东北大学 自动化 控制系统计算机辅助设计实验18744.docx

《东北大学 自动化 控制系统计算机辅助设计实验18744.docx》由会员分享，可在线阅读，更多相关《东北大学 自动化 控制系统计算机辅助设计实验18744.docx（39页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、 控制系统计算机辅助设计东北大学11控制系统计算机辅助设计_x2014_x2014_MATLAB语言与应用控制系统计算机辅助设计第一部分1 functioon dx=lorennzeq(tt,x)dx=-x(2)-x(3);x(1)+0.2*x(22);0.2+(x(1)-5.7)*x(3); x0=0;0;00; t,yy=odee45(llorenzzeq,0,1000,x0); plott(t,y) figuure;pllot3(yy(:,1),y(:,2),y(:,3),gridd,2functioon y,yeq=f2a(x)yeq=;y=4*x(11)2+xx(2)22-4; Ae

2、q=;Beeq=;A=;B=; xm=0;0; xM=;x0=0;0; f1=iinlinee(x(11)2-22*x(1)+x(2); x,ff=fmiincon(f1,x00,A,B,Aeq,BBeq,xmm,xM,f2a);xx,fans = 1.00000 0f =-13（a） s=tff(s);G=(ss3+4*s+2)/s3/(s2+22)/(ss2+1)3+2*s+5Transfeer funnctionn: s3 + 44 s + 2-s11 + 5 s99 + 9 s7 + 2 s6 + 112 s55 + 4 s4 + 12 ss3（b） z=tff(z,0.1); H=(

3、zz2+0.568)/(z-1)/(z22-0.2*z+0.999)Transfeer funnctionn: z22 + 0.568-z3 - 11.2 z2 + 11.19 zz - 0.99Samplinng timme: 0.14 A=00 1 0;0 0 11;-5 -4 -133; B=00;0;2; C=11 0 0;0 0 00;0 0 0; D=00; G=sss(A,B,C,D); Ga = x1 x2 x3 x1 0 1 0 x2 0 0 1 x3 -5 -4 -13b = u1 x1 0 x2 0 x3 2c = x1 xx2 x33 y1 1 0 00 y2 0 0

4、00 y3 0 0 00d = u1 y1 0 y2 0 y3 0Continuuous-ttime mmodel. G=tff(G)Transfeer funnctionn fromm inpuut to outpuut. 22 #1: - ss3 + 13 s2 + 44 s + 5 #2: 00 #3: 00 GG=zzpk(G)Zero/poole/gaain frrom innput tto outtput. 2 #1: - (s+12.72) (s2 + 0.28836s + 0.39932) #2: 00 #3: 00根据微分方程也也可以直接写写出传递函数数模型： num=2;

5、den=1,133,4,5; G=tff(num,den); GTransfeer funnctionn: 2-s3 + 113 s22 + 4 s + 55 GG=zzpk(G)Zero/poole/gaain: 22-(s+12.772) (ss2 + 0.28336s + 0.39332)5 num=1,2; den=1,1,0.16; H=tff(num,den,Ts,11); HTransfeer funnctionn: z + 2-z2 + zz + 0.16Samplinng timme: 16functioon H=ffeedbaack(G11,G2,kkey)if nargg

6、in=22;key=-1;ennd,H=GG1/(syym(1)-key*GG1*G2);H=siimple(H); symms J KKp Ki s; gc=(Kp*s+Ki)/ss; g=(ss+1)/(J*s22+2*s+5); gg=ffeedbaack(g*gc,1) gg=ffeedbaack(g*gc,1)gg =(Ki + Kp*s)*(s + 1)/(J*s3 + (Kp + 2)*s2 + (Ki + Kp + 5)*s + Ki)7（a） s=tff(s); G=(2211.877*s+3117.64)/(s+220)/(ss+94.334)/(ss+0.16684);

7、Gc=(169.66*s+4000)/s/(s+4); Hs=11/(0.001*s+11); GG=ffeedbaack(G*Gc,Hss)Transfeer funnctionn: 359.3 s33 + 3.732e0004 s2 + 11.399ee005 ss + 1227056-0.01 s6 + 22.185 s5 + 142.1 s44 + 24444 s3 + 44.389ee004 ss2 + 1.399e0005 s + 1277056 zpk(GG)Zero/poole/gaain: 359333.1522 (s+1100) (s+2.3358) (s+1.4499)-

