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]Lecture64-Forced response 系统强迫响应

2015/10/21 ME369-系统模型、分析与控制 6.4系统强迫响应 School of Mechanical Engineering ME369-lecture 6.4 Shanghai Jiao Tong University Fall 2015 阶(1 st order)系统-实例 T T。+T(t) T。+T V =Rig+K MCdr_(T,+T)-(亿+D T=Ki。=Jno+bo dt R 2(s) K T(s) 1 'm(s) R(Jos+b+KK,) T(s)(MCRs+1) School of Mechanical Engineering ME369-lecture 6.4 Shanghai Jiao Tong University Fall 2015 1

2015/10/21 1 ME369-lecture 6.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 6.4 系统强迫响应 ME369-系统模型、分析与控制 ME369-lecture 6.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University + _ Vemf Ja Ra ia Vin  b V R i K in a a b    T K i J b    t a a  ( ) ( ) ( ) t in a a b t s K V s R J s b K K     T0 T T 0  b 0 T T t  ( ) T T 0  b 0 0 ( ) ( ) MC dT T T T T b dt R     ( ) 1 ( ) ( 1) b T s T s MCRs   一阶（1 st order）系统--实例

2015/10/21 阶系统一实例（续） R RC虫+p,=P d R Tce。 RC des tee dt Ba+x。二， K dt 77777 School of Mechanical Engineering ME369-lecture 6.4 Shanghai Jiao Tong University Fall 2015 阶系统的模型表达 rde(t) R() 1☐C(s dt +c(t)=(t) (时间常数) C(s) 1 R(s)Ts+1 R(s)_ 1 C(s) Ts+1 s平面 School of Mechanical Engineering ME369-lecture 6.4 Shanghai Jiao Tong University Fall 2015 2

2015/10/21 2 ME369-lecture 6.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University P i Po R C RC dpo dt  po  pi R C RC deo dt  eo  ei ei + - + - eo K B B K dxo dt  xo  xi xi xo 一阶系统—实例（续） ME369-lecture 6.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University ( ) 1 ( ) 1 C s R s Ts   一阶系统的模型表达 （时间常数） ( ) ( ) ( ) dc t T c t r t dt  

2015/10/21 阶系统一单位阶跃响应 111T R(S)=- C(s)= Ts+1s s Ts+1 t)=1,t≥0) c0=1-e7,(0≥0) slope c() 斜率-1/T c(t)=1-e-iT c(T)=63.2% c(3T)=95% c(4T)=98.2% 0 2T 3T AT dt School of Mechanical Engineering ME369-lecture 6.4 Shanghai Jiao Tong University Fall 2015 阶系统一单位阶跃响应（续） slope c(t)◆ 斜率=1/T c(0=1-et7 j04 s平面 爹 8 2T 4T School of Mechanical Engineering ME369-lecture 6.4 Shanghai Jiao Tong University Fall 2015 3

2015/10/21 3 ME369-lecture 6.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University slope 1 R s( ) s  1 1 1 ( ) 1 1 T C s Ts s s Ts       1 ( ) 1 ,( 0) t T c t e t    c T (3 ) 95%  c T (4 ) 98.2%  c T( ) 63.2%  1 0 0 ( ) 1 1 | | t T t t dc t e dt T T      r t t ( ) 1,( 0)   一阶系统—单位阶跃 响应 ME369-lecture 6.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University slope 一阶系统—单位阶跃 响应（续）

2015/10/21 阶系统一单位速度响应 R-子 1 +C(s)= 111T,T 1 rt)=t,(t≥0) c0=1-T+Te7,4≥0) r(t) c(t) e=T 输出增长速率=输入增长速率 r( c(n) c(t)=r(t-T) 0 入 t School of Mechanical Engineering ME369-lecture 6.4 Shanghai Jiao Tong University Fall 2015 阶系统一单位脉冲响应 1 R(s)=1 Cs)=1 Ts+1 1 r(t)=6t) c0=7e宁，2≥0) 1- c(t) 1/T 方ex c(3T)=5% c(4T)=1.8% T2T3747 School of Mechanical Engineering ME369-lecture 6.4 Shanghai Jiao Tong University Fall 2015 4

2015/10/21 4 ME369-lecture 6.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 ( ) ,( 0) t T c t t T Te t      2 1 R s( ) s  2 2 1 1 1 ( ) 1 1 T T C s Ts s s s s T        r t t t ( ) ,( 0)   输出增长速率=输入增长速率 c t r t T ( ) ( )   一阶系统—单位速度响应 ME369-lecture 6.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 1 ( ) ,( 0) t T c t e t T    R s( ) 1  T s T Ts C s 1 1 1 1 1 ( )      r t t ( ) ( )   c T (3 ) 5%  c T (4 ) 1.8%  一阶系统—单位脉冲响应

2015/10/21 [讨论]线性定常系统 C(s)1 r(t)=6t) c(t)= R(s)Ts+1 T j⊙◆ s平面 r(t)=1 c0=1-e r(t)=t c0=1-T+7e 衰减系数：1/T 线性定常系统的一个性质 输入信号微分←→响应微分 输入信号积分←→响应积分 (积分时间常数←零初始条件) School of Mechanical Engineering ME369-lecture 6.4 Shanghai Jiao Tong University Fall 2015 练习1]一阶系统 绘出一阶系统矩形信号的响应形状 School of Mechanical Engineering ME369-lecture 6.4 Shanghai Jiao Tong University Fall 2015 5

2015/10/21 5 ME369-lecture 6.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 1 ( ) t T c t e T   1 ( ) t T c t t T Te     t T c t e 1 ( ) 1    ( ) 1 ( ) 1 C s R s Ts   衰减系数：1/T r t t ( )  r t( ) 1  r t t ( ) ( )   输入信号微分响应微分 输入信号积分响应积分 (积分时间常数 零初始条件) 线性定常系统的一个性质 [讨论]线性定常系统 ME369-lecture 6.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [练习1]一阶系统 绘出一阶系统矩形信号的响应形状