不确定性闭环系统特征上下界的二阶摄动法

Upper and lower bounds of eigenvalues of uncertain closed-loop systems with second-order perturbation

用凸模型理论讨论了参数不确定系统的振动控制问题,把不确定系统的振动控制转化为确定性问题来处理。讨论了不确定参数对闭环系统特征值的影响,提出了闭环系统特征值上下界的二阶摄动估计的计算方法,并通过数值算例证明了该方法的有效性。

By using the convex model theory, the vibration control problem of structures with uncertain parameters is discussed, which is approximated by a deterministic one. The uncertain parameters are modeled to be a convex elliptical set rather than a probabilistic set. This does not require the probabilistic distribution descriptions of the uncertain parameters. The feedback gain matrices derived from the deterministic systems are applied to the actual uncertain systems, and a method for estimating the upper and lower bounds of the real and imaginary parts of eigenvalues of the closed-loop systems is presented by combining the second-order matrix perturbation and optimization. The numerical results show that the present method is effective.