8、(s2 + 3.6667s + 3.5011) (s2 + 11.733s + 3339.1) (s22 + 2203.1ss + 1.07e0004)（b） z=tff(z); G=(335786.7*z-1+1088444)/(z-1+4)*(z-11+20)*(z-11+74.004); Gc=11/(z-1-1); H=1/(0.5*z-1-1); GG=ffeedbaack(G*Gc,H)Transfeer funnctionn: -1084444 z66 + 1.844e0004 z5 + 11.789ee004 zz4-1.144e0005 z6 + 22.876ee004 zz

9、5 + 274.22 z4 + 7822.4 z3 + 447.52 z2 + 0.5 z Samplinng timme: unnspeciified zpk(GG)Zero/poole/gaain: -0.948821 z4 (z-0.5) (z+0.33)-z (z+0.3035) (z+00.044338) (zz+0.011355) (z2 - 0.11z + 0.022396)Samplinng timme: unnspeciified8 s=tff(s);c1=feeddback(1/(s+1)*s/(s2+2),(44*s+2)/(s+11)2);c2=feeddback(1/

10、s22,50);G=feedbback(cc1*c2,(s2+2)/(ss3+144)Transfeer funnctionn: s66 + 2 s5 + s4 + 14 s3 + 28 ss2 + 14 s-s10 + 3 s99 + 555 s8 + 1755 s7 + 3000 s6 + 13223 s55 + 26656 s4 + 33715 ss3 + 77732 s2 + 55602 ss + 14400 9 s=tff(s); G=(ss+1)22*(s22+2*s+400)/(s+5)2/(ss2+3*s+1000)/(s2+3*ss+25000); G1=cc2d(G,0.0

11、1)Transfeer funnctionn:4.716e-005 zz5 - 0.00001396 z4 + 9.5996e-0005 z33 + 8.18e -0005 z2 - 00.00011289 zz + 4.355e-005 -z6 - 55.592 z5 + 13.226 z44 - 177.06 zz3 + 12.588 z2 - 5.0032 z + 0.88521Samplinng timme: 0.01step(G1) G2=cc2d(G,0.1)Transfeer funnctionn:0.00039982 z5 - 00.00033919 zz4 - 0.00003

12、36 zz3 + 0.00007842 z2 - 0.0000766 z + 00.00033214-z6 - 22.644 z5 + 4.0444 z44 - 3.94 z3 + 22.549 z2 - 1.0556 z + 0.22019Samplinng timme: 0.1step(G2) G3=cc2d(G,1)Transfeer funnctionn:8.625e-005 zz5 - 4.48ee-005 z4 + 6.5445e-0006 z33 + 1.211e-005 zz2 - 3.299e-006 zz + 1.011e-007-z6 - 00.04199 z5 - 0.

13、007092 z4 - 0.000045499 z3 + 0.00024955 z2 - 3.347e-005 zz + 1.125e-007 Samplinng timme: 1 stepp(G3)10（a） G=1/(s3+2*s22+s+2);pzmapp(G)系统极点均在虚虚轴左侧，系系统稳定（b） G=1/(6*s4+3*ss3+2*s2+ss+1); pzmaap(G)系统极点在虚轴轴右侧侧，系系统不稳定（c） G=1/(s4+s3-33*s2-s+2); pzmaap(G)系统极点在虚轴轴右侧侧，系系统不稳定11（a） z=tff(z,0.1); H=(-3*z+22)/(z3-

14、0.22*z2-0.25*z+0.005); pzmaap(H)系统所有极点均均在单位圆内内，所以系统统稳定（b） z=tff(z,0.1); H=(33*z2-0.39*z-0.009)/(zz4-1.7*z33+1.044*z2+0.2688*z+0.024); pzmaap(H)系统所有极点不不全单位圆内内，所以系统统不稳定12 A=-0.2 00.5 0 0 0;00 -0.55 1.6 0 0;00 0 -114.3 885.8 00;0 0 0 -333.3 1000;0 00 0 0 -10; B=00;0;0;0;30; C=00 0 0 0 0; G=sss(A,B,C,0)

