自动控制原理第二章习题课答案.ppt

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。,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,=,2-3-1,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,(s2,+3),2,(s+2)te,st,s,2,+3s,=+e,-3t,-e,-t,-e,-t,2,3,1,12,3,4,t,2,(2-4-2),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:,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),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,1,2-9,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),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,1H,+,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),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),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,H3,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,4G,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-G1,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,4G,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),返回,