《控制系統(tǒng)計(jì)算機(jī)仿真》上機(jī)報(bào)告

蘭州理工大學(xué)《控制系統(tǒng)計(jì)算機(jī)仿真》上機(jī)報(bào)告院系: 申,信學(xué)院 班級(jí): 基地二班 姓名: 文志浩 學(xué)號(hào): 08220104 時(shí)間:2011年5月9日電氣工程與信息工程學(xué)院

2-2用MATLAB語(yǔ)言求下列系統(tǒng)的狀態(tài)方程、傳遞函數(shù)、零極點(diǎn)增益和部分分式形式的模型參數(shù),并分別寫(xiě)出其相應(yīng)的數(shù)學(xué)模型表達(dá)式:(い々)- +75-+245+24y=[o254+1053+3552+505+y=[o2*2.25一5-1.25-0.5''4'2.25-4.25-1.25-0.25X+20.25-0.5-1.25一121.25-1.75-0.25-0.750(2)X=?u02]x解:⑴G(s)=_53+752+245+24_

54+1〇53+355解:⑴G(s)=1)傳遞函數(shù)轉(zhuǎn)化為狀態(tài)方程:?num=[7,24,24]num=TOC\o"1-5"\h\z7 24 24?den=[10,35,50,24]den=10 35 50 24?[A,B,C,D]=tf2ss(num,den)A=-3.5000 -5.0000 -2.40001.0000 0 00 1.0000 0B=100c=0.7000 2.4000 2.4000D=0狀態(tài)方程為:2)傳遞函數(shù)轉(zhuǎn)換為零極點(diǎn)增益:?num=[7,24,24]num=7 24 24?den=[10,35,50,24]den=10 35 50 24?[Z,P,K]=tf2zp(num,den)Z=-1.7143+0.6999i-1.7143-0.6999iP=-1.2973+0.9838i-1.2973-0.9838i-0.90530.7000零極點(diǎn)增益方程為:3)傳遞函數(shù)轉(zhuