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[05]Lecture44-system Transfer function 系统传递函数

ME369-系统模型、分折与控制 4.4系统传递函数 School of Mechanical Engineering ME369-Lecture 4.4 Shanghai Jiao Tong University Fall 2015 系统闭环传递函数定义 Disturbance扰动N(s) R(s) E(s) G,(s) C(s) G(s) B(s) H(s) 闭环已闭合 系统闭环传递函数：回路接通后，输出量与输入量的比值 输入？R(S), N(s) School of Mechanical Engineering ME369-Lecture 4.4 Shanghai Jiao Tong University Fall 2015 1

1 ME369-Lecture 4.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 4.4 系统传递函数 ME 369– 系统模型、分析与控制 ME369-Lecture 4.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 系统闭环传递函数: 回路接通后， 输出量与输入量的比值 系统闭环传递函数定义 Disturbance 扰动 输入 ? R(s), N(s) 闭环已闭合

系统开环传递函数定义 R(s) C() G(s) (s) H(s) 视为闭环未闭合 系统开环传递函数：反馈信号B(S)和偏差信号E(S)之间的传递函数 G(S)= B(s) =G(s)H(s) E(s) Feed forward TF Feedback TF 前向通道传递函数 反馈通道传递函数 School of Mechanical Engineering ME369-Lecture 4.4 Shanghai Jiao Tong University Fall 2015 以设定量为输入的系统闭环传递函数 扰动N(s) R(s) G,(s co B(s) H(s) 设Ns)=0 Cx(5)= G(s)G(s) R(s)1+G,(s)G,(s)H(s) School of Mechanical Engineering ME369-Lecture 4.4 Shanghai Jiao Tong University Fall 2015 2

2 ME369-Lecture 4.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University ( ) ( ) ( ) k B s G s E s  Feed forward TF 前向通道传递函数 Feedback TF 反馈通道传递函数  G s H s ( ) ( ) 系统开环传递函数:反馈信号B(s)和偏差信号E(s)之间的传递函数 视为闭环未闭合 系统开环传递函数定义 ME369-Lecture 4.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 2 1 2 ( ) ( ) ( ) ( ) 1 ( ) ( ) ( ) C s G s G s R R s G s G s H s   设 N(s)=0 以设定量为输入的系统闭环传递函数

以扰动量为输入的系统闭环传递函数 扰动V(s) 设R(s=0 R(s) G( G.co Cy(s) G2(s) N(s) 1+G(s)G2(S)H(S) B(s) H(s) N(s) C() G,(s) 一 G(s)H(s) School of Mechanical Engineering ME369-Lecture 4.4 Shanghai Jiao Tong University Fall 2015 设定量、扰动量均考虑时 扰动V(s) R(s) E(s) G(s) G(s)co B(s) H(s) C(s)=Cg(s)+Cv(s) G(s)G,(s) 1+G(s)G2(S)H(s) R(S)+ G3(s) 1+G(s)G(s)H(s) N(s) G,(s) [G(s)R(s)+N(s】 1+G(s)G,(s)H(s) School of Mechanical Engineering ME369-Lecture 4.4 Shanghai Jiao Tong University Fall 2015 3

3 ME369-Lecture 4.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 2 1 2 ( ) ( ) ( ) 1 ( ) ( ) ( ) C s N G s N s G s G s H s   设 R(s)=0 以扰动量为输入的系统闭环传递函数 ME369-Lecture 4.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 2 2 1 2 1 2 2 1 1 2 ( ) ( ) ( ) 1 ( ) ( ( ) ( ) ( ) ( ) ( ) ( ) [ ( ) ( ) ( )] 1 ( ) ( ) ( ) ( ) 1 ( ) ( ) ( ) ) R N G s G s G s G s G s H s G C s C s C s R s N s G s G s G s H s s R s N s G s G s H s          设定量、扰动量均考虑时

系统误差传递函数的定义 扰动W(s) !闭环已闭合 R(s) E(s) C(s) -G(S 输入：R(s)orN(s) 输出：E(s) B(s) H(s) 设N(s=0 设R(s=O E(s) 回回限 H)G,间小G间 GO E(s) E(s) -G2(s)H(s) R(s)1+G,(s)G,(s)H(s) N(s)1+G(s)G2(s)H(s) E(s)= 1 -G,(s)H(s) N(s) 1+G(s)G,(s)H(s) R(s)+G(s)G,(5)H(s) School of Mechanical Engineering ME369-Lecture 4.4 Shanghai Jiao Tong University Fall 2015 讨论]系统各种传递函数 CR(s) G(s)G,(s) E(s) 1 R(s）1+G(s)G,(s)H(s) R(s)1+G(s)G2(s)H(s) C(s) G,(s) E(s) -G2(s)H(s) N(s)1+G(s)G2(s)H(s) N(s)1+G(s)G2(s)H(s) 相同的特征多项式(character polynomial) 1+G(s)Gz(s)H(s) School of Mechanical Engineering ME369-Lecture 4.4 Shanghai Jiao Tong University Fall 2015 4

4 ME369-Lecture 4.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 输入:R(s)or N(s) 输出:E(s) 系统误差传递函数的定义 ！闭环已闭合 1 2 ( ) 1 ( ) 1 ( ) ( ) ( ) E s R s G s G s H s   设 R(s)=0 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 G s G s H s G s H s N s E s    2 1 2 1 2 1 ( ) ( ) ( ) ( ) ( ) 1 ( ) ( ) ( ) 1 ( ) ( ) ( ) G s H s E s R s N s G s G s H s G s G s H s      设 N(s)=0 ME369-Lecture 4.4 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 相同的特征多项式（character polynomial ） 1+G1 (s)G2 (s)H(s) 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 1 2 G s G s H s G s G s R s C s R   1 ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 G s G s H s G s N s C s N   1 ( ) ( ) ( ) 1 ( ) ( ) 1 2 R s G s G s H s E s   1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 G s G s H s G s H s N s E s    [讨论]系统各种传递函数