自动控制原理及其应用答案第二版课后答案

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1、,,,第二章习题课,(2-1a),u,o,i,2,=,R,2,,,C,＋,－,＋,－,u,i,u,o,R,1,R,2,2-1(a),,试建立图所示电路的动态微分方程。,,解：,输入量为,u,i,，输出量为,u,o,。,u,i,=u,1,+u,o,u,1,=i,1,R,1,i,c,=C,du,c,dt,=,dt,d,(,u,i,-u,o,),,i,1,=i,2,-i,c,,u,1,=,[ ],R,1,+,u,o,u,o,-,C,d,(,u,i,-u,o,),dt,R,2,R,2,u,i,=u,o,R,1,-C R,1,R,2,+C R,

2、1,R,2,+u,o,R,2,du,i,dt,dt,du,o,u,o,R,1,+C R,1,R,2,+u,o,R,2,=R,2,u,i,+C R,1,R,2,du,o,du,i,dt,dt,＋,－,＋,－,C,u,c,＋,R,1,R,2,u,i,,i,1,i,2,－,＋,－,u,o,i,c,,,C,第二章习题课,(2-1b),2-1(b),,试建立图所示电路的动态微分方程。,,u,o,,,,,,,,,,,＋,＋,－,－,u,i,R,1,L,R,2,C,,i,1,=i,L,+i,c,u,L,=L,di,L,dt,u,o,i,L,=i,2,=,R,2,,u,L,=,L,R,2,du

3、,o,dt,i,c,= = +C,du,c,dt,CL,R,2,d,2,u,o,dt,2,du,o,dt,,+,u,o,R,2,CL,R,2,d,2,u,o,dt,2,du,o,dt,i,1,=,+C,u,o,i,2,=,R,2,输入量为,u,i,，输出量为,u,o,。,u,i,=u,1,+u,o,u,1,=i,1,R,1,i,c,=C,du,c,dt,=,dt,d,(,u,i,-u,o,),习题课一,(2-2),求下列函数的拉氏变换,。,(1) f(t)=sin4t+cos4t,解,:,∵L,[,sinwt,],=,w,w,2,+s,2,s,w,2,+s,

4、2,∴L,[,sin4t+cos4t,],=,4,s,2,+16,s,s,2,+16,=,s+4,s,2,+16,+,L,[,coswt,],=,(2) f(t)=t,3,+e,4t,3!,解,:,L,[,t,3,+e,4t,],= + = +,3!,s,3+1,1,s-4,s,4,1,s-4,(3) f(t)=t,n,e,at,解,:,L,[,t,n,e,at,]=,n!,(s-a),n+1,(4) f(t)=(t-1),2,e,2t,解,:,L,[,(t-1),2,e,2t,]=,e,-(s-2),2,(s-2),3,2-3-1,,函数的拉氏变换。,F

5、(s)=,s+1,(s+1)(s+3),解,：,A,1,=(s+2),s+1,(s+1)(s+3),s=-2,= -1,(s+1)(s+3),A,2,=(s+3),s+1,s=-3,= 2,F(s)= -,2,s+3,1,s+2,f(t)=2e,-3t,-e,-2t,F(s)=,s,(s+1),2,(s+2),2-3-2,,函数的拉氏变换。,解,:,f(t)= e,st,+lim,[,e,st,],s,(s+1),2,s=-2,d,ds,s,s+2,s -1,,=-2e,-2t,+lim( e,st,+ e,st,),s

6、 -1,,st,s+2,2,(s+2),2,=-2e,-2t,-te,-t,+2e,-t,=(2-t)e,-t,-2e,-2t,F(s)=,2s,2,-5s+1,s(s,2,+1),2-3-3,,函数的拉氏变换。,解,:F(s)(s,2,+1),s=+j,=A,1,s+A,2,s=+j,A,1,=1, A,2,=-5,A,3,=F(s)s,=,1,s=0,∴,f(t)=1+cost-5sint,F(s)= + +,1,s,s,2,+1,s,-5,s,2,+1,2-3-4,,函数的拉氏变换。,(4) F(s)=,s+2,,s(s+1),2,(s+3),解,:,f

7、(t)= e,st,+ e,st,s+2,(s+1),2,(s+3),s=0,s+2,s(s+1),2,s=-3,+ lim,s -1,d,[,e,st,],s+2,s(s+3),ds,= + e,-3t,+lim,[ + ],2,3,1,12,s -1,(-s,2,-4s-6)e,st,(s,2,+3),2,(s+2)te,st,s,2,+3s,= + e,-3t,- e,-t,- e,-t,2,3,1,12,3,4,t,2,

8、(2-4-1),求下列微分方程。,d,2,y(t),dt,2,+5 +6y(t)=6,，,初始条件：,dy(t),dt,y(0)=y(0)=2,。,·,解,:,s,2,Y(s)-sY(0)-Y(0)+5sY(s)-5Y(0)+6Y(s)=,1,s,′,A,1,=sY(s),s=0,∴,y(t)=1+5e,-2t,-4e,-3t,A,2,=(s+2)Y(s),s=-2,A,3,=(s+3)Y(s),s=-3,A,1,=1 , A,2,=5 , A,3,=-4,,∴,Y(s)=,6+2s,2,+12s,s(s,2,+5s+6),(2-4-2),求下列微分方程。,d,3,y(t),

9、dt,3,+4 +29 =29,,d,2,y(t),dt,2,dy(t),dt,初始条件,:,y(0)=0 , y(0)=17 , y(0)=-122,·,·,·,解,:,2-5-a,,试画题,2-1,图所示电路的动态结构图,,,并求传递函数。,＋,－,＋,－,C,u,c,＋,R,1,R,2,u,i,,i,1,i,2,－,＋,－,u,o,i,c,,,C,解,:,u,i,=R,1,i,1,+u,o,，,i,2,=i,c,+i,1,U,I,(s)=R,1,I,1,(s)+U,O,(s),du,c,i,c,=C,dt,I,2,(s)=I,C,(s)+I,1,(s),

