动态非线性压电驱动机电耦合动力学系统建模及其宽带高精度位移控制系统研究

摘要：研究了压电陶瓷驱动器的复杂非线性滞回动力学系统建模及其位移跟踪控制问题。首先采用状态空间方程，建立了一种新型压电驱动机电耦合动力学系统集总参数（Piezo-actuated Electromechanical Coupling Lumped Parameter－PECLP）模型。该模型首次将动态本征非线性集成到压电叠堆的滞回特性中，并兼顾考虑了驱动器中弹性和运动部件的动力学特性。在此基础上，利用微分几何的输入输出线性化方法，导出了一个简化的线性规范型子系统。根据该子系统，设计了一种基于LQ方法的非线性位移跟踪控制系统。与现有控制系统的对比仿真结果表明，本文提出的控制系统不仅消除了驱动器的稳态定位误差，有效的实现整体动态性能的最优化, 而且将其在-3dB的截止频率从638Hz扩展到5217Hz，频带宽度提高了将近一个数量级。较好的改善了驱动器的高速频响特性。

On modeling of dynamic nonlinear piezo-actuated electromechanical coupling dynamic system and wideband high precision displacement control

Abstract: The modeling and displacement tracking control of piezoceramic actuator with complex nonlinear hysteresis behaviour is studied. First, a novel PECLP model is proposed by using the state space function. In this model, the intrinsic dynamic nonlinearity is combined into the piezoceramic stack’s hysperesis for the first time, and the dynamics of elastic and motive components within actuator are considered simultaneously. Then, the input-output linearization theory of differential geometry is utilized to deduce a simplified subsystem provided with linear normal form. By adopting this subsystem, a LQ based nonlinear displacement tracking control system is developed for piezoceramic actuator. At last, some computer simulations are conducted. In contrast with conventional control system, the simulation results show that the developed nonlinear displacement tracking control system exhibits the better tracking precision without static error, and global optimization of system dynamic capability. Furthermore, the frequency bandwidth is expended by one order of magnitude approximately from 638Hz to 5217Hz at -3dB. A satisfied high-speed frequency response characteristic can be achieved.