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]Lecture63-Steady state error 稳态误差

ME369-系统模型、分析与控制 6.3稳态误差 School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 T讨论]误差(Error)&偏差(Deviation) 测量作用（） 执行作用（手） 给定信号 热电偶 比较作用（雕） 调压器 恒温箱 -220V 恒温箱 给定信号 (控制对象) 温度 (被调量) 2 热电偶 School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 1

1 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 6.3 稳态误差 ME369-系统模型、分析与控制 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University [讨论]误差(Error) &偏差 (Deviation)

[讨论]误差&偏差（续） N(s) R(s) E(s) C(s) G,(S) G,(s) B(s) H(s) 偏差 误差 E(s)=R(s)-B(s) E'(s)=C,(s)-C(s) =R(s)-C(s)H(s) C,(s)=R(s)/H(s) E'(s)=R(s)/H(s)-C(s) E'(s)=E(s)/H(s) School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fal12015 误差指标 (t◆ c(r) 强烈振荡过程 误差允许范围 振荡过程 微振荡过程 0 J=flel)ldi J=tle()ldi e,=lime(t) 1-+00 J=[e'(Odi J-te()di School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 2

2 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 偏差 R(s) C(s)H(s) E(s) R(s) B(s)     误差 E'(s) C (s) C(s)  r  ( ) ( ) / ( ) C s R s H s r  E'(s)  R(s)/ H(s) C(s) E'(s)  E(s)/ H(s) [讨论]误差&偏差 (续) ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University    0 2 J e (t)dt    0 2 J te (t)dt    0 J | e(t)| dt    0 J t | e(t)| dt 误差指标 lim ( ) s t e e t   误差允许范围

稳态误差定义 误差 e(t) E(s) N(s) G(s)=G(s)G,(s) R(s) E(s) C(s) 稳态误差 e,=lime(t) G(s) G,(s) B(s) =ess +esN H(s) N(s)=0 R(s)=0 es =lime(t)=limsE(s) ea lime(t)=limsE(s) 的 -U School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 [例1]稳态误差 求某一单位反馈系统的稳态误差 1 G(s)= Ts r(t)=sinot es=lims- -R(s) 01+Gs)H(s School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 3

3 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 0 lim ( ) lim ( ) ss t s e e t sE s     1 2 G s G s G s ( ) ( ) ( )  N s( ) 0  R s( ) 0  0 lim ( ) lim ( ) sN t s e e t sE s     稳态误差定义 误差 lim ( ) s t e e t  稳态误差  et( ) ss sN   e e E s( ) ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 G s( ) Ts 求某一单位反馈系统的稳态误差  r t t ( ) sin   0 1 1 im ( ) ) l ( ( ) ss s e G s H s s s R    [例1]稳态误差

[例2]稳态误差 试求单位反馈系统当输入信号为单位阶跃函数和单位斜坡函数时的稳态误差 20 G(s)= (0.5s+1)(0.04s+1) e=lim1+G(s)H(s) R(S) School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fal12015 稳态误差系数一定义 e=lime(t)=lims- R(s) 1-+00 s→01+G(s)H(s) 单位阶跃输入Rs)=I 11 1 e=1+G(s)H(s)s1+G(0)H(0)1+K 稳态位置误差系数 单位斜坡输入风)-宁 11 1 1 e=lims +G(5)H(s)s2 limsG(s)H(s) 稳态速度误差系数 单位抛物线输入 RS)-了 1 1 1 .=吗'1+GsH95- ims2G(s)H(s)K。稳态加速度误差系数 +0 School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 4

4 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 20 ( ) (0.5 1)(0.04 1) G s s s    试求单位反馈系统当输入信号为单位阶跃函数和单位斜坡函数时的稳态误差 0 1 lim ( ) 1 ( ) ( ) ss s e s R s  G s H s   [例2]稳态误差 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 0 (0) ( 1 1 lim 1 ( ) ( ) 1 0) 1 ss s e s  G s H s s G H    0 1 lim ( ) lim ( ) 1 ( ) ( ) ss t s e e t s R s   G s H s    1 1 K p   1 R s( ) s 单位阶跃输入  稳态位置误差系数 0 0 2 1 1 lim 1 ( ) ( ) lim ( ) ( 1 ) ss s s e s G s H s s sG s H s      2 1 R s( ) s 单位斜坡输入  稳态速度误差系数 0 2 0 3 1 1 lim 1 ( ) ( ) lim 1 ( ) ( ) s ss s s G e s  G s H s s s H s     单位抛物线输入 3 1 R s( ) s  1 K v  1 K a  稳态误差系数 —定义 稳态加速度误差系数