10、I,C,(s)=CsU,C,(s),即,: =,I,1,(s),U,I,(s)-U,O,(s),R,1,[,U,I,(s)-U,O,(s),],Cs=I,C,(s),,U,O,(s),U,I,(s),=,1,R,1,＋,( sC)R,2,1+,1,R,1,＋,( sC)R,2,=,R,2,+R,1,R,2,sC,R,1,+R,2,+R,1,R,2,sC,,,,,,,,,1,R,1,,sC,,,,,,,,R,2,,,U,I,(s),,,-,U,O,(s),I,C,(s),I,1,(s),I,2,(s),＋,＋,,,,,,,,1,R,

11、1,sC,R,2,＋,( ),,U,I,(s),-,U,O,(s),2-5-b,试画出题,2-1,图所示的电路的动态结构图,,,并求传递函数。,,u,o,,,,,,,,,,,＋,＋,－,－,u,i,R,1,L,R,2,C,,解：,u,i,=R,1,I,1,+u,c,u,c,=u,o,+u,L,u,L,=L,di,L,dt,i,L,=,u,o,R,2,i,1,=i,L,+i,c,i,c,=C,du,c,dt,U,i,(s)=R,1,I,1,(s)+U,C,(s),U,C,(s)=U,O,(s)+U,L,(s),U,L,(s)=sLI,L,(s),I,1,(s)=I,L,(s)

12、+I,C,(s),∴,,,,,,,,,,,,,,,,,,,,,,,,1,R,1,,Cs,sL,R,2,I,1,＋,U,O,U,i,I,C,-,-,U,C,=U,O,+U,L,I,L,U,L,I,2,(s)=,U,O,(s),R,2,I,C,(s)=CsU,C,(s),I,1,(s)=,U,O,(s),R,2,I,1,(s)=,U,I,(s)+U,C,(S),R,1,即：,I,L,(s)=I,1,(s)-I,C,(s),I,C,(s)=,U,C,(s),Cs,解,:,电路等效为,:,2-6-a,用运算放大器组成的有源电网络如图所示,,,试采用复数阻抗法写出它们的传递函数。,U,O,=,－,R,3

13、,＋,SC,R,2,R,2,＋,1,U,I,R,1,U,O,R,3,SC,R,2,R,2,1,SC,·,＋,1,＋,=,－,R,1,+R,3,+R,2,R,3,CS,=,－,R,1,(R,2,SC+1),R,2,R,3,=,－,( + ),R,1,(R,2,SC+1),R,1,R,1,R,2,=,－,( +R,3,),(R,2,SC+1),1,=,R,2,1,R,3,R,2,SC,＋,＋,R,1,－,C(S)=,U,O,(S),U,I,(S),∴,,,,,,,－,＋,＋,∞,△,C,R,1,R2,R3,u,i,u,o,

14、,,,,,,－,＋,＋,∞,△,C,R,1,R2,R3,u,i,u,o,,,,,,,－,＋,＋,∞,△,C,R,1,R2,R3,u,i,u,o,,,R,4,R,5,2-6-b,用运算放大器组成的有源电网络如力所示,,,试采用复数阻抗法写出它们的传递函数。,=,－,R,5,R,4,+ R,5,U,O,(R,3,SC+1),R,2,R,3,SC+R,2,+R,3,U,O,U,I,=,(R,2,R,3,SC+R,2,+R,3,)(R,4,+R,5,),R,1,(R,3,SC+1)R,5,－,=,－,(R,4,+R,5,)(R,2,+R,3,)( SC+1),R,2,R,3,R,2,

15、+R,3,R,1,R,5,(R,3,SC+1),U,I,R,1,=,R,5,R,4,+ R,5,U,O,R,2,＋,R,3,SC,SC,R,3,SC,＋,1,－,R,5,R,4,+ R,5,U,O,R,2,＋,R,3,R,3,SC,＋,1,－,c(t),t,0,T,K,δ,(t),2-8,设有一个初始条件为零的系统，系统的输入、输出曲线如图，求,G(s),。,c(t),t,0,T,K,δ,(t),,c(t)=,,K,T,t-,(t-T),K,T,,C(s)=,,K,(1-e ),Ts,2,-TS,C(s)=G(S),第二章习题课,(2-8),解,:,2-9,若系统在单位阶跃输入作用时，已知

16、初始条件为零的条件下系统的输出响应，求系统的传递函数和脉冲响应。,r(t)=I(t),c(t)=1-e +e,-2t,-t,解,:,R,(,s,)=,1,s,G(S)=C(s)/R(s),1,s+2,1,s,-,C(s)=,1,s,+,1,+,=,s(s+1)(s+2),(s,2,+4s+2),,=,(s+1)(s+2),(,s,2,+4s+2,),,C(s)=,(s+1)(s+2),(,s,2,+4s+2,),,脉冲响应,:,2,s,+,2,=1+,1,s,+,1,-,c(t)=,δ,(,t,),+2e +e,-2t,-t,第二章习题课,(2-,９,),2-10,已知系统的微分方程组

17、的拉氏变换式，试画出系统的动态结构图并求传递函数。,解,:,X,1,(s)=,R,(s),G,1,(s)-,G,1,(s)[,G,7,(s)-,G,8,(s)],C(s),X,2,(s)=,G,2,(s)[,X,1,(s)-,G,6,(s),X,3,(s),],X,3,(s)=,G,3,(s)[,X,2,(s)-,C,(s),G,5,(s),],C,(s)=,G,4,(s),X,3,(s),,,,,,,,,,,,G,1,,,,G,2,,,,G,3,,,,G,5,-,-,-,C(s),-,R(s),,,G,4,,,G,6,,,,,,,,,,G,8,,G,7,,X,1,(s)={,R,(s)-C(

