中文摘要：

基于系统能控矩阵特征根距离原点的位置反映系统能控性大小的原理，提出一种通过计算系统能控矩阵最小模特征根来确定三级倒立摆最优摆长组合的方法。通过对不同摆长组合所构成的三级倒立摆系统在相同控制策略下的控制系统的仿真实验性能的对比，验证了在综合考虑系统位移量以及控制量大小的情况下，根据所提出的方法设计出的三级倒立摆系统的摆杆长度组合是最优的，并使用该方法得到了一定范围内三级倒立摆的最优摆长比值与固定摆杆的不同长度之间的对应关系。

英文摘要：

Based on the principle that the distance of controllability matrix eigenvalue to origin indicates the relative controllability of a system, a method for calculating the minimal module eigenvalue of controllability matrix to select the optimal link group for triple inverted - pendulum is proposed. Through comparing simulation control system performance with different link group system under same control strategy and considering both the effects of displacement and control value, it is demonstrated that the proposed method is useful to select an optimal link group. By using this method, the relationship between optimal link rate and different length of the fixed link in a certain region is obtained.