控制系统型次定义 ess lims- R(s) s-0 1+G(s)H(s) KII,3+D G(s)H(s)= sΠ+) i-l 0型系统 1型系统 2型系统 School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 0型系统的稳态误差 KIIGs+D 1=0 KIIGs+D) G(s)H(s)= Gs+D s+) Ki,s+l） K-limG(s)H(s)-lim s+D 1 ep1+Kp r04 IIG8+D dr) r(n K,limsG(s)H(s)=lims- s+) 1 d(t) IIGs+D K,=lmG(sH(=lim产 0G+ K School of Mechanical Engineering ME369-lecture 6.3 Shanghal Jiao Tong University Fall 2015 5

5 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 1 ( 1) ( ) ( ) ( 1) m i i n i i K s G s s s H T s            0 1 lim ( ) 1 ( ) ( ) ss s G s s H e s R s    0型系统 1型系统 2型系统 … 控制系统型次定义 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 1 ( 1) ( 1) m i i n i i K s T s           1 0 0 1 ( 1) lim ( ) ( ) lim ( 1) m i i p n s s i i K s K G s H s T s            1 1 ssp p e K   1 0 0 1 ( 1) lim ( ) ( ) lim ( 1) m i i v n s s i i K s K sG s H s s T s            1 ssv v e K  2 2 1 0 0 1 ( 1) lim ( ) ( ) lim ( 1) m i i a n s s i i K s K s G s H s s T s           1  ssa a e K  1 1 ( 1) ( ) ( ) ( 1) m i i v i v n i K s G s s H s T s          v=0 0型系统的稳态误差

1型系统的稳态误差 KIIGs+D =1 KII(+D G(s)H(s)= s+) sfGa+D K。=limG(s)H(s) 1 eap-T+Kp K,lim sG(s)H(s) d) 1 ea-K. K.=lims'G(s)H(s) ) c(r) 1 esd= Ka School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fal12015 2型系统的稳态误差 KI(E+1) =2 KT+D G(s)H(s)= siCs+D GD K=limG(s)H(s) 1 eap=1+Kp r)4 K,limsG(s)H(s) 340 c(t) 1 ean-K, K。=lims2Gs)H(s) r() 1 0 K。 School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 6

6 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 1 1 ( 1) ( 1) m i i n i i K s s T s          0 lim ( ) ( ) p s K G s H s   1 1 ssp p e K   0 lim ( ) ( ) v s K sG s H s   1 ssv v e K  2 0 lim ( ) ( ) a s K s G s H s   1 ssa a e K  1 1 ( 1) ( ) ( ) ( 1) m i i v i v n i K s G s s H s T s          v=1 1型系统的稳态误差 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 0 lim ( ) ( ) p s K G s H s   1 1 ssp p e K   0 lim ( ) ( ) v s K sG s H s   1 ssv v e K  2 0 lim ( ) ( ) a s K s G s H s   1 ssa a e K  1 1 ( 1) ( ) ( ) ( 1) m i i v i v n i K s G s s H s T s          1 2 2 1 ( 1) ( 1) m i i n i i K s s T s            v=2 2型系统的稳态误差

[讨论]稳态误差系数与稳态误差 KIIG8+D K. G(s)H(s）= Type 0 R 0 0 i+ Type 1 0 Type 2 0 0 单位阶跃输入 单位速度输入 单位加速度输入 eop ear eu Type 0 1/(1+0 国 Type 1 0 L/K Type 2 0 0 1/R School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 [例3]稳态误差系数法求稳态误差 Desired K G()=- (rs+万 H(s)=1 ○ Sensor signal Magnetic disk head Motor School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 7

7 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University Kp Kv Ka Type 0 K 0 0 Type 1  K 0 Type 2   K 单位阶跃输入 essp 单位速度输入 essv 单位加速度输入 essa Type 0 1/(1+K)   Type 1 0 1/K  Type 2 0 0 1/K 1 1 ( 1) ( ) ( ) ( 1) m i i v i v n i K s G s s H s T s          [讨论]稳态误差系数与稳态误差 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 1 ( ) H(s)=1 ( 1) ，    K G s s s [例3]稳态误差系数法求稳态误差

复合控制-输入量补偿 G.() R(s) E(s) G(s) C(s) School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 复合控制一干拢量补偿 N(s) G.(S) R(s) E(s) G(s) ⑧ G,(s) C(s) School of Mechanical Engineering ME369-lecture 6.3 Shanghai Jiao Tong University Fall 2015 8

8 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 复合控制--输入量补偿 ME369-lecture 6.3 Fall 2015 School of Mechanical Engineering Shanghai Jiao Tong University 复合控制—干拢量补偿