18、s)[,G,7,(s)-,G,8,(s)],}G,1,(s),C(s)[,G,7,(s)-,G,8,(s)],G,6,(s),X,3,(s),X,1,(s),X,2,(s),C,(s),G,5,(s),X,3,(s),,,,,,,,,,,,,,G,1,,,,G,2,,,,G,3,,,,G,5,-,-,-,C(s),-,R(s),,,G,4,,,G,2,G,6,,,,,,,,,,G,8,,G,7,,,,,,,,,,,,,,G,1,G,2,,,,G,5,-,C(s),-,R(s),,,,,,G,7,-,G,8,1+,G,3,G,2,G,6,G,3,G,4,,,,,,,,-,C(s),R(s),,,

19、,,,G,7,-G,8,1+,G,3,G,2,G,6,+G,3,G,4,G,5,G,1,G,2,G,3,G,4,1+,G,3,G,2,G,6,+G,3,G,4,G,5,+G,1,G,2,G,3,G,4,(G,7,-G,8,),G,1,G,2,G,3,G,4,R,(,s,),C,(,s,),=,第二章习题课,(2-10),,解,:,2-11(a),,,,,,,,,,G,1,(s),,,,,,,G,2,(s),,G,3,(s),,H,1,(s),_,_,+,R(s),C(s),,,,,,,,,H,2,(s),,,,,,,,,,G,1,(s),,,,,,,G,2,(s),,,H,1,(s),_,_,

20、+,R(s),C(s),,,,,,,,,H,2,(s),G,3,(s),求系统的传递函数,,1+,G,2,H,1,G,2,,G,1,+,G,3,,1+,G,1,H,2,1+,G,2,H,1,G,2,,1+,G,2,H,1,G,2,,=,1+,G,2,H,1,+,G,1,G,2,H,2,G,2,,R,(,s,),C,(,s,),=,1+,G,2,H,1,+,G,1,G,2,H,2,G,2,G,1,+,G,2,G,3,,,,,,,,,,G,1,(s),,,,,,,G,2,(s),,G,3,(s),,H,1,(s),_,_,+,R(s),C(s),,,,,,,,,G,1,(s)H,2,(s),第二章

21、习题课,(2-11a),2-11(a),,,,,,,,,,G,1,(s),,,,,,,G,2,(s),,G,3,(s),,H,1,(s),_,_,+,R(s),C(s),,,,,,,,,H,2,(s),求系统的传递函数,解,:,L,1,L,1,=-G,2,H,1,L,2,L,2,=-G,1,G,2,H,1,P,1,=G,1,G,2,P,2,=G,3,G,2,Δ,1,=,1,Δ,2,=,1,R,(,s,),C,(,s,),=,Σ,n,k=,1,P,k,Δ,k,Δ,Δ,=1+,G,2,H,1,+,G,1,G,2,H,2,1+,G,2,H,1,+,G,1,G,2,H,2,G,2,G,1,+G,2,G

22、,3,,=,第二章习题课,(2-11a),解,:,2-11(b),,,,,,,,,,G,1,(s),,,,,,G,2,(s),,G,3,(s),,G,4,(s),_,+,+,R(s),C(s),,,,,,,,,H(s),,求系统的传递函数,,,,,,,,,,G,1,(s),,,,,,G,2,(s),,G,3,(s),,G,4,H,_,+,R(s),C(s),,,,,,,,H(s),,,,,1+,G,4,G,1,H,G,1,,,,,,,,,,,,,,,G,2,(s),,G,3,(s),_,+,R(s),C(s),,,,,,,H(s),1+,G,4,HG,1,G,1,,,,,,,,,,,,,,,G

23、,2,,G,3,_,+,R(s),C(s),,,,,,,1+,G,4,HG,1,G,1,,,HG,1,,1+,G,4,HG,1,G,1,+G,3,,(,1,+,HG,1,G,4,),1,+,G,4,HG,1,G,2,,(,1,+,HG,1,G,4,),1,+,G,4,G,1,H,+,G,1,G,2,H,,,,R,(,s,),C,(,s,),=,1,+,G,1,G,2,H,+,G,1,G,4,H,G,1,G,2,+,G,2,G,3,+G,1,G,2,G,3,G,4,H,第二章习题课,(2-11b),解,:,2-11(b),,,,,,,,,,G,1,(s),,,,,,G,2,(s),,G,3,(s

24、),,G,4,(s),_,+,+,R(s),C(s),,,,,,,,,H(s),,求系统的传递函数,R,(,s,),C,(,s,),=,1,+,G,1,G,2,H,+,G,1,G,4,H,G,1,G,2,+,G,2,G,3,+G,1,G,2,G,3,G,4,H,L,1,L,1,=-G,1,G,2,H,L,1,=-G,1,G,4,H,L,2,P,1,=G,1,G,2,Δ,1,=,1,P,2,=G,3,G,2,Δ,=1+,G,4,G,2,H,+,G,1,G,2,H,Δ,2,=1,+,G,1,G,4,H,第二章习题课,(2-11b),,H,1,,,,,_,+,+,+,,,,,,,G,1,+,C(s)

25、,R(s),,,G,3,,,,,,,,G,2,,2-11c,求系统的闭环传递函数 。,解,:,,H,1,,,,,_,+,,,,,,,G,1,+,C(s),R(s),,,G,3,,,,,,,,G,2,,,,H,1,,,,R,(,s,),C,(,s,),1+,G,1,G,2,+,G,1,H,1,–,G,3,H,1,G,1,G,2,,(1,–,,G,3,H,1,),=,,,,,_,,,,,,G,1,C(s),R(s),,,,G,2,,,,H,1,+G,2,1-,G,3,H,1,1,,第二章习题课,(2-11c),,H,,,,,_,,,,,,G,1,+,C(s),R(s),,,G,2,,,,,2-11

26、d,求系统的闭环传递函数 。,解,: (1),,,,,,_,,,,,G,1,+,C(s),R(s),,,G,2,,,,,,,HG,2,,1+,G,2,H,1,(,G,1,+,G,2,),R,(,s,),C,(,s,),=,(2),L,1,L,1,=-G,2,H,P,1,=G,1,Δ,1,=,1,P,2,=G,2,Δ,2,=,1,第二章习题课,(2-11d),-,,,,,,,,,_,,,,,G,1,+,C(s),R(s),,G,2,,,,,,,G,3,,,G,4,,2-11e,求系统的闭环传递函数 。,解,:,(1),,,,,,_,,C(s),R(s),,,,,G,1,+G,2,,G,3,-G,

