自动控制原理及其应用黄坚课后答案.pdf-资料库

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(a)(a)(a)(a) 第二章习题课　　　　(2-1)(2-1)(2-1)(2-1) 第二章习题课第二章习题课第二章习题课 khdaw.com uuuuiiii-u-u-u-uoooo RRRR1111 =C=C=C=C 2-12-12-12-1 试建立图所示电路的动态微分方程试建立图所示电路的动态微分方程试建立图所示电路的动态微分方程试建立图所示电路的动态微分方程解：解：解：解：输入输入输入输入uuuuiiii 输出输出输出输出uuuuoooo uuuu1111=u=u=u=uiiii-u-u-u-uoooo uuuuooooi=i=i=i=RRRR2222 dddd((((uuuuiiii-u-u-u-uoooo)))) dtdtdtdt iiii1111=i-i=i-i=i-i=i-i2222 ++++ ＋＋＋＋ uuuu1111 RRRR1111RRRR2222 uuuuiiii uuuuoooo iiii1111====RRRR1111 ==== iiii ---- ---- dudududu1111 uuuuoooo----RRRR2222 ====uuuuiiii-u-u-u-uoooo CCCCdddd((((uuuuiiii-u-u-u-uoooo)))) iiii2222=C=C=C=C dtdtdtdt RRRR1111 RRRR2222(u(u(u(uiiii-u-u-u-uo o o o )=R)=R)=R)=R1111uuuu0000-CR-CR-CR-CR1111RRRR2222((((dudududuiiii dudududuoooo ---- )))) dtdtdtdt dtdtdtdt dudududuiiiidtdtdtdt +R+R+R+R1111uuuuoooo+R+R+R+R2222uuuu0000=CR=CR=CR=CR1111RRRR2222 +R+R+R+R2222uuuuiiii CRCRCRCR1111RRRR2222 dudududuoooo dtdtdtdt uuuu1111 CCCC iiii2222 iiii1111 dtdtdtdt 第二章习题课　　　　(2-1)(2-1)(2-1)(2-1) 第二章习题课第二章习题课第二章习题课 LLLLuuuu1111 iiii1111 RRRR2222 iiii2222 iiii CCCC RRRR1111 ＋＋＋＋ uuuuiiii ---- ++++ (b)(b)(b)(b) 解：解：解：解： ((((uuuuiiii-u-u-u-u1111)))) uuuuoooo i=ii=ii=ii=i1111+i+i+i+i2222 i=i=i=i= RRRR1111 ---- uuuuoooo iiii2222=C=C=C=Cdudududu1111 dudududu1111 uuuuiiii-u-u-u-u1111 uuuuoooo+C+C+C+CRRRR2222 iiii1111====RRRR2222 ====RRRR1111 dtdtdtdt dtdtdtdt dudududuoooodtdtdtdt dudududuoooodtdtdtdt uuuu1111=u=u=u=uoooo++++LLLL uuuu1111-u-u-u-uoooo====LLLL RRRR2222 RRRR2222 dudududuoooo uuuuoooo --------uuuuiiii uuuuoooo dddd2222uuuuoooo LLLL dudududuoooo + CLCLCLCL +C+C+C+C + + + ==== dtdtdtdt RRRR2222 RRRR1111RRRR2222 RRRR2222 dtdtdtdt RRRR1111 RRRR1111 dtdtdtdt2222 uuuuiiii dddd2222uuuuoooo LLLL dudududuoooo 1111 CLCLCLCL 1111 +(C++(C++(C++(C+ +++++(+(+(+( )u)u)u)uoooo ==== dtdtdtdt ) ) ) ) RRRR1111 RRRR2222 RRRR2222 RRRR1111 dtdtdtdt2222 RRRR1111RRRR2222 khdaw.com www.khdaw.com www.khdaw.com

