胡寿松自动控制原理习题解答第四章

1、g(s) =1x03f( /2(s+l/3) 5(77172)kj5+1/3)5(5+1/2)1/21/3 jo4-34-28xito)4-284-4d)(dg(j) =5(0.25+1)(0.55+1)io/;5(5+5)(5+2)j(5 + 5)(5+2)3j, = -3.7863= -0.88r77i+7t7 = 0 3j2 + ,4j + ,0=0 cl = -0.88g(s) =kx(s+)5(5 4-0.5) 5(5+0.5)00.5+t/5 + 10j2 + 25j + l5 = 0j( =-6.5171，=-0.29d、=-1.7 d2 = -0.29/q5)j(5+2)(j+

2、3)(3)g(s) =g(5) =尺 + 5)5(5+ 2)(5+ 3)0 2 2d2 = -2.5964 d. = -0.8865d = -0.8865（5）=ks+2)(j+l+y2)(5+l-/2)11尺(友+2a：j5+2)(5+1+ )2)(5+!-j2)(5+1 + 2)(5+1-j2)pl= .12 p2 =1-2it = 0,土 1,土 2,= + - = 18045o-90i35o4 =方 + h 180, 一 45 + = 22510)(5+ 10-jio)ks20)5(5+10+ jl0)(5+10-jlo)10zi =pi= 0 jo p2=.1010p5=10-20=

3、 (2i + l) +it = 0,土 1，土 2,ev = 180ep = i80 + = 0(2)ks+z)52(5+ 10)(5+20)k = k /10=1154 + 30j3 + 200i2 + /t k隹 z = o/tz+l-200 = 0 /t-30=0at = 30 z= 199/30g（5）=5(5 +1)(5 + 3.5)(5 +3+ j2)(s +3-72)g(s) =s(s + 1)(5 + 3 j)(5 + 3 + j2)(s + 3 - ；2)p) = 0 j 0 p2 = 10 p3 =3.50 p4 =321ij + 3.+ j2+ j + 3.-j24d4

4、+ 35j3 + i 5d2 + i46d + 45.5 = 0 j. =-2.4 + j .265 人=-2.4 - jl .265 d =-0.44= (2i+l) +女=0.土1，土2,ev = iso0p=0en = 180- n 600= 180 - 146.45 - 135 - 90 - 75.7 = 93plplp、 p2p3 p4p1 psp6p =l80-,r -“_eoo -edo =180 +146.45 +135 + 90 + 75.7 = -93 pipi p2p4 piai pspiroot locus10111_l12-10-8-4-20real axis? +

5、10.5/ + 43.5? + 79.5? + 45.55 + k. 010.5仞4-79.5仞2 + 尺* =0(ty - 43.5tw + 45.5fy = 0(-2 jo)v2(dx = 6.5136a)2 = 1.0356= 6.5136a)2 = 1.0356k =13o)= 1.0356a)= i .0356g戶+2)s(s+)z(5+2)-z5-z(5+l) = 180(5= (7+ jcoz(a+ ；ft+2)-z(a+ y)-z(t+ ；+l) = 180 0)cl)coarctanarctan = arctan+ 18()2+ aa1 + ax y1+ xyarclan x

6、 - arctan y = arclan(3.35135, =-2.461 + 3.3513 s, =-2.461-;3.35134-12s2(s +，h(s)=2)(5)h(s) = + 2sh(s)p, = (o，yo)仏= (o，;o) p3 = (-2，/o) p4 = (5，yo)root locus-10.8-6-4-202468real axis2 h(j) = 1 + 25g(s)h(s) =k2s+)kg(s+0.5)u+2)(5+ 5) j2(s+2)(5 + 5)s2(s+ 2)(5 + 5) + /fc(5 + 0.5) = 54 + is3 + ioj2 + ks +

7、 o.sk, = 05= jet)仞4-10d/+0.5a =0kr =45.5()k* 53 + 2s2 +3j53 + 252+35+k5+2k = 0p, = 0 jo p2=1 jl.414 p. = i 1.414g(s) =欠(j+10)53 + 3s2 + 2sj3 + 3j2+(k + 2)5+1ok = o丄 _l_1 _1j, = -0.43444=-14.5j + 7+t+j + 2 j + io 2j3 + 33j2 + 6(w + 2o=o4-14g(s) =g(s) =real axis20(5 + 4)(5 + h)30(5+ b)5(5+10)p, = (-2，

8、j4) p: = (-2，-川z,=(-4j0)(s + 4)(5 + /?)+20= j2+45+20 +/;(5+4) = 06(5+4)s: + 4i + 20g-(5)= pb*s2 + 405p! = (0. ；()= (-40, jo)15root locus4-154-29g(5) =(5+l)2(+2)2pi = p2 =(-2j0)zi = z2 = (-1,)0)4-16g(s) =尺(1-45(5+2)29p,=(o,joxp2 = (-2jo)j2-2d-2 = 0j, = - 0.732d2 = 2.732dx = -0.732 d2 = 2.732s(s+2)-ks

9、- 1)=52 + 2s-ks-i) = 0s = -0.732/t =0.5674g(s) =5(5+1)root locus0.6040:j0 2 -044).6 -4).8!1111-1-09-0.8-0741s-0504-0.3-0.2-010real axis2 0kts(s + 1)g(s)h(s) =5(5 + 1)374-19root locusreal axis尺=105* + 6s+ 10 = 00.9483.16pi = p2= (0, jo)，p3 = (-2, jo),p4 = (-4jo)sfxv ajeui6eiu|z,=(1，7o?+6? + 8s2-尺.(s+

10、l = 0a = p, = (o,jo).p, = (-2j0)，p4 = (-4 jo)4-204-31gc(s)k,s k,s2 k,52/(5 + 20)1 gc(s)ktsg(s) =1000_s2 + 105 + lok,s 5+20gs) =10005(5+10+ io/cj(5+2o)?十 3052 + 2(x)5 + 1000+10kz5(+ 20) = 0(j),10kx20)j3 + 3053 + 2005+1001010052 + 105+10/,52 5+20gs) =looo5(5+105+10)(5+20)? + 3052 + 2005 + 1000+ i0kz52(i + 20) = 010k2(5 十 20p + 30? + 200.s.+ i003 g(5)= /cf52/(s+20)10( j+20)10053 + 3()52 + 2(x)5+ 10,52 5+ 20卯）=10005(5: + 10x：(5+305+200)/ + 3052 + 2(x)5 + 1000+ 10kz52 = 0lokts