27、4,C,(,s,),=,R,(,s,),1+(,G,1,+G,2,)(,G,3,-G,4,),(,G,1,+G,2,),1+,G,1,G,3,+,G,2,G,3,–,G,1,G,4,-,G,2,G,4,=,(,G,1,+G,2,),第二章习题课,(2-11e),L,1,L,2,L,3,L,4,,L,2,=G,1,G,4,L,3,=-G,2,G,3,L,4,=G,2,G,4,(2),L,1,=-G,1,G,3,P,1,=G,1,Δ,1,=,1,P,2,=G,2,Δ,2,=,1,1+,G,1,G,3,+,G,2,G,3,–,G,1,G,4,-,G,2,G,4,=,(,G,1,+G,2,),C,(s

28、),R,(s),,,,,,,_,,,,,G,1,+,C(s),R(s),,G,2,,,,2-11f,求系统的闭环传递函数 。,,,,,_,,C(s),R(s),,,,,G,1,,1-,G,2,G,2,C,(,s,),=,R,(,s,),1+,1-,G,2,G,1,G,1,G,2,1+,G,1,G,2,–,G,2,G,1,,(1,–,,G,2,),=,第二章习题课,(2-11f),解,:,(1),,(2),L,1,L,1,=-G,1,G,2,L,2,L,2,=G,2,P,1,=G,1,Δ,1,=,1-,G,2,Δ,=1+,G,1,G,2,-,G,2,C,(,s,),R,(,s,),1+,G,1,

29、G,2,–,G,2,G,1,,(1,–,,G,2,),=,2-12(a),,R(s),,,,,,,,,G,1,(s),,,,,G,2,(s),,H,2,(s),_,+,C(s),,,,,,,H,3,(s),,,,H,1,(s),_,,,+,D(s),解,:,求,:,D,(,s,),C,(,s,),R,(,s,),C,(,s,),D,(,s,)=0,1-,G,2,H,2,G,2,,G,(,s,)=,1-,G,2,H,2,G,1,G,2,,C,(,s,),=,R,(,s,),1+,1-,G,2,H,2,G,1,G,2,H,3,1-,G,2,H,2,G,1,G,2,,1-G,2,H,2,+,G,1,

30、G,2,H,3,G,2,G,1,=,,R,(,s,)=0,结构图变,,换成：,,,,,,,,,,,,G,2,(s),,H,2,(s),_,+,C(s),,,,,,,G,1,H,3,,,G,1,H,1,_,,D(s),,1-,G,2,H,2,G,2,,1,-,G,1,H,1,C,(,s,),=,D,(,s,),1+,1-,G,2,H,2,G,2,1-,G,2,H,2,G,2,,G,1,H,3,(,1,-,G,1,H,1,),1-G,2,H,2,+,G,1,G,2,H,3,G,2,(1-,G,1,H,1,),=,第二章习题课,(2-12a),2-12(b),求,:,D,(,s,),C,(,s,),

31、R,(,s,),C,(,s,),,R(s),,,,,,G,n,+,+,D,(,s,),解,:,D,(,s,)=0,G,(,s,)=,1+G,1,G,2,H,G,1,G,2,,,,,,,,,,,,,,,,,,,,G,1,,G,2,,H,_,_,C(s),C,(,s,),=,R,(,s,),1+,1+,G,1,G,2,H,G,1,G,2,,1+G,1,G,2,H,G,1,G,2,,1+G,1,G,2,H+,G,1,G,2,G,1,G,2,=,,R,(,s,)=0,,,,,,G,n,+,+,D,(,s,),结构图变,,换成：,,,,,,,,,,,,,,,,,,,G,1,,G,2,,H,-,-,C(s

32、,),,,,G,n,+,+,D,(,s,),,,,,,,,,,,,,,,,,,,,,,,G,1,,G,2,,H,-,-,C(s),,,,G,n,/,G,1,+,+,D,(,s,),,,1+G,1,G,2,H,G,1,G,2,,,,,,,,,,,,,,-,C(s),,+,D,(,s,),,,,1+G,1,G,2,H,G,2,G,n,,,,1+G,1,G,2,H,G,2,G,1,,,系统的传递函数,:,),C,(,s,),=,D,(,s,),1+,1,(,1,+,1+G,1,G,2,H,G,1,G,2,,1+G,1,G,2,H,G,n,G,2,,1+G,1,G,2,+,G,1,G,2,H,=,1+

33、G,n,G,2,+,G,1,G,2,H,第二章习题课,(2-12b),2-13(a),求,:,R,(,s,),E,(,s,),R,(,s,),C,(,s,),C(s),E,(,s,),,,,,,,,,,,,,,,,,,G,1,,G,2,,G,3,_,_,+,R(s),,,,解,:,L,1,L,1,=-G,2,L,2,L,2,=-G,1,G,2,G,3,P,1,=G,2,G,3,P,2,=G,1,G,2,G,3,R,(,s,),C,(,s,),=,1,+,G,2,+,G,1,G,2,G,3,G,2,G,3,+G,1,G,2,G,3,Δ,1,=,1,Δ,2,=,1,E,(,s,),,结构图变,,换

34、成：,,,,,,,,,,,,,,,,,G,1,,G,2,+,-,E(s),,,,G,3,-,R,(,s,),,,,,,,,,,,,,,,,,,G,1,+,-,E(s),R,(,s,),,,,,1+,G,2,G,3,G,2,,,,,,,,,,,,,,-,E(s),,-,R,(,s,),,,,1+,G,2,G,2,G,3,,,G,1,G,2,G,3,1+G,2,,系统的传递函数,:,),E,(,s,),=,R,(,s,),1+,1,(,1,-,G,1,G,2,G,3,1+G,2,,1+,G,2,G,2,G,3,1+G,2,+,G,1,G,2,G,3,=,1+G,2,-,G,2,G,3,第二章习题课

