This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) probl...This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods.展开更多
目前使用调谐质量阻尼器(tuned mass damper,TMD)对输电塔进行振动控制时,仅针对设计好的塔设计TMD,常忽略TMD对结构动力特性的影响。该文提出把输电塔和TMD视为一个系统,针对整个系统进行一体化设计。以系统传递函数的H∞范数为优化目...目前使用调谐质量阻尼器(tuned mass damper,TMD)对输电塔进行振动控制时,仅针对设计好的塔设计TMD,常忽略TMD对结构动力特性的影响。该文提出把输电塔和TMD视为一个系统,针对整个系统进行一体化设计。以系统传递函数的H∞范数为优化目标,采用遗传算法对角钢截面进行优化。在计算H∞范数时,用串联多质点模型模拟塔架结构以简化计算。为保证优化结果满足静力工况且不增加用钢量,引入惩罚函数来调整个体的适应度。最后以某输电塔为例进行优化计算,结果表明,一体化设计进一步降低了输电塔的地震响应,同时能保证结构满足静力工况且总质量不超过原设计的用钢量。该方法不需要求解时域响应,计算效率较高。展开更多
基金supported by National Natural Science Foundation of China(Nos.61004017 and 60974103)
文摘This paper derives the bounded real lemmas corresponding to L∞norm and H∞norm(L-BR and H-BR) of fractional order systems. The lemmas reduce the original computations of norms into linear matrix inequality(LMI) problems, which can be performed in a computationally efficient fashion. This convex relaxation is enlightened from the generalized Kalman-YakubovichPopov(KYP) lemma and brings no conservatism to the L-BR. Meanwhile, an H-BR is developed similarly but with some conservatism.However, it can test the system stability automatically in addition to the norm computation, which is of fundamental importance for system analysis. From this advantage, we further address the synthesis problem of H∞control for fractional order systems in the form of LMI. Three illustrative examples are given to show the effectiveness of our methods.
文摘目前使用调谐质量阻尼器(tuned mass damper,TMD)对输电塔进行振动控制时,仅针对设计好的塔设计TMD,常忽略TMD对结构动力特性的影响。该文提出把输电塔和TMD视为一个系统,针对整个系统进行一体化设计。以系统传递函数的H∞范数为优化目标,采用遗传算法对角钢截面进行优化。在计算H∞范数时,用串联多质点模型模拟塔架结构以简化计算。为保证优化结果满足静力工况且不增加用钢量,引入惩罚函数来调整个体的适应度。最后以某输电塔为例进行优化计算,结果表明,一体化设计进一步降低了输电塔的地震响应,同时能保证结构满足静力工况且总质量不超过原设计的用钢量。该方法不需要求解时域响应,计算效率较高。
