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[15]Lecture83-compensation系统校正

ME369-系统模型、分析与控制 8.3系统校正 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 校正装置 PD控制校正网络及超前校正网络 响应的快速性（带宽）个 PI控制校正网络及滞后校正网络 稳态精度（系统增益）个 PID控制校正网络及滞后-超前校正网络 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 1

1 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 8.3 系统校正 ME369-系统模型、分析与控制 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 校正装置 响应的快速性(带宽) 稳态精度(系统增益) PD控制校正网络及超前校正网络 PI控制校正网络及滞后校正网络 PID控制校正网络及滞后-超前校正网络

PD及超前Lead)校正装置(compensator) K2 <1 Kp=- R T=RC d=K+K: T=RC -是 G(s）= U。=aTs+l U,(s) aTs+l Gs)==a+ X,(s)aTs+ G(s)= U,(s) US) -K(Ts+1) Ts+1 G.(s)=a aTs+1 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fal12015 超前校正装置 G(s）=a Ts+1 Ts+1 aTs+l G.(S)= aTs+1 L(o)◆ L(o)◆ 1 -201g 201gG 201gv√a -10g =1013a 201ga gpo)◆ a)◆ P. 1、系统的开环增益下降→增加放大器，以保持态精度要求！！！ 2、在整个频率范围内都产生相位超前 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 2

2 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University ( ) 1 ( ) ( ) 1 o c i U s Ts G s a U s aTs     2 1 2 1 R a R R    T R C 1 1 1  ( ) 1 ( ) ( ) 1 o c i X s Ts G s a X s aTs     2 1 2 1 K a K K    1 1 B T K  1 ( ) 1 c Ts G s a aTs    PD 及超前(Lead) 校正装置（compensator） 1 ( ) ( ) ( 1) ( ) o c p i U s G s K T s U s     T R C 1 1 1  2 1 p R K R  BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 ( ) 1 c Ts G s a aTs    1、系统的开环增益下降  增加放大器，以保持态精度要求！！！ 超前校正装置 1 ( ) 1 c Ts G s aTs    2、在整个频率范围内都产生相位超前

超前校正装置（续） 2、在整个频率范围内都产生相位超前 do =0→0m= 1 -a arcsin( √a +a a= 1-sin 1+sin a↓→gn个 a-0.05,pn=65° a=0.1,pm=55° 12 16 1/ School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fal12015 PI及滞后校正(Lag)装置 x,( u(r 0 B=R+R: B= C+C. C K反 T=RC2 T=G T=RC2 U(s) =-K,1+) Ts+1 U,(s) G(s)= BTs+1 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 3

3 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 2、在整个频率范围内都产生相位超前 1 0 m d d aT       1 sin( ) 1 m a arc a      1 sin 1 sin m m a      a   m  a=0.05， m65° a=0.1，m55° 超前校正装置（续） BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 2 2 2 2 C C C C T K     1 2 2 2 2 R R R T R C     1 ( ) 1 c Ts G s Ts    PI 及滞后校正（Lag)装置 T R C  2 2 2 1 p R K R  ( ) 1 (1 ) ( ) o p i U s K U s Ts   

滞后校正装置 Ts+1 1、在整个频率范围内都产生相位滞后 G(s)= BTs+1 -arcsin(B-1 B+1 d-0→0. 1 L(↑ d B个→9。个 →“远离校正后系统的。c -20lg√B -20 -201g6 号器 pm)4 P. 12 16 2、 ↓开环对数频率特性的中高频部分 →增益交界频率↓ ,稳定裕量个 3、 如果增加放大器维持对数频率特性的中高频部分 →稳态精度个 School of Mechanical ME369-lecture 8.3 Fal12015 滞后校正装置（续） G(s)=B Ts+1 L)◆ 已校正 BTs+1 201ga L(o) 未校正 0 0)4 0 未校正 -90 已校正 (,) -180 @) School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 4

4 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao 1 ( ) 1 c Ts G s Ts    1、在整个频率范围内都产生相位滞后 1 0 m d d T        2、 开环对数频率特性的中高频部分 增益交界频率 , 稳定裕量 3、 如果增加放大器维持对数频率特性的中高频部分 稳态精度 1 sin( ) 1 m arc        滞后校正装置 2 1 T   [ , ] 2 10  c c β   m  ωm远离校正后系统的ωc BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 滞后校正装置(续） 1 ( ) 1 c Ts G s Ts     

PID及滞后超前校正装置 B=5+ + T=RC T=R2C2 T=R,C T=R C2 U.(s) GU(S) -+五+ 1 旺 (Ts+1)(T,s+1) G.(S)= T (T+T)s T+T, TTs2+(T+BT)s+1 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fal12015 滞后-超前校正装置 (Ts+1)T,s+1) T3>T.B>1 G(s)= G s+lIs+D_I+五+ 1 TTs+(T+BT)s+1 (T+BT)s T+BT, (T+T)s T+T, G(s）= Ts+1 Ts+l 工s+1阿，+1 L(o 1、前半段：相位滞后 0 如低频段提高增益将改善稳态性能 20dB/dec 20dB/dee 201g6 p@)4 2、后半段：相位超前 ↑相位裕量， Toc ↑动态性能 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 5