35、,(2-13a),R(s),,,,,,G,4,(s),+,C(s),,,,E(s),,,,,,,,,G,1,(s),,G,2,(s),-,+,,,,G,3,(s),,,,,第二章习题课,(2-14),,D(s),X(s),2-14,求,:,R,(,s,),C,(,s,),解,:,D,(,s,)=0,,结构图变换为,,R(s),,,,,,G,4,(s),+,C(s),,,,,,,,,,,,G,1,(s),,G,2,(s),-,+,,,,G,3,(s),,,,,,,G,3,(s),,(,G,1,+,G,2,),(,G,3,+,G,4,),1+(,G,1,+G,2,)G,3,G,1,+G,2,C,(

36、,s,),R,(,s,),=,1+,G,3,(G,1,+G,2,),(G,1,+,G,2,)(G,3,+G,4,),,D(s),第二章习题课,(2-14),,R(s),,+,,,,,,,,-,E(s),,,,,,,,G,3,G,2,G,1,,E,(,s,),R,(,s,),=,1+,G,3,(G,1,+G,2,),1,R(s),,,,,,G,4,(s),+,C(s),,,,E(s),,,,,,,,,G,1,(s),,G,2,(s),-,+,,,,G,3,(s),,,,,X(s),求,:,R,(,s,),E,(,s,),2-14,解,:,D,(,s,)=0,结构图变换为,,G,3,(,G,1,+

37、,G,2,),D,(,s,),C,(,s,),,D(s),R(s),,,C(s),,,,,G,4,(s),+,,,E(s),,,,,,,,,G,1,(s),,G,2,(s),-,+,,,,G,3,(s),,,,,X(s),求,:,2-14,解,:,R,(,s,)=0,D,(,s,),C,(,s,),=1,E,(,s,),X,(,s,),=,G,2,(s),E,(,s,),X,(,s,),第二章习题课,(2-14),C,1,(s),R,1,(s),第二章习题课,(2-15),求,:,2-15,+,,,,,,,,G,1,,G,2,,G,3,C,1,(s),,,,R,1,(s),,,,,,,+,-,

38、,H,2,,,,H,1,,,,,,,,,G,4,,G,5,-,,,,,G,6,,C,2,(s),R,2,(s),解,:,结构图变换为,,+,,,,,,,,G,1,,G,2,,G,3,C,1,(s),,,R,1,(s),,,,,-,,H,2,,,H,1,,,,,,G,4,,G,5,-,,,,1+,G,4,G,4,G,5,H,1,H,2,1+,G,4,G,4,G,5,H,1,H,2,1+,G,1,G,1,G,2,,,1+G,4,+G,1,G,4,G,5,H,1,H,2,-G,1,G,2,-G,1,G,2,G,4,G,1,G,2,G,3,(1+G,4,),=,C,1,(s),R,1,(s),1+G,

39、4,+G,1,G,4,G,5,H,1,H,2,G,1,G,2,(1+G,4,),=,C,2,(s),R,2,(s),,,G,3,C,1,(s),,R,1,(s),,,,,,,+,+,,,,,,,G,1,,G,2,-,,H,2,,,,H,1,,,,,,,,,,,,G,4,,G,5,,G,6,-,,,,C,2,(s),R,2,(s),求,:,2-14,解,:,结构图变换为,,+,,,,,,,,G,4,,G,5,,G,6,C,2,(s),,R,2,(s),,,-,,H,1,,H,2,,,,,G,2,,G,1,-,,,,,,,,,第二章习题课,(2-15),1+,G,4,G,4,G,5,G,1,H,1

40、,H,2,1-G,1,G,2,,,1+G,4,+G,1,G,4,G,5,H,1,H,2,-G,1,G,2,-G,1,G,2,G,4,G,4,G,5,G,6,(1-G,1,G,2,),=,=,1+,1+,G,4,G,6,G,4,G,5,G,1,H,1,H,2,1-,G,2,G,2,1+,G,4,G,4,G,5,C,2,(s),R,2,(s),C,2,(s),,,,,,,,,,,,,,,,G,4,,G,5,,G,6,-,+,+,,,,,,,G,1,,G,2,-,,,H,2,,,,,,H,1,,,R,1,(s),,,,G,3,C,1,(s),R,2,(s),求,:,2-14,解,:,结构图变换为,,

41、,,,,,,,,,,,,G,4,,G,5,,G,6,-,+,-,,,,,,G,1,,G,2,,,H,2,,,,,,H,1,R,1,(s,),,C,2,(s),第二章习题课,(2-15),C,2,(s),R,1,(s),1+,G,4,H,2,G,4,G,5,G,1,1-G,1,G,2,,1+G,4,+G,1,G,4,G,5,H,1,H,2,-G,1,G,2,-G,1,G,2,G,4,G,1,G,4,G,5,G,6,H,2,=,=,1+,G,6,H,1,C,2,(s),R,1,(s),G,1,1-G,1,G,2,1+,G,4,H,2,G,4,G,5,G,1,1-G,1,G,2,1+,G,4,H,2

42、,G,4,G,5,C,2,(s),,,G,6,,R,1,(s),,,,,,,,,,,,,,,G,4,,G,5,-,+,+,,,,,,,G,1,,G,2,-,,H,2,,,,,,H,1,,,,,,G,3,C,1,(s),R,2,(s),求,:,2-14,解,:,结构图变换为,,第二章习题课,(2-15),,,,,,,,,,G,1,,G,2,,G,3,+,+,,,,,G,5,,G,4,,,-H,1,,,,,R,2,(s),,C,1,(s),,,H,2,,,,-,C,1,(s),R,2,(s),,,,,,,,,,,,G,1,,G,2,,G,3,+,+,,,,,G,5,,G,4,,,-H,1,,,,,

