非线性简支梁振动的H_∞控制

H_∞ control of nonlinear simply supported beam vibrations

研究具有实际工程应用背景的非线性简支梁振动的H∞控制问题.在不考虑时滞、热效应等因素的情况下,应用振动分析原理及Hamilton原理,建立了压电复合梁弯曲振动的动力学模型.利用哈密顿仿射输入系统的特殊结构和性质,将非线性H∞控制设计推广到无穷维情形.通过求解Hamilton Jacobi Isaacs不等式,得到一个最优控制方法,并给出压电驱动器和传感器的控制条件.实例模拟验证上述方法的有效性和可行性.

The H_∞control problem of nonlinear beam vibrations with engineering background is discussed. Based on vibration analyses theory and Hamilton theory, the dynamic model of the flexural vibrations of a simply supported piezoelectric composite beam is presented without considering hysteresis phenomena or the influence of thermal effects.By taking advantage of the special structure and properties of Hamiltonian Affine Input Systems, nonlinear H_∞ design can be extended to the infinite dimensions. By solving Hamilton-Jacobi-Isaacs inequality, an optimal control law can be found. Piezoelectric actuator and piezoelectric sensor are designed to satisfy the control law. The feasibility and efficiency of the proposed methods by the simulations are tested.