第二章习题课　　　　(2-2)(2-2)(2-2)(2-2) 第二章习题课第二章习题课第二章习题课 khdaw.com 解：解：解：解： 2-2 2-2 2-2 2-2 求下列函数的拉氏变换。求下列函数的拉氏变换。求下列函数的拉氏变换。求下列函数的拉氏变换。 (1) f(t)=sin4t+cos4t (1) f(t)=sin4t+cos4t (1) f(t)=sin4t+cos4t (1) f(t)=sin4t+cos4t = ωωωω = L L L L[[[[sinsinsinsinωωωωtttt]]]]= = ωωωω2222+s+s+s+s2222 = 4444 sin4t+cos4t LLLL[[[[sin4t+cos4t = sin4t+cos4t]]]]= sin4t+cos4t = ssss2222+16+16+16+16 ssss ssss2222+16+16+16+16++++ L L L L[[[[coscoscoscosωωωωtttt]]]]==== ssss ωωωω2222+s+s+s+s2222 ==== s+4s+4s+4s+4 ssss2222+16+16+16+16 (2) f(t)=t (2) f(t)=t3333+e+e+e+e4t4t4t4t (2) f(t)=t (2) f(t)=t 解：解：解：解： LLLL[[[[tttt3333+e+e+e+e4t4t4t4t]]]]= = = = 3!3!3!3! 1111 6s+24+s 6s+24+s + 6s+24+s 6s+24+s4444 + + s-4s-4s-4s-4 + ssss4444(s+4)(s+4)(s+4)(s+4) ssss4444 = = = = 第二章习题课　　　　(2-2)(2-2)(2-2)(2-2) 第二章习题课第二章习题课第二章习题课 (3) f(t)=t (3) f(t)=tnnnneeeeatatatat (3) f(t)=t (3) f(t)=t 解：解：解：解： LLLL[[[[ttttnnnneeeeatatatat]=]=]=]= n!n!n!n! (s-a)(s-a)(s-a)(s-a)n+1n+1n+1n+1 (4) f(t)=1(t- (4) f(t)=1(t-ττττ)e)e)e)e2t2t2t2t (4) f(t)=1(t- (4) f(t)=1(t- 解：解：解：解： LLLL[[[[1(t-1(t-1(t-1(t-ττττ)e)e)e)e2t2t2t2t]=]=]=]=eeee----ττττssss1111 s-2s-2s-2s-2 khdaw.com www.khdaw.com www.khdaw.com

第二章习题课　　　　(2-3)(2-3)(2-3)(2-3) 第二章习题课第二章习题课第二章习题课 khdaw.com 解：解：解：解： 2-32-32-32-3 求下列函数的拉氏反变换。求下列函数的拉氏反变换。求下列函数的拉氏反变换。求下列函数的拉氏反变换。 (1) F(s)= s+1s+1s+1s+1 (1) F(s)= (1) F(s)= (1) F(s)= AAAA1111 + AAAA2222 + + s+2s+2s+2s+2 s+3s+3s+3s+3 + = = = = (s+2)(s+3)s=-2s=-2s=-2s=-2=-1=-1=-1=-1 (s+2)(s+3) (s+2)(s+3) (s+2)(s+3) (s+2)(s+3) (s+2)(s+3) (s+2)(s+3) (s+2)(s+3) AAAA1111=(s+2)=(s+2)=(s+2)=(s+2) s+1s+1s+1s+1 AAAA2222=(s+3)=(s+3)=(s+3)=(s+3) s+1s+1s+1s+1 (s+2)(s+3) (s+2)(s+3) (s+2)(s+3) (s+2)(s+3)s=-3s=-3s=-3s=-3 1111 - - s+2s+2s+2s+2 - - F(s)= F(s)= F(s)= F(s)= 2222 s+3s+3s+3s+3 f(t)=2e-3t-3t-3t-3t-e-e-e-e-2t-2t-2t-2t f(t)=2e f(t)=2e f(t)=2e =2=2=2=2 (2) F(s)= ssss (2) F(s)= (2) F(s)= (2) F(s)= 第二章习题课　　　　(2-3)(2-3)(2-3)(2-3) 第二章习题课第二章习题课第二章习题课 AAAA2222 AAAA3333 AAAA1111 + + = + s+1s+1s+1s+1 s+2s+2s+2s+2 + + = + = + = + (s+1)(s+1)(s+1)(s+1)2222 ssss (s+1)(s+1)(s+1)(s+1)2222(s+2)(s+2)(s+2)(s+2) 解：解：解：解： AAAA1111=(s+1)=(s+1)=(s+1)=(s+1)2222 (s+1)(s+1)(s+1)(s+1)2222(s+2)(s+2)(s+2)(s+2)s=-1s=-1s=-1s=-1 ssss dddd [[[[AAAA2222= = = = s+2s+2s+2s+2]]]] dsdsdsds AAAA3333=(s+2)=(s+2)=(s+2)=(s+2) =2=2=2=2 s=-1s=-1s=-1s=-1 ssss (s+1)(s+1)(s+1)(s+1)2222(s+2)(s+2)(s+2)(s+2)s=-2s=-2s=-2s=-2 f(t)=-2e f(t)=-2e-2t-2t-2t-2t-te-te-te-te-t-t-t-t+2e+2e+2e+2e-t-t-t-t f(t)=-2e f(t)=-2e =-1=-1=-1=-1 =-2=-2=-2=-2 khdaw.com www.khdaw.com www.khdaw.com

khdaw.com 第二章习题课　　　　(2-3)(2-3)(2-3)(2-3) 第二章习题课第二章习题课第二章习题课 AAAA1111s+As+As+As+A2222 AAAA3333 + + = = ssss + + = = ssss2222+1+1+1+1 F(s)(sF(s)(sF(s)(sF(s)(s2222+1)+1)+1)+1)s=+js=+js=+js=+j=A=A=A=A1111s+As+As+As+A2222s=+js=+js=+js=+j -2-5j+1 -2-5j+1 -2-5j+1=jA=jA=jA=jA1111+A+A+A+A2 2 2 2 -2-5j+1 j j j j A A A A2222=-5=-5=-5=-5 解：解：解：解： s s s s 2s2s2s2s2222-5s+1-5s+1-5s+1-5s+1 =A=A=A=A1111s+As+As+As+A2 2 2 2 s=s=s=s=jjjj s=s=s=s=jjjj -5j-1=-A -5j-1=-A1111+jA+jA+jA+jA2 2 2 2 AAAA1111=1=1=1=1 -5j-1=-A -5j-1=-A AAAA3333=F(s)s=F(s)s=F(s)s=F(s)s s=0s=0s=0s=0 F(s)= 1111 ssss + + + + + + + + F(s)= F(s)= F(s)= ssss ssss2222+1+1+1+1 -5-5-5-5 ssss2222+1+1+1+1 (3) F(s)=2s2s2s2s2222-5s+1-5s+1-5s+1-5s+1 (3) F(s)= (3) F(s)= (3) F(s)= s(ss(ss(ss(s2222+1)+1)+1)+1) = = = =1111 f(t)=1+cost-5sint f(t)=1+cost-5sint f(t)=1+cost-5sint f(t)=1+cost-5sint 第二章习题课　　　　(2-3)(2-3)(2-3)(2-3) 第二章习题课第二章习题课第二章习题课 (4) F(s)= s+2s+2s+2s+2 (4) F(s)= (4) F(s)= (4) F(s)= s(s+1) s(s+1)2222(s+3)(s+3)(s+3)(s+3) s(s+1) s(s+1) AAAA1111 AAAA2222 ++++s+1s+1s+1s+1 (s+1)(s+1)(s+1)(s+1)2222 2222 3333AAAA3333= = = = 解：解：解：解： ==== -1-1-1-1 2222AAAA1111= = = = (s+2)(s+2)(s+2)(s+2) dddd[[[[ ]]]] s(s+3) s(s+3) s(s+3) s(s+3) AAAA2222= = = = d d d dssss AAAA3333++++ AAAA4444 ++++ ssss s+3s+3s+3s+3 1111 -3-3-3-3 12121212AAAA4444= = = = 4444AAAA2222= = = = [s(s+3)-(s+2)(2s+3)] [s(s+3)-(s+2)(2s+3)] [s(s+3)-(s+2)(2s+3)] [s(s+3)-(s+2)(2s+3)] = = = = s=-1s=-1s=-1s=-1 -t-t-t-teeee-t-t-t-t 2222 [s(s+3)] [s(s+3)] [s(s+3)] [s(s+3)]2222 3333 ++++ 2222 1111 eeee-t-t-t-t ----4444 ++++ 12121212 3333 f(t)=f(t)=f(t)=f(t)= -3-3-3-3 4444= = = = s=-1 s=-1 s=-1 s=-1 khdaw.com eeee-3t-3t-3t-3t www.khdaw.com www.khdaw.com

+5+5+5+5 ···· 第二章习题课　　　　(2-4)(2-4)(2-4)(2-4) 第二章习题课第二章习题课第二章习题课 khdaw.com 2-4 2-4 2-4 2-4 求解下列微分方程。求解下列微分方程。求解下列微分方程。求解下列微分方程。 dydydydy((((tttt)))) dddd2222yyyy((((tttt)))) y(0)=y(0)=2 y(0)=y(0)=2 y(0)=y(0)=2 y(0)=y(0)=2 (1) (1) (1) (1) +6y+6y+6y+6y((((tttt))))=6=6=6=6 dtdtdtdt2222 dtdtdtdt (0)+5sY(s)-5y(0)+6Y(s)= 6666ssss Y(s)-sy(0)-y''''(0)+5sY(s)-5y(0)+6Y(s)= 解：解：解：解：ssss2222Y(s)-sy(0)-y Y(s)-sy(0)-y (0)+5sY(s)-5y(0)+6Y(s)= Y(s)-sy(0)-y (0)+5sY(s)-5y(0)+6Y(s)= )-2s-2+5sY5sY5sY5sY((((ssss))))-10+6Y-10+6Y-10+6Y-10+6Y((((ssss))))= = = = 6666ssss ssss2222YYYY((((ssss)-2s-2+ )-2s-2+ )-2s-2+ AAAA2222 AAAA1111 + AAAA3333 Y(s)=Y(s)=Y(s)=Y(s)=6+2s6+2s6+2s6+2s2222+12s+12s+12s+12s + + s+2s+2s+2s+2 s+3s+3s+3s+3 + + + = = ssss + + = = s(ss(ss(ss(s2222+5s+6)+5s+6)+5s+6)+5s+6) AAAA3333=-4=-4=-4=-4 AAAA1111=1=1=1=1 AAAA2222=5 =5 =5 =5 y(t)=1+5e y(t)=1+5e-2t-2t-2t-2t-4e-4e-4e-4e-3t-3t-3t-3t y(t)=1+5e y(t)=1+5e 第二章习题课　　　　(2-4)(2-4)(2-4)(2-4) 第二章习题课第二章习题课第二章习题课 (2) (2) (2) (2) 2222dydydydy((((tttt)))) dtdtdtdt +y+y+y+y((((tttt))))=t=t=t=t y(0)=0 y(0)=0 y(0)=0 y(0)=0 khdaw.com www.khdaw.com www.khdaw.com