43、R,2,(s),,C,1,(s),,,H,2,,,,-,,G,2,,1+,G,4,G,4,G,5,1-G,1,G,2,-G,1,H,1,,1+G,4,+G,1,G,4,G,5,H,1,H,2,-G,1,G,2,-G,1,G,2,G,4,-G,1,G,2,G,3,G,4,G,5,H,1,=,=,1+,1+,G,4,G,4,G,5,G,1,H,1,1-,G,2,G,2,1+,G,4,G,4,G,5,C,1,(s),R,2,(s),H,2,-G,1,H,1,1-,G,2,G,2,G,2,G,3,,,G,3,C,1,(s),,R,1,(s),,+,,,,,,,G,1,,G,2,,,,,,,,+,-,,

44、H,2,,,,H,1,,,,,,,,,G,4,,G,5,-,,,,,G,6,C,2,(s),,R,2,(s),C,1,(s),R,1,(s),求,2-15,第二章习题课,(2-15),解,:,L,1,=G,1,G,2,L,3,=-G,4,L,2,=-G,1,G,4,G,5,H,1,H,2,P,1,=G,1,G,2,G,3,Δ,=1-G,1,G,2,+G,1,G,4,G,3,5,H,1,H,2,+G,4,-G,1,G,2,G,4,Δ,1,=1,+,G,4,1+G,4,+G,1,G,4,G,5,H,1,H,2,-G,1,G,2,-G,1,G,2,G,4,G,1,G,2,G,3,(1+G,4,),=

45、,C,1,(s),R,1,(s),,,G,3,C,1,(s),,R,1,(s),,+,,,,,,,G,1,,G,2,,,,,,,,+,-,,H,2,,,,H,1,,,,,,,,,G,4,,G,5,-,,,,,G,6,C,2,(s),,R,2,(s),C,2,(s),R,2,(s),求,2-15,解,:,L,1,=G,1,G,2,L,3,=-G,4,L,2,=-G,1,G,4,G,5,H,1,H,2,P,1,=G,4,G,5,G,6,Δ,=1-G,1,G,2,+G,1,G,4,G,5,H,1,H,2,+G,4,-G,1,G,2,G,4,Δ,1,=1,-,G,1,G,2,1+G,4,+G,1,G,

46、4,G,5,H,1,H,2,-G,1,G,2,-G,1,G,2,G,4,G,4,G,5,G,6,(1-G,1,G,2,),=,C,2,(s),R,2,(s),第二章习题课,(2-15),,,G,3,C,1,(s),,R,1,(s),,+,,,,,,,G,1,,G,2,,,,,,,,+,-,,H,2,,,,H,1,,,,,,,,,G,4,,G,5,-,,,,,G,6,C,2,(s),,R,2,(s),C,1,(s),R,2,(s),求,2-15,解,:,L,1,=G,1,G,2,L,3,=-G,4,L,2,=-G,1,G,4,G,5,H,1,H,2,Δ,=1-G,1,G,2,+G,1,G,4,G

47、,5,H,1,H,2,+G,4,-G,1,G,2,G,4,Δ,1,=1,P,1,=-G,1,G,2,G,3,G,4,G,5,H,1,1+G,4,+G,1,G,4,G,5,H,1,H,2,-G,1,G,2,-G,1,G,2,G,4,-G,1,G,2,G,3,G,4,G,5,H,1,=,C,1,(s),R,2,(s),第二章习题课,(2-15),,,G,3,C,1,(s),,R,1,(s),,+,,,,,,,G,1,,G,2,,,,,,,,+,-,,H,2,,,,H,1,,,,,,,,,G,4,,G,5,-,,,,,G,6,C,2,(s),,R,2,(s),C,2,(s),R,1,(s),求,2-

48、15,解,:,L,1,=G,1,G,2,L,3,=-G,4,L,2,=-G,1,G,4,G,5,H,1,H,2,Δ,=1-G,1,G,2,+G,1,G,4,G,5,H,1,H,2,+G,4,-G,1,G,2,G,4,Δ,1,=1,P,1,=G,1,G,4,G,5,G,6,H,2,1+G,4,+G,1,G,4,G,5,H,1,H,2,-G,1,G,2,-G,1,G,2,G,4,G,1,G,4,G,5,G,6,H,2,=,C,2,(s),R,1,(s),第二章习题课,(2-15),,3-1,设温度计需要在一分钟内指示出响应值的,98%,，,并且假设温度计为一阶系统，求时间常数,T,。如果将温度计放

49、在澡盆内，澡盆的温度以,10,o,C/min,的速度线性变化，求温度计的误差。,第三章习题课,(3-1),解,:,,c(t)=c(,∞)98%,t=4T=1 min,,r(t)=10t,,e(t)=r(t)-c(t),,c(t)=10(t-T+,e,),-t/T,=10(T-,e,),-t/T,e,ss,=lim,,t,→∞,,e(t),=10T,=2.5,T=0.25,3-2,电路如图，设系统初始状态为领．,第三章习题课,(3-2),解,:,求系统的单位阶跃响应,,,及,u,c,(t,1,)=8,,,时的,t,1,值．,R,1,Cs+1,R,1,/,R,0,G,(,s,)=,,R,0,=20

50、 k,Ω,,,,R,1,=200,k,Ω,,C=2.5,μ,F,,,u,c,(t)=K(1– e,t,T,-,),K,Ts,,+,,1,=,T=R,1,C=0.5,,,K=R,1,/R,0,=10,,=10(1– e,-2t,),,8=10(1– e,-2t,),0.8=1– e,-2t,e,-2t,,=0.2,,,t=0.8,,-,,∞,+,+,R,1,R,0,C,u,r,u,c,g(t)=,e,-t/T,T,K,,t,1,=0.8,,,=4,,(2),求系统的单位脉冲响应，单位斜坡,,响应,,,及单位抛物响应在,t,1,时刻的值．,第三章习题课,(3-2),解,:,u,c,(t)=K(,t

51、-,T+T,e,-t/T,),,=4,,R(s)=,1,s,2,R(s)=1,R(s)=,1,s,3,T,2,=K(,s,s+1/T,+,T,s,2,-,1,s,3,-,T,2,),=1.2,,1,s,3,K,Ts,,+,,1,U,c,(s)=,-0.5t+0.25-0.25e,-2t,),1,2,t,2,u,c,(t)=10(,3-3,已知单位负反馈系统的开环传递函数，求系统的单位阶跃响应。,4,s(s+5),G(s)=,第三章习题课,(3-3),解,:,=,,s,2,+5s+4,,C(s),R(s),4,s(s+1)(s+4),C(s)=,4,R(s)=,s,1,1/3,s+4,1,s,+