15、a = x11 x2 x3 xx4 x5 x1 -0.22 00.5 0 0 0 x2 00 -00.5 1.6 0 0 x3 00 0 -14.3 85.8 0 x4 00 0 0 -33.3 100 x5 00 0 0 0 -10b = u1 x1 0 x2 0 x3 0 x4 0 x5 30c = x1 xx2 x33 x4 x5 y1 0 0 00 0 0d = u1 y1 0Continuuous-ttime mmodel. pzmaap(G)系统所有极点均均在虚轴左侧侧，所以系统统稳定或 eig(G)ans = -0.22000 -0.55000 -14.33000 -33.330

16、00 -10.00000极点均在左半轴轴，所以系统统稳定13数值解： f=(t,x)-5*xx(1)+22*x(2);-4*xx(2);-3*x(11)+2*xx(2)-44*x(3)-x(4);-3*xx(1)+22*x(2)-4*x(4); t_fiinal=110; x0=1 2 00 0; t,xx=odee45(f,0,t_finall,x0); plott(t,x)解析解functioon Gaa,Xa=ss_auugmentt(G,ccc,dd,XX)G=ss(G);Aa=GG.a;Caa=G.c;Xa=X;Ba=G.b;D=GG.d;if (lenngth(ddd)0&sum(

17、aabs(ddd)1e-5), if (abs(dd(4)1e-5), Aa=Aa ddd(2)*BBa,dd(3)*Baa;. zeross(2,leength(Aa),dd(11),-ddd(4);ddd(4),dd(1); Ca=Ca ddd(2)*DD dd(33)*D;Xa=XXa;1;00;Ba=Ba;00;0; elsse, Aa=Aa ddd(2)*BB;zeroos(1,llengthh(Aa) dd(11); Ca=Ca ddd(2)*DD;Xa=Xa;11;Ba=B;0; enddendif (lenngth(ccc)0&sum(aabs(ccc)1ee-5),MM=le

18、nggth(ccc); Aa=Aa BBa zerros(leength(Aa),MM-1);zzeros(M-1,llengthh(Aa)+1). eye(M-1);zeross(1,leength(Aa)+MM); Ca=Ca DD zeroos(1,MM-1);Xa=XXa;cc(1);iii=1; forr i=2:M,ii=ii*i;Xa(leength(Aa)+ii)=cc(i)*iii; endd,endGa=ss(AAa,zerros(siize(Caa),CCa,D); cc=2;ddd=-3,0,2,22;x0=1;2;0;1; A=-5,2,00,0;0,-4,0,0;-

19、3,2,-4,-1;-33,2,0,-4;BB=0;00;0;1;C=22 1 0 0;D=0; G=sss(A,B,C,D); Ga,xx0=ss_auugmentt(G,ccc,dd,xx0);Gaa.a,xxx0ans = -5 22 0 0 0 0 00 0 -44 0 0 0 0 00 -3 22 -4 -1 0 0 00 -3 22 0 -4 0 2 11 0 00 0 0 -3 -2 00 0 00 0 0 2 -3 00 0 00 0 0 0 0 00ans = 1 22 0 1 1 0 22 symss t;y=Ga.c*expm(Ga.a*t)*xxx0; lateex(y

20、); lattex(y)ans =-6,e-5,t+110,ee-4,t14（a） s=tff(s); g=(ss+6)*(s-6)/s/(s+3)/(ss+4+4ii)/(s+4-4i); rloccus(g)（b） s=tff(s); G=(ss2+2*s+2)/(s4+s3+114*s22+8*s); rloccus(G)K s=tff(s); G=(ss-1)/(s+1)5; G.iooDelayy=2Transfeer funnctionn: s - 1exp(-2*s) * - s5 + 5 s4 + 110 s33 + 100 s2 + 5 s + 1 rloocus(ppade

21、(GG,2)16（a） s=tff(s); G=8*(s+1)/s2/(s+155)/(s2+6*ss+10); nyquuist(GG), nyquuist(GG),griid bodee(G) figuure;niicholss(G),ggrid gm,pm,wgg,wp=margiin(G)gm = 30.44686pm = 4.22340wg = 1.55811wp =0.2336 GG=ffeedbaack(G,1)Transfeer funnctionn: 8 s + 8-s5 + 221 s44 + 1000 s33 + 1550 s22 + 8 s + 88 pzmaap(GG