5 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 2 2 1 2 1 2 ( 1)( 1) ( ) ( ) 1 c T s T s G s TT s T T s        1 2 2 R R R    T R C 1 1 1  T R C 2 2 2  1 2 2 K K K    1 1 1 C T K  2 2 2 C T K  PID 及滞后超前校正装置 1 2 1 2 1 2 1 2 ( ) ( ) 1 [1 ] ( ) o c i U s G U s T T TT s  T T s T T        T R C 1 1 1  T R C 2 2 2  R C1 2   BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 2 2 1 2 1 2 ( 1)( 1) ( ) ( ) 1 c T s T s G s TT s T T s        2 1 T T   , 1  1 2 1 2 1 2 1 2 1 2 1 2 1 2 ( 1)( 1) 1 [1 ] ( ) ( ) c T s T s T T TT G s T T s T T T T s T T              1 1 2 2 T T T T       1 2 1 2 1 1 ( ) 1 1 c T s T s G s T T s s        滞后-超前校正装置 相位裕量， c 动态性能 如低频段提高增益将改善稳态性能 1、前半段： 相位滞后 2、后半段：相位超前

校正示范-1]频域超前校正 单位反馈系统，开环传递函数 G()=4K s(s+2) 请设计串联校正装置，使得K,=20s1,andy>=50°，Kg>=10dB [Step1]根据稳态指标，确定开环增益K [Step2]绘制未校正系统BODE图 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 校正示范-1]频域超前校正（续） [Stp3]计算未校正系统穗定裕量 6* 4 C, 600 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 6

6 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 单位反馈系统，开环传递函数 请设计串联校正装置，使得 Kv=20s -1 , and γ>=50°,Kg>=10dB [Step1] 根据稳态指标，确定开环增益K 4 ( ) ( 2) s K G s s s   [校正示范-1]频域超前校正 [Step 2] 绘制未校正系统BODE图 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [Step 3] 计算未校正系统稳定裕量 [校正示范-1]频域超前校正(续）

[校正示范-1]频域超前校正（续） Ts+1 G(s)= L()↑ als+l 已校正 L(o) 未校正 20g0 l) m◆ 未校正 己校正 -90° y(@.) -180 (@)=0 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 校正示范-1]频域超前校正（续） E(o [Stp4】确定最大相位超前角m School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 7

7 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 ( ) 1 c Ts G s aTs    [校正示范-1]频域超前校正(续） BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [Step 4] 确定最大相位超前角m [校正示范-1]频域超前校正(续）

[校正示范-1]频域超前校正（续） [Step5]确定a,并取m。-m L(4 9 -61 -40 0001 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 校正示范-1]频域超前校正（续） L(4 [Step6]确定转折颜率 0 4463 184 -62 -40 o↑ 0 0, -180 0601 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 8

8 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [Step 5] 确定，并取c=m [校正示范-1]频域超前校正(续） BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [Step 6] 确定转折频率 [校正示范-1]频域超前校正(续）

[校正示范-1]频域超前校正（续） [St即7]确定校正后的开环传递函数 L(o 1 G.G. [Step8]校验 w) a0, School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 校正示范-1]频域超前校正（续） Uni-Step ResPonses 14 compensated system 12 Uncompensated system 0.2 t sec School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 9

9 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [Step 7]确定校正后的开环传递函数 [Step 8] 校验 [校正示范-1]频域超前校正(续） BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [校正示范-1]频域超前校正(续）

校正示范-2]频域滞后校正 单位反馈系统，开环传递函数 K G,(s)= s(s+10.5s+1) 请设计串联校正装置，使得K,=5s1,andy>-40° [Step1]根据稳态指标，确定开环增益K [Step2]绘制未校正系统BODB图 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 校正示范-2]频域滞后校正（续） [St即3]计算未校正系统稳定裕量 31 一0 0 一1 School of Mechanical Engineering ME369-lecture 8.3 Shanghai Jiao Tong University Fall 2015 10

10 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University ( 1)(0.5 1) ( )    s s s K G s 单位反馈系统，开环传递函数 s 请设计串联校正装置，使得 Kv=5s -1 , and γ>=40° [Step 1] 根据稳态指标，确定开环增益K [Step 2 ] 绘制未校正系统BODE图 [校正示范-2]频域滞后校正 BE315-Lecture 8.3 Fall 2011 ME369-lecture 8.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [Step 3]计算未校正系统稳定裕量 [校正示范-2]频域滞后校正（续）