基于扩张状态观测器的压电结构复合滑模振动控制

Composite Sliding Mode Vibration Control for a Piezoelectric Structure Based on Extended State Observer

针对压电固支板振动系统的模型不确定、高次谐波和外部激励等干扰问题,设计出一种基于线性扩张状态观测器与滑模控制的复合振动主动控制策略。首先,基于辅助变量法建立压电固支板结构的数学模型,进而设计线性扩张状态观测器对系统状态变量与总干扰进行实时估计,再通过前馈通道补偿的方式,抵消模型误差、外界激励等干扰对系统的影响;然后,基于估计值设计滑模控制器,利用较小的切换项增益抑制观测器的估计误差,从而降低滑模控制的抖振,并利用李雅普诺夫稳定判据准则分析所提振动控制系统的全局稳定性。最后,基于NI-PCIe6343采集系统,搭建振动控制实验平台,并对设计的复合振动主动控制策略进行实验。实验验证结果表明,所提振动控制策略对压电固支板的振动幅值降低87.5%,具有较强的抗干扰能力且对压电固支板的振动抑制性能良好。

A composite vibration active control strategy based on a sliding mode control(SMC)and extended state observer(ESO)is proposed to suppress the vibration of a piezoelectric structure in the presence of total disturbances,i.e.,model uncertainty,higher harmonic,external disturbance,etc.First,the model of an all-clamped piezoelectric plate structure is established based on an auxiliary variable method.In addition,an ESO is used to estimate the state variables and general disturbance of the system in real time.The influences of parameter perturbation,external excitation and some other disturbances are counteracted via the feedforward channel compensation.Then,the sliding mode controller is designed based on the estimated values and the smaller switching gain is used to reduce the disturbance estimation error of the SMC.the Lyapunov stability criterion is used to analyze the global stability of the proposed vibration control method.Finally,based on NI-PCIe 6343 acquisition system,the vibration control experiment platform is set up to verify the vibration performances of the proposed control strategy.The experimental results show that the vibration amplitude of the all-clamped piezoelectric plate is reduced by 87.5%.Therefore,the proposed vibration control method possesses the satisfactory disturbance rejection and a good vibration suppression performance.