第二章习题课　　　　(2-5)(2-5)(2-5)(2-5) 第二章习题课第二章习题课第二章习题课 2-5 2-5 2-5 2-5 试画题图所示电路的动态结构图，试画题图所示电路的动态结构图，试画题图所示电路的动态结构图，试画题图所示电路的动态结构图，并求传递函数。并求传递函数。并求传递函数。并求传递函数。解：解：解：解： CsCsCsCsCsCsCsCs I(s)I(s)I(s)I(s) cccc iiii1111 RRRR1111 RRRR2222 iiii2222 iiii UUUUcccc(s)(s)(s)(s) ++++ uuuurrrr ---- ++++ uuuucccc ---- khdaw.com (1)(1)(1)(1) UUUUcccc(s)(s)(s)(s) UUUUrrrr(s)(s)(s)(s) ____ UUUUrrrr(s)(s)(s)(s) UUUUcccc(s)(s)(s)(s)==== RRRR2222RRRR2222 IIII1111(s)(s)(s)(s) ++++ ++++ 1111 RRRR1111 IIII2222(s)(s)(s)(s) 1111 +sC)R +sC)R +sC)R +sC)R2222 ( ( ( ( RRRR1111 1111 +sC)R +sC)R +sC)R +sC)R2222 1+(1+(1+(1+( RRRR1111 RRRR2222+R+R+R+R1111RRRR2222sCsCsCsC ==== RRRR1111+R+R+R+R2222+R+R+R+R1111RRRR2222sCsCsCsC (2)(2)(2)(2) LLLL1111=-R=-R=-R=-R2 2 2 2 /Ls/Ls/Ls/Ls LLLL2222=-/LCs=-/LCs=-/LCs=-/LCs2222 LLLL3333=-1/sCR=-1/sCR=-1/sCR=-1/sCR1111 LLLL1 1 1 1 LLLL3333=R=R=R=R2222/LCR/LCR/LCR/LCR1111ssss2222 I(s)I(s)I(s)I(s) UUUUrrrr(s)(s)(s)(s) 1111 RRRR1111 LLLL3333 ____ UUUU1111(s)(s)(s)(s) UUUUrrrr(s)(s)(s)(s) UUUUcccc(s)(s)(s)(s) 第二章习题课　　　　(2-5)(2-5)(2-5)(2-5) 第二章习题课第二章习题课第二章习题课解：解：解：解： RRRR1111 iiii LLLLuuuu1111 iiii1111 iiii2222 CCCC RRRR2222 ＋＋＋＋ uuuurrrr ---- ++++ uuuucccc ---- IIII2222(s)(s)(s)(s) ---- IIII1111(s)(s)(s)(s) 1111 CsCsCsCs ---- LLLL2222 RRRR2222 PPPP 1 1 1 1=R=R=R=R2222/LCR/LCR/LCR/LCR1111ssss2222 ΔΔΔΔ1111=1=1=1=1 UUUU1111(s)(s)(s)(s)UUUUcccc(s)(s)(s)(s) IIII1111(s)(s)(s)(s) RRRR2222RRRR2222 UUUUcccc(s)(s)(s)(s) LLLL1111 1111 LsLsLsLs khdaw.com ====RRRR1111CLsCLsCLsCLs2222+(R+(R+(R+(R1111RRRR2222C+L)s+R C+L)s+R C+L)s+R1111+R+R+R+R2222 C+L)s+R www.khdaw.com www.khdaw.com

第二章习题课　　　　(2-6)(2-6)(2-6)(2-6) 第二章习题课第二章习题课第二章习题课 2-62-62-62-6 试采用复阻抗写出传递函数。试采用复阻抗写出传递函数。试采用复阻抗写出传递函数。试采用复阻抗写出传递函数。 khdaw.com uuuurrrr RRRR1111 RRRR2222 RRRR3333 CCCC - + ∞ Δ + uuuucccc 第二章习题课　　　　(2-7)(2-7)(2-7)(2-7) 第二章习题课第二章习题课第二章习题课 2-72-72-72-7 试证明两系统为相似系统。试证明两系统为相似系统。试证明两系统为相似系统。试证明两系统为相似系统。 cccc2222 iiii2222 iiii1111 RRRR2222 RRRR1111 cccc1111 ++++ uuuuoooo ---- ＋＋＋＋ uuuuiiii ---- iiii kkkk1111 xxxxiiii ffff1111 xxxx0000 yyyy ffff2222 kkkk2222 khdaw.com www.khdaw.com www.khdaw.com

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