自动控制原理及其应用答案第二版课后答案

,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,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,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,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(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 -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(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,(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),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),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,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)+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,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,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,+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,(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,(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)=,(,t,),+2e +e,-2t,-t,第二章习题课,(2-,),2-10,已知系统的微分方程组的拉氏变换式，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(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),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),_,_,+,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,2,1,=,1,2,=,1,R,(,s,),C,(,s,),=,n,k=,1,P,k,k,=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,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,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),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,2,1,=,1,P,2,=G,3,G,2,=1+,G,4,G,2,H,+,G,1,G,2,H,2,=1,+,G,1,G,4,H,第二章习题课,(2-11b),H,1,_,+,+,+,G,1,+,C(s),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,2,2-11d,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,1,1,=,1,P,2,=G,2,2,=,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,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,1,1,=,1,P,2,=G,2,2,=,1,1+,G,1,G,3,+,G,2,G,3,G,1,G,4,-,G,2,G,4,=,(,G,1,+G,2,),C,(s),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,1,1,=,1-,G,2,=1+,G,1,G,2,-,G,2,C,(,s,),R,(,s,),1+,G,1,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,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,),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,),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+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,3,1,=,1,2,=,1,E,(,s,),结构图变,换成：,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,(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,(,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,+,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),+,-,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,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,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,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,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,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,+,-,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,=1-G,1,G,2,+G,1,G,4,G,3,5,H,1,H,2,+G,4,-G,1,G,2,G,4,1,=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,),=,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,=1-G,1,G,2,+G,1,G,4,G,5,H,1,H,2,+G,4,-G,1,G,2,G,4,1,=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,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,=1-G,1,G,2,+G,1,G,4,G,5,H,1,H,2,+G,4,-G,1,G,2,G,4,1,=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,2-15,解,:,L,1,=G,1,G,2,L,3,=-G,4,L,2,=-G,1,G,4,G,5,H,1,H,2,=1-G,1,G,2,+G,1,G,4,G,5,H,1,H,2,+G,4,-G,1,G,2,G,4,1,=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 k,R,1,=200,k,C=2.5,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-,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,+,=,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,%,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,n,2,n,=1,=0.5,=,1,n,=0.866,d,=,n,2,1-,=60,o,-,1,=tg,2,1-,t,r,=,d,-,=,3.14-3.14/3,0.866,=2.42,t,p,=,d,3.14,0.866,=,=3.63,%=,100%,e,-,1-,2,=16%,-1.8,e,t,s,=,3,n,=6,t,s,=,4,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,=,600,n,2,n,=70,=1.43,=,24.5,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-,n,=0.3,e,-,1-,2,e,1-,2,=3.3,n,2,1-,3.14,0.1,=,=31.4,2,1-,/,=ln3.3,=1.19,2,1-,),2,/,(,=1.42,9.86,2,=1.42-1.42,2,=0.35,=,33.4,n,n,n,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：,%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,n,=,t,s,=,3,n,0.3,n,10,T,0.05,0.3,e,-,1-,2,0.35,28.6,n,2,=,n,T,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),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),1.5,3-0,5-0.25K0,0.25K0,0,3-14,已知系统结构如图，试确定系统稳定时,值范围。,第三章习题课,(3-14),R(s),-,s+1,s,10,s(s+1),C(s),解,:,G(s)=,s,2,(s+1),10(,s+1),(s)=,s,3,+s,2,+10,s+10,10(,s+1),s,3,s,2,1 10,1,10,s,1,b,31,s,0,10,b,31,=,10,-10,1,0,1,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,=0,e,ss1,=,R,0,1+K,s,2,R(s)=,1,s,2,+,s,3,2,+,=,1,21,K,=0,e,ss2,=,K,a,=0,e,ss3,=,e,ss,=,=1,K,=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),=2,K,p,=,e,ss1,=,0,s,2,(0.1s,2,+0.4s+1),=,(2s+1),K,=,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,s,s,2,C(s),单位阶跃输入,:,G(s)=,s,2,+K,1,s,K,1,(s)=,s,2,+K,1,s+K,1,K,1,确定,K,1,和,值,。,%=20%,t,s,=1.8(5%),2,n,=K,1,2,=,K,1,n,=0.2,e,-,1-,2,t,s,=,3,n,=1.8,=0.45,n,3,1.8*0.45,=,=3.7,2,n,K,1,=,=13.7,=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,K,1,=,s(,s+1),K,1,1,1,=1,K,p,=,e,ss1,=,0,R(s)=,1,s,R(s)=,s,2,1,K,=K,e,ss2,=,=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,=0.7,时,单位斜坡输入的稳态误差,e,ss,=0.25,第三章习题课,(3-18),解,:,确定,K,和,值,。,-,s,-,K,s(s+2),R(s),C(s),G(s)=,s,2,+2s+K,s,K,=,s(,s+1),2+K,1,2+K,K,(s)=,s,2,+(2+K,)s+K,K,2,n,=2+K,2,=,K,n,=2*0.7,K,e,ss,=,2+K,K,=0.25,=,0.25K,-2,K,K,=31.6,=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,(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,0,(1),(2),j,0,(3),j,0,(4),j,0,60,0,90,0,60,0,第四章习题课,(4-1),(5),j,0,(6),j,0,j,0,(7),(8),j,0,60,0,45,0,135,0,36,0,108,0,4-2,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,(s)=,s+1+K,r,K,r,=0,s=-1-K,r,j,0,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,j,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,=,+,180,o,4,）分离点和会合点,A,(,s,),B,(