotors

Abstract

In this paper suppression of the transient flexural vibrational disturbances in long rotors, with fluid film bearings, is investigated. The rotor is described by a series of distributed shafts connected by the lumped discs, and the system is mounted on lumped fluid film bearings. Upon determination of the dynamic stiffness matrix of the system, the best approximate transfer function matrix description of the rotor, is determined. Initially vibration suppression by simple diagonal Proportional + Integral (PI) controllers is studied and via direct search optimisation techniques the PI parameters which exhibit fast vibration suppression is found. The resulted high integration rate, and low proportional gain PI controller, theoretically provided fast suppression time. However, it is shown that due to the strong coupling effect in the rotor system, and high rate of integration, the closed loop relative stability is weak, and feasibility of controller is questionable. Therefore, an alternative simple first order controller without integration action, that is named “attenuation filter “is suggested that can produce stronger stability and produces significant (not full) vibration suppression. The closed loop multivariable control of the rotor system comprising two vibration sensors and two magnetic actuators using such attenuation filter, is then simulated. The response to step disturbances, has provided 95% suppression with significantly fast response. It is concluded that although the attenuation filter may not provide 100% suppression, but it more reliable since the integration of the error, that results weak stability is avoided.

Comparing the Performance of Robust Controllers for Vibration Suppression in Long Rotor Systems

“…Acoustics 2024, 6, FOR PEER REVIEW 2 Recently vibration suppression in long flexible rotors was studied, in which the existence of realizable controllers subject to any kind of disturbance was investigated and commented upon [12]. However, the comparative performance of robust vibration controllers in both the time and frequency domain for long and flexible rotors has not been carried out yet.…”

“…The above partitioned flexibility matrix is described in [12] based on the dynamic stiffness matrix method (DSMM), in which each of the sub-matrices is described in [12].…”

“…x pq and y pq in (3) and ( 4) are the real and imaginary parts of the transfer function G ' . From the multivariable frequency response matrix in Equations ( 3) and (4), estimates of the transfer functions can be obtained in the following form [12]:…”

“…The schematic diagram of the closed-loop vibration control system for the rotor sys tem is shown in Figure 2: In the above open-loop system, the transfer function matrix is as follows: The individual transfer functions in (6) were estimated via [12] ( ) The input control effort vector is u(s), and the measurement variable vector is y(s). The controller designated by the matrix K(s) should be designed to apply the control force u(s) to the rotor system G(s) via the actuators.…”

“…In this paper, the long flexible rotor system that is described in [12] is considered for investigation. The H ∞ optimality criteria was selected for the purposes of comparison.…”