基于线性矩阵不等式的转子系统振动主动控制

Active vibration control strategy based on linear matrix inequality for rotor system

建立了转子系统的状态空间模型.在不平衡等外界干扰的作用下,为了抑制转子系统的瞬态振动和使转子系统具有鲁棒性,基于线性矩阵不等式设计了H2、H∞和H2/H∞混合状态反馈控制律.以一个简单的悬臂转子系统为例,验证了H2/H∞混合控制在转子系统振动控制中的可行性和有效性,分析了转子系统在H2/H∞混合控制作用下的频域和时域特性.结果表明,H2/H∞混合控制策略有效地抑制了转子系统的瞬态振动,使系统具有较强的鲁棒性,改善了转子系统的频域和时域特性.

A state space model was developed for a rotor system. Under external disturbance, such as unbalance excitation, H2 and H∞ controls were formulated separately by means of linear matrix inequality （LMI）, and both objectives were combined as a mixed control problem to attenuate the transient vibration of the rotor system and make it have robust performance. With a cantilever rotor system as example, the performances of the rotor system in both frequency and time domains were analyzed to verify the feasibility and validity of the mixed H2/H∞ control strategy in active vibration control for rotor system. Mixed H2/H∞ control strategy can effectively suppress the transient vibration of the rotor system and maintain good robust performance, so the performances of the rotor system in both frequency and time domains are improved.