22、)通过以上的分析析，可以看出出该系统是稳稳定的。采用阶跃响应进进行验证如下下图： pzmaap(GG) stepp(GG)（b） Z=-1.31;-0.0554;0.9957; P=00;1;0.368;00.99; G=zppk(Z,PP,0.455,Ts,0.1)Zero/poole/gaain:0.45 (zz+1.311) (z-0.9577) (z+0.0544)- z (zz-1) (z-0.999) (zz-0.3668)Samplinng timme: 0.1 nyquuist(GG);griid bodee(G) nichhols(GG),griid gm,pm,wgg,wp

23、=margiin(G)gm = 0.99578pm = -1.77660wg = 10.44641wp = 10.77340 GG=ffeedbaack(G,1); pzmaap(GG) stepp(GG)17 z=-2.5;p=0;-0.5;-50; G=zppk(z,pp,100/2.5*00.5*500); z=-1;-2.5;p=-0.55;-50Gc=zppk(z,pp,10000); GG=ffeedbaack(G*Gc,1) Zero/poole/gaain: 100000000 (s+11) (s+2.5)2-(s+1) (s2 + 4.999s + 66.239) (s22

24、+ 955.01s + 1.0002e0006) bodee(GG)通过bode图图可以看出该该系统是稳定定的。验证如下： stepp(GG)第二部分2 Y=dssolve(D4y+5*D3yy+6*D22y+4*DDy+2*yy=exp(-3*t)+exp(-5*t)*sin(4*t+ppi/3),.)y(0)=11,Dyy(0)=11/2,D2y(00)=1/22,D33y(0)=0.2); lateex(Y)3Simulinnk仿真图形形：系统输出曲线：系统误差曲线：4x1(t)=ssin(x22(t)*eexp(-22.3*x44(t)x2(t)=xx1(t)x3=sin(x2*exx

25、p(-2.3*x4)x4=x35Simulinnk仿真图形形：阶跃响应曲线：6 s=tff(s);g=2100*(s+11.5)/(s+1.75)*(s+16)*(s+11.5+3*j)*(ss+1.5-3*j); gc=552.5*(s+1.55)/(s+14.866); stepp(feeddback(g,1) stepp(feeddback(g*gc,1)通过两个图比较较可以看出，原原系统超调量量过大，震荡荡严重，加入入控制器后，系系统变得不稳稳定。7 A=00 1 0 0;0 00 1 0;-3 1 2 3;22 1 0 0; B=11 0;2 1;3 22;4 3; Q=diiag(

26、11,2,3,4); R=eyye(2); K,SS=lqrr(A,B,Q,R)K = -0.00978 1.22118 1.88767 0.77871 -3.88819 -0.44668 2.66713 1.00320S = 5.44400 0.66152 -2.33163 0.00452 0.66152 1.88354 -0.00138 -0.77582 -2.33163 -0.00138 1.99214 -0.33859 0.00452 -0.77582 -0.33859 0.88540 eig(A-B*KK)ans = -12.25563 -1.67786 + 0.99881i -1.

27、67786 - 0.99881i -1.46627 stepp(ss(AA-B*K,B,eyee(4),zzeros(4,2)8 A=-0.2 00.5 0 0 0;00 -0.55 1.6 0 0;00 0 -114.3 885.8 00;0 0 0 -333.3 1000;0 00 0 0 -10; B=00;0;0;0;30; C=11 0 0 0 0; D=0; G=sss(A,B,C,D); polee(G)ans = -0.22000 -0.55000 -14.33000 -33.33000 -10.00000 zeroo(G)ans = Emptty mattrix: 0-by-1 P=-1 -2 -3 -44 -5; K=pllace(AA,B,P)K = Colummns 1 throuugh 4 0.00004 0.00004 -0.00035 0.33946 Colummn 5 -1.44433 eig(A-B*KK)ans = -5.00000 -4.00000 -3.00000 -2.00000 -1.000009 openn_systtem(siimulinnk)PID控制参数数如下：0.407225 0.199096 0.219866 7.93997 0.90111 78.2337738