压电柔性臂的ARMAX模型辨识降阶及最优极点移动控制

ARMAX model identification and vibration suppression of a piezoelectric flexible manipulator using optimal pole shifting control

研究了压电柔性臂的系统模型辨识和振动主动抑制问题。基于自回归滑动平均模型(ARMAX,Auto-Regressive Moving Average Exogenous)确立了系统辨识模型,且其辨识精度高达97.9%,并采用平衡降阶法对高阶的辨识模型进行降阶,得到低阶模型,通过多频激励实验证实了降阶模型与实际结构具有较高的吻合度。针对柔性臂的振动控制,提出了一种基于线性二次型(Linear Quadratic,LQ)最优极点移动控制法,从求逆的角度,通过移动系统极点来确定LQ的最优状态加权矩阵Q,该方法简单有效地解决了状态加权矩阵Q和输入加权矩阵R的选择问题,具有明显的物理工程意义。试验结果证实了ARMAX模型对于压电柔性臂系统模型辨识的适用性及平衡降阶方法对模型降阶的可行性,并验证了线性二次型最优极点移动策略对柔性臂振动控制的有效性。

The experimental identification and active vibration suppression of a piezoelectric flexible manipulator system are presented in this paper.Based on the Autoregressive Moving Average model(ARMAX),the identified model is established through experimental identification and a fitness of97.9%is achieved.Then,a balanced reduction method is employed to ob-tain a reduced order model.The coincidence between the reduced model and the actual system is verified through a multi-fre-quency excitation test.Based on the linear quadratic(LQ)control,an optimal pole shifting control is proposed.The essential point of this method is that the weighting matrixes of the LQ control are derived by shifting the system closed-loop poles.Thus,a simple and effective method to get the state variable and input weighting matrixes is obtained.The effectiveness of the proposed ARMAX model and model reduction method is verified by experiments and the feasibility of the optimal pole shifting method is demonstrated.