实参数摄动下结构奇异值计算的新方法

A new method for calculating structured singular value subject to real parameter uncertainty

中文关键词  鲁棒性  结构奇异值μ  实参数不确定性  遗传算法

英文关键词  robustness  structured singular value μ  real parameter uncertainty  genetic algorithm

中文摘要

      基于结构奇异值(μ)方法的鲁棒稳定性分析与综合设计的关键在于μ的准确计算, 而MATLAB鲁棒工具箱中计算实参数摄动的μ的上下界差别太大. 本文提出了具体针对实参数对角摄动下的μ的上界和数值准确值计算的新方法. 利用实数摄动条件, 通过奇异性约束展开的方法将实参数摄动的μ计算问题转化为无约束的单目标全局优化问题, 然后采用遗传算法和迭代过程求解两个优化问题. 最后通过两个控制系统的算例验证上述算法的准确性, 并同MATLAB工具箱计算结果进行了对比讨论. 本文方法可以应用到实参数摄动下复杂问题的鲁棒稳定性分析中.

英文摘要

      The key to robust stability analysis and synthesis based on the structured singular value (μ) method is to calculate μ accurately. However, there is a large gap between the upper and lower bounds of μ in the MATLAB robust toolbox subject to real parameter uncertainty. We present a new method for calculating the upper bound and the accurate value of μ subject to real diagonal uncertainty. Under the condition of real parameter perturbation, the singular constraint condition is decomposed so that the calculation problem of μ with real uncertainty is converted to a global optimization problem without constraints, which includes only one objective. Then the genetic algorithm and iterative procedure are adopted to obtain the optimal solutions. Finally, these two methods are validated separately by two control systems; the results are discussed and compared with those obtained by using MATLAB toolbox. These methods can be applied to complex problems of robust stability analysis with real parameter perturbation.