52、,=,4/3,s,+,1,-,1,3,c(t)=1+,-4t,-t,4,3,-,e,e,3-4,已知单位负反馈系统的开环传递函数，求系统的上升时间,t,r,、峰值时间,t,p,、超调量,σ,%,和调整时间,t,s,。,1,s(s+1),G(s)=,第三章习题课,(3-4),解,:,=,s,2,+s+1,,C(s),R(s),1,2,,=,1,ω,n,2,ω,n,ζ,=1,ζ=0.5,=,1,ω,n,=0.866,d,ω,,=,ω,n,2,ζ,1-,,=60,o,-,1,ζ,=tg,,β,2,1-,,ζ,t,r,=,d,ω,π,β,-,,=,3.14-3.14/3,0.866,=2.42,t,p

53、,=,d,ω,π,3.14,0.866,,=,=3.63,σ,%=,100%,e,-,ζ,ζ,π,1-,2,=16%,-1.8,e,t,s,=,ζ,3,ω,n,=6,t,s,=,ζ,4,ω,n,=8,3-6,已知系统的单位阶跃响应,:,c(t)=1+0.2e,-60t,-10t,-1.2e,(1),求,系统的闭环传递函数。,(2),求,系统的阻尼比和无阻尼振荡频率。,第三章习题课,(3-6),解,:,0.2,s+60,1,s,+,C(s)=,1.2,s,+,10,-,s(s+60)(s+10),=,600,=,,s,2,+70s+600,,C(s),R(s),600,R(s)=,s,1,2,,

54、=,600,ω,n,2,ω,n,ζ,=70,ζ=1.43,=,24.5,ω,n,3-7,设二阶系统的单位阶跃响应曲线如图，系统的为单位反馈，求系统的传递函数。,t,c(t),0,1,0.1,1.3,解,:,第三章习题课,(3-7),t,p,=,=0.1,2,1-,,ζ,π,ω,n,=0.3,e,-,ζ,ζ,π,1-,2,e,ζ,ζ,π,1-,2,=3.3,ω,n,2,ζ,1-,,3.14,0.1,=,=31.4,2,1-,,ζ,π,/,ζ,=ln3.3,=1.19,2,1-,,ζ,π,),2,/,ζ,(,=1.42,9.86,2,ζ,=1.42-1.42,2,ζ,ζ=0.35,=,33.4,ω

55、,n,ω,n,ω,n,ζ,s(s+2,),G(s)=,2,1115.6,s(s+22.7),=,3-8,已知单位负反馈系统的开环传递函数，求系统,K,、,T,值以满足动态指标：,σ,%≤30%,，,t,s,≤0.3(5%),。,K,s(Ts+1),G(s)=,第三章习题课,(3-8),解,:,=,Ts,2,+s+K,,C(s),R(s),K,s,2,+,=,T,1,s+,T,K,T,K,T,1,2,ω,n,ζ,=,t,s,=,ζ,3,ω,n,≤,0.3,ω,n,ζ,≥,10,T,≤,0.05,≤,0.3,e,-,ζ,ζ,π,1-,2,ζ,≥,0.35,≥,28.6,ω,n,2,,=,ω,n,T

56、,K,=817.96,K,≥,40.9,3-11,已知闭环系统的特征方程式，试用劳斯判据判断系统的稳定性。,第三章习题课,(3-11),(1),s,3,+20s,2,+9s+100=0,解：,劳斯表如下：,s,1,,s,0,,s,3,,s,2,,1,9,20,100,4,,100,系统稳定。,(3) s,4,+8s,3,+18s,2,+16s+5=0,,1,18 5,s,4,,s,3,,8,16,劳斯表如下：,s,2,,16,5,s,1,,216,,16,,s,0,,5,系统稳定。,3-12,已知单位负反馈系统的开环传递函数，试确定系统稳定时,K,值范围。,第三章习题课,(3-12),

57、G(s)=,s(s+1)(0.5s,2,+s+1),K(0.5s+1),解,:,0.5s,4,+1.5s,3,+2s,2,+s++0.5Ks+K=0,,0.5,2 K,s,4,,s,3,,1.5,1+0.5K,s,2,,,b,31,,,,b,31,=,,,1.5,*2-0,5(1+0.5K),,,,1.5,,3-0,5-0.25K>0,,,0.25K<2.5,,,=1.67-0.167K,s,1,,,,K,,,b,41,,,,b,41,=,,(1.67-0.167K)(1+0.5K)-1.5K,1.67-0.167K,3-13,已知系统结构如图，试确定系统稳定时,τ,值范围。,第

58、三章习题课,(3-13),-,１,s,1+,τ,s,-,10,s(s+1),R(s),C(s),解,:,G(s)=,s,2,+s+10,10(1+,s,τ,),s,1,=,s(s,2,+s+10,10(s+1),s,τ,),Φ,(s)=,s,3,+s,2,+10,10(s+1),s,2,+10s+10,τ,,1,10,s,3,,s,2,,(1+10,,τ,),10,s,1,,,b,31,,,s,0,,10,,b,31,=,,10(1+10,,τ,),-10,1+10,,τ,>0,τ,>0,3-14,已知系统结构如图，试确定系统稳定时,τ,值范围。,第三章习题课,(3-14),R(s),-,τ,

59、s+1,s,10,s(s+1),C(s),解,:,G(s)=,s,2,(s+1),10(,τ,s+1),Φ,(s)=,s,3,+s,2,+10,s+10,τ,10(,τ,s+1),s,3,,s,2,,1 10,,,1,10,τ,s,1,,,b,31,,,s,0,,10,,b,31,=,,10,,τ,-10,1,,>0,τ,>1,r(t)=I(t)+2t+t,2,3-16,已知单位反馈系统的开环传递函数，试求,K,p,、,K,v,和,K,a,,．并求稳态误差,e,ss,．,第三章习题课,(3-16),解：,(0.1s+1)(0.2s+),(1) G(s)=,20,K,p,=20,,υ

60、,=0,e,ss1,=,R,0,1+K,s,2,R(s)=,1,s,2,+,s,3,2,+,=,1,21,K,υ,=0,,e,ss2,=,∞,K,a,=0,,e,ss3,=,∞,,e,ss,=,∞,,υ,=1,K,υ,=10,K,a,=0,,e,ss3,=,∞,,e,ss,=,∞,s(s+2)(s+10),(2) G(s)=,200,s(0.5s+1)(0.1s+1),=,10,K,p,=∞,,,e,ss1,=,0,e,ss2,=,K,,2,=,2,10,,s,2,(s,2,+4s+10),(3) G(s)=,10(2s+1),υ,=2,K,p,=∞,,,e,ss1,=,0,s,2,(0.1s

61、,2,+0.4s+1),=,(2s+1),K,υ,=,∞,,,e,ss2,=,0,K,a,=,1,,,e,ss3,=,2,,e,ss,=,2,3-17,已知系统结构如图。,第三章习题课,(3-17),解,:,-,R(s),-,K,1,τ,s,１,s,2,C(s),单位阶跃输入,:,G(s)=,s,2,+K,1,s,τ,K,1,Φ,(s)=,s,2,+K,1,s+K,1,τ,K,1,确定,K,1,和,τ,值,,。,,σ,%=20%,t,s,=1.8(5%),2,ω,n,ζ,=K,1,τ,2,,=,K,1,ω,n,=0.2,e,-,ζ,ζ,π,1-,2,t,s,=,ζ,3,ω,n,=1.8,ζ=0

62、.45,ω,n,3,1.8*0.45,=,=3.7,2,,ω,n,K,1,=,=13.7,τ,=0.24,(2),求系统的稳态误差：,r(t)=I(t), t ,,1,2,t,2,,解,:,G(s)=,s,2,+K,1,s,τ,K,1,=,s(,s+1),τ,K,1,1,τ,1,υ,=1,K,p,=∞,,,e,ss1,=,0,R(s)=,1,s,R(s)=,s,2,1,K,υ,=K,e,ss2,=,τ,=0.24,R(s)=,s,3,1,K,a,=0,,e,ss3,=,∞,第三章习题课,(3-17),3-18,已知系统结构如图。为使,ζ,=0.7,时,,单位斜坡输入的稳态误差,e,ss,=0.

63、25,第三章习题课,(3-18),解,:,确定,K,和,τ,值,,。,-,τ,s,-,K,s(s+2),R(s),C(s),G(s)=,s,2,+2s+K,s,τ,K,=,s(,s+1),τ,2+K,1,τ,2+K,K,Φ,(s)=,s,2,+(2+K,)s+K,τ,K,2,ω,n,ζ,=2+K,τ,2,,=,K,ω,n,,=2*0.7,K,,,e,ss,=,,2+K,,τ,K,,=0.25,,=,,0.25K,-2,τ,K,,K,=31.6,τ,=0.186,+,R(s),G(s,),F(s),C(s),+,-,D,1,(s),D,2,(s),E(s),3-19,系统结构如图。,第三章习题课

64、,(3-19),解,:,,r(t)=d,1,(t)=d,2,(t)=,I(t),求,r(t,),作下的稳态误差．,e,ssr,=lim s,·,1+G(s)F(s),s,→,0,s,1,=,,1+G(0)F(0),1,(2),求,d,1,(t),和,d,2,(t),同时作用下的稳态误差．,,e,ssd,= lim s,-F(s),1+G(s)F(s),s,→0,-1,1+G(s)F(s),+,s,1,[,],E,d,(s)=,-G,2,(s)H(s),1+G,1,(s)G,2,(s)H(s),·,D(s),,=,,1+G(0)F(0),-[1+F(s)],(3),求,d,1,(t),作用下的稳

65、态误差．,G(s)=K,p,+,K,s,Js,1,F(s)=,e,ssd,= lim s,-F(s),1+G(s)F(s),s,→0,s,1,-,s,→0,s,1,= lim s,1+(K,p,+,K,s,Js,1,),Js,1,=0,返回,4-1,已知系统的零、极点分布如图，大致绘制出系统的根轨迹。,第四章习题课,(4-1),解,:,j,σ,0,ω,(1),(2),j,σ,0,ω,(3),j,σ,0,ω,(4),j,σ,0,ω,60,0,90,0,60,0,第四章习题课,(4-1),(5),j,σ,0,ω,,,(6),j,σ,0,ω,j,σ,0,ω,(7),(8),j,σ,0,ω,60,0,

66、45,0,135,0,36,0,108,0,4-2,已知开环传递函数，试用解析法绘制出系统的根轨迹，并判断点,(-2+j0),(0+j1),,,(-3+j2),是否在根轨迹上。,第四章习题课,(4-2),解,:,K,r,(s+1),G(s)=,K,r,Φ,(s)=,s+1+K,r,K,r,=0,s=-1-K,r,j,σ,0,ω,系统的根轨迹,,s=-1,-1,K,r,=,→,∞,s=-,∞,s=-2+j0,-2,s=0+j1,0+j1,-3+j2,s=-3+j2,σ,j,ω,0,4-3,已知系统的开环传递函数，试绘制出根轨迹图。,第四章习题课,(4-3),解,:,s(s+1)(s+5),(1) G(s)=,K,r,(s+1.5)(s+5.5),,1,）开环零、极点,p,1,,p,1,=0,p,2,p,2,=-1,p,3,,p,3,=-5,2,）实轴上根轨迹段,p,1,~,p,2,z,1,,z,1,=-1.5,z,2,,z,2,=-5.5,z,1,~,p,3,z,2,~-,∞,,3,）根轨迹的渐近线,n-m=,1,θ,=,+,180,o,,4,）分离点和会合点,A,(,s,),B,',(