[例6]劳斯判据一相对稳定必性 试判断系统有几个特征方程根位于与虚轴平行的直线一-1的右侧。 D(s)=s3+7s2+14s+22=0 School of Mechanical Engineering ME369-lecture 6.2 Shanghai Jiao Tong University Fall 2015 [讨论]系统阶次与稳定性 D(s)=aos"+as"+...+as+a=0 (a>0) 1st order system a>0 a4>0 (necessary condition) 一阶系统 2nd order system a>041>0a2>0 (necessary condition) 二阶系统 3rd order system -a>04>0a,>0a3>0 (necessary condition) 三阶系统 aaz >aas 4th order system a>0a>0 a,>0a3>0a4>0 四阶系统 (necessary condition) aaas aa +aas School of Mechanical Engineering ME369-lecture 6.2 Shanghal Jiao Tong University Fall 2015 1010 ME369-lecture 6.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 3 2 D s s s s ( ) 7 14 22 0      试判断系统有几个特征方程根位于与虚轴平行的直线s=-1的右侧。 [例6]劳斯判据—相对稳定必性 ME369-lecture 6.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 st order system 一阶系统 1 0 1 1 ( ) ... 0 n n D s a s a s a s a n n         0 ( 0) a  0 (necessary condition) a  0 1 a  0 0 a  0 1 a  0 2 a  0 0 a  0 1 a  0 2 a  0 3 a  0 1 2 0 3 a a a a  0 a  0 1 a  0 2 a  0 3 a  0 2 2 1 2 3 0 3 1 4 a a a a a a a   4 a  0 [讨论]系统阶次与稳定性 2 nd order system 二阶系统 3 rd order system 三阶系统 4 th order system 四阶系统 (necessary condition) (necessary condition) (necessary condition)