Abstract: A non-linear graded optimal control scheme is proposed and used in the piezoelectric vibration reduction control of non-linear beams. The dynamic model of a non-linear vibration reduction beam with piezoelectric damper is built. The non-linear dynamic differential equations of the vibration reduction system are deduced. The differential equation is linearized into a set of linear equations by means of perturbation. The state space equations are obtained by decoupling in the space coordinates. The vibration reduction system is controlled by the non-linear graded controllers.

Key words: vibration and wave, vibration reduction, optimal control, piezoelectric, beam, non-linear control

摘要： 提出非线性的分阶最优控制方法，并将其应用于梁的非线性振动压电减振控制。建立梁压电减振系统动力学模型，导出减振系统的非线性动力学运动微分方程，利用摄动法，实现非线性微分方程的线性化。将各阶线性方程解耦，化为状态空间方程。设计非线性分阶控制器，对减振系统进行分阶最优控制。仿真算例验证这种控制方法的有效性。

关键词: 振动与波, 减振, 最优控制, 压电, 梁, 非线性控制