上海交通大学：《系统模型、分析与控制 Modeling、Analysis and Control》课程教学资源[08]Lecture65-Free Response 系统自由响应

2015/10/21 ME369-系统模型、分析与控制 6.5系统自由响应 School of Mechanical Engineering ME369-lecture 6.5 Shanghai Jiao Tong University Fall 2015 阶系统的自由响应 少+ay=0 y(0)=A 特征方程 S+a=0 yie(t)）=Aeam a>0 4=0 a<0 Time (f) Time(f) Time (f) School of Mechanical Engineering ME369-lecture 6.5 Shanghai Jiao Tong University Fall 2015 1

2015/10/21 1 ME369-lecture 6.5 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 6.5 系统自由响应 ME369-系统模型、分析与控制 ME369-lecture 6.5 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 一阶系统的自由响应 y ay   0 y A (0)  ( ) at free y t Ae  特征方程 s a   0

2015/10/21 阶系统的自由响应 i+aj+aoy=0 y0)=A 特征方程 s2+a3+a=0 不等实根S,≠S2 ymee(t)=Ae+e 相等实根S1=S2 yree(t)=Ae+Ate 共轭复根： ,2=a±jB yiee(t)=Ae cos(Bt+) School of Mechanical Engineering ME369-lecture 6.5 Shanghai Jiao Tong University Fall 2015 阶系统的自由响应（不等实根） yie()）=Ae+A,e (馬0) ↑mg ↑mg. ↑1g Real Real Real y(1) (0 0 Time(f) Time(f) Time(f School of Mechanical Engineering ME369-lecture 6.5 Shanghai Jiao Tong University Fall 2015 2

2015/10/21 2 ME369-lecture 6.5 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 0 y a y a y    0 2 1 0 s a s a    0 1 2 1,2 1 0 1 4 2 2 a      s a ay A (0)  二阶系统的自由响应 特征方程 1 2 1 2 ( )   s t s t free 不等实根 y t Ae A e 1 1 1 2 ( )   s t s t free y t Ae A te ( ) cos( )     at free y t Ae t 共轭复根 s j 1,2     s s 1 2  相等实根 s s 1 2  ME369-lecture 6.5 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 二阶系统的自由响应（不等实根） 1 2 1 2 ( )   s t s t free y t Ae A e 1 2 ( 0) & ( 0) s s   1 2 ( 0) & ( 0) s s   1 2 ( 0) & ( 0) s s  

2015/10/21 阶系统的自由响应（相等实根） yee(t)）=Ae+A,tep 马=30 ↑1mg ↑mg ↑mg Real Real Real y(0 y(0 Time (r) Time (f) Time (f School of Mechanical Engineering ME369-lecture 6.5 Shanghai Jiao Tong University Fall 2015 阶系统的自由响应（共轭复根） yie()=Ae“cos(Bt+) a0 Img. ↑Ig mg. Real Real Real yH(1) yH(() (0 Time (r) Time(f) Time(r) School of Mechanical Engineering ME369-lecture 6.5 Shanghai Jiao Tong University Fall 2015 3

2015/10/21 3 ME369-lecture 6.5 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 二阶系统的自由响应（相等实根） 1 1 1 2 ( )   s t s t free y t Ae A te 1 2 s s   0 1 2 s s   0 1 2 s s   0 ME369-lecture 6.5 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 二阶系统的自由响应（共轭复根） ( ) cos( )     at free y t Ae t   0   0   0