Active vibration control based on linear matrix inequality for rotor system under seismic excitation

Abstract

For a flexible rotor system under seismic excitation, H 2, H ∞ and mixed H 2/ H ∞ control strategies were formulated by means of linear matrix inequality (LMI) to attenuate the transient vibration of the flexible rotor system under a nonstationary seismic excitation and to improve robust performance of the flexible rotor system. A double-disc cantilever flexible rotor system was used as an example to verify the feasibility and the validity of the H 2, H ∞ and mixed H 2/ H ∞ control strategies in active vibration control for a rotor system subjected to nonstationary El Centro seismic excitation. The performances of the rotor system in both frequency and time domains were analysed based on numerical optimization technique, which bases on an efficient convex optimization software. The feasibility and the effectiveness of the control strategies presented in active vibration control for a rotor system were verified. It is shown that for the H ∞ control, the displacement responses of the rotor system are effectively suppressed in the frequency domain, but transient-response performances are not so good. For the H 2 control, the transient responses of the rotor system attenuate quickly, but the frequency-response performances are not so good. The effectiveness of the mixed H 2/ H ∞ control to suppress the displacement responses of the rotor system in the frequency domain and the transient response in time domain greatly depends on the H ∞ performance index. If the H ∞ performance index in the mixed H 2/ H ∞ control is properly chosen, the mixed H 2/ H ∞ control can effectively suppress both the displacement responses of the rotor system in the frequency domain and the transient response in time domain.