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[13]Lecture72-frequency characteristic plots 频率特性图

2015/11/14 ME369-系统模型、分析与控制 7.2频率特性图 School of Mechanical Engineering ME369-lecture 7.2 Shanghai Jiao Tong University Fall 2015 伯德图/波德图(Bode diagrams)定义 -对数幅频图(Magnitude Plot) L(@)=201g|G(j@)|vs logo@ 对数相频图(Phase Plot) p(o)=∠Gjo)vs log1oo 20 150 decade (dec) 40 一个十倍频程 0 02 04 0.60.8 1 0 10e 0 个 一个十倍颜程 倍频程 倍频程 150 60 octave School of Mechanical Engineering ME369-lecture 7.2 Shanghai Jiao Tong University Fall 2015 1

2015/11/14 1 BE315-Lecture 7.2 Fall 2011 ME369-lecture 7.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 7.2 频率特性图 ME369-系统模型、分析与控制 BE315-Lecture 7.2 Fall 2011 ME369-lecture 7.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 伯德图/波德图（Bode diagrams ）定义 decade (dec) L G j ( ) 20lg | ( ) |       ( ) ( )  G j VS 10 log  --对数幅频图(Magnitude Plot ) VS 10 log  --对数相频图(Phase Plot ） octave

2015/11/14 尼奎斯特图Nyquist plot、polar plot)定义 一（对数幅频图） IGjo)lvs∠G(Ujo) lm◆ Im Uo) 9(1) Re 0 Re G(jw) G60m) GG2） [极坐标系] [直角坐标系] School of Mechanical Engineering ME369-lecture 7.2 Shanghai Jiao Tong University Fall 2015 环节的频率响应-增益环节/放大环节 G(jo)=K L(@)=201g K G(j@)FU-(@)+V2(@)=K p(o)=0° ∠G(jo)=arctan V(@) U(a) 14420 0 201gK Im 20 180 0 -90 -180 0 K Re 0 10 10 10 (rad/sec) School of Mechanical Engineering ME369-lecture 7.2 Shanghal Jiao Tong University Fall 2015 2

2015/11/14 2 BE315-Lecture 7.2 Fall 2011 ME369-lecture 7.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 尼奎斯特图(Nyquist plot、polar plot）定义 [极坐标系] [直角坐标系] --（ 对数幅频图） | ( ) | G j VS G j ( )  BE315-Lecture 7.2 Fall 2011 ME369-lecture 7.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University G j K ( )   2 2 | ( ) | ( ) ( ) G j U V K       ( ) ( ) arctan[ ] ( ) V G j U      L K ( ) | 20lg    ( ) 0  环节的频率响应--增益环节/放大环节

2015/11/14 环节的频率响应-积分环节 1 Gj0)==-j G(j@)1 1 L(@)=-201g@ ∠Gjo)=arctan(-o-） p(@)=-90° 0 0 20dB/dec Imt 40 0=0 0 e 悬 % -90 -180 0.1 10 100 0=0 w (radlsec) School of Mechanical Engineering ME369-lecture 7.2 Shanghal Jiao Tong University Fall 2015 环节的频率响应一微分环节 G(jo)=j@ G(j@)=@ p(o)=90 G(jo)=arctan( L(@)=201g@ 20dB/dec Imt 0 0=0 -20 180 1 90 0=0 45 0 Re 0 0.1 10 100 (radisec) School of Mechanical Engineering ME369-lecture 7.2 Shanghal Jiao Tong University Fall 2015 3

2015/11/14 3 BE315-Lecture 7.2 Fall 2011 ME369-lecture 7.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 1 G j j ( ) j       1 | ( ) | G j   1 ( ) arctan( ) 0 G j      L( ) 20lg      ( ) 90   环节的频率响应--积分环节 BE315-Lecture 7.2 Fall 2011 ME369-lecture 7.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University G j j ( )    | ( ) | G j  ( ) arctan( ) 0 G j     L( ) 20lg     ( ) 90  环节的频率响应—微分环节

2015/11/14 环节的频率响应一惯性环节 1 G(jo)= iTo+l 0 1/2 Re 0=00 45 l@=0" G(j o=1/T 1Gjo)川 U(o) () 0 ∠GUw) 1 1 To r2a2+1 =-arctan(To) T2o2+1 T2o2+1 0 1/T 00 School of Mechanical Engineering ME369-lecture 7.2 Shanghai Jiao Tong University Fall 2015 环节的频率响应一惯性环节（续） L(@)=-20lgTo+1 L(@)=-20lgVF2o2+1≈0 低频渐近线 0<<宁 0dB水平线 转折频率 (corner frequency/break frequency 1 L(@)=-201g @T 高频渐近线 02个 10 -20dB/dec斜线 0 渐近线吗 -10 -20dB/dec 20 实际幅频特性 I 30 School of Mechanical Engineering ME369-lecture 7.2 Shanghai Jiao Tong University Fall 2015 4

2015/11/14 4 BE315-Lecture 7.2 Fall 2011 ME369-lecture 7.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 ( ) 1 G j jT     ( ) arctan( ) G j T      2 2 | ( ) | 1 1 G j T     2 2 ( ) 1 1 U T     2 2 ( ) 1 V T T       环节的频率响应—惯性环节 BE315-Lecture 7.2 Fall 2011 ME369-lecture 7.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 2 2 L T ( ) 20lg 1      1 T   2 2 L T ( ) 20lg 1 0       L T ( ) 20lg     1 T   低频渐近线 1 (0 ) T    1 ( ) T     0dB 水平线 -20dB/dec 斜线 转折频率 （corner frequency/break frequency ） 1 T   高频渐近线 环节的频率响应—惯性环节（续）

2015/11/14 环节的频率响应一惯性环节（续） 0 渐近线吗 0 20dB/dec 名 实际幅频特性 -30 0= △L(o)=-20lg√To2+1=-3 0> T AL(@)=-201gv1+T22 AL(@)=-201gv1+T@2+20lgT@ -3 转折频率 A0 School of Mechanical Engineering ME369-lecture 7.2 Shanghai Jiao Tong University Fal12015 环节的频率响应一惯性环节（续） (@)=-arctan(T@) 0=0 0(0)=0 p(o)=-45 0→0 p(0)=-90° 0 (gp)/)7 - mm 渐近线皿 -20dB/dec 20 实际幅频特性 30 转折频率 是 -45 90 1/T @(radlsec) School of Mechanical Engineering ME369-lecture 7.2 Shanghai Jiao Tong University Fall 2015 5

2015/11/14 5 BE315-Lecture 7.2 Fall 2011 ME369-lecture 7.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 2 2     L T ( ) 20lg 1   1 T   1 T   2 2      L T T ( ) 20lg 1 20lg    1 T   2 2       L T ( ) 20lg 1 3   环节的频率响应—惯性环节（续） BE315-Lecture 7.2 Fall 2011 ME369-lecture 7.2 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University    ( ) arctan( )   T  ( ) 0   1 T    ( ) 45    ( ) 90     0 环节的频率响应—惯性环节（续）