小区间参数不确定性高阶系统的振动控制研究

Vibration control of a high-order uncertain system with small interval parameters

针对复杂高阶不确定性系统的鲁棒H_∞振动控制难题,基于小区间参数不确定性系统降阶方法的研究,系统地给出了包含降阶对象的构建、不确定性系统的降阶、鲁棒控制器的求解以及鲁棒性验证等在内的一整套研究策略和分析方法。为保障整个分析和求解过程的顺利进行,分析了高阶矩阵指数函数一阶偏导数求解困难的根源以及利用数值微分法的解决策略,并给出了一类维数较小的不确定性矩阵分解方法。最后通过算例表明了整个分析过程和求解方法的合理性和可行性。

For the robust H∞ vibration control of a high-order complicated uncertain system, based on the study on reduction of an uncertain system with small interval parameters, a set of research strategy and analysis method was presented, including construction of an object to be reduced, reduction of an uncertain system, solving method of a robust controller and verification of robustness, and so on. In order to ensure the whole process of analysis and calculation going well, the calculation of the first order partial derivatives of a high-order matrix exponential was studied and a decomposing form of the uncertainty matrix with lower dimensions was given. Finally, the rationality and feasibility of the suggested method were proved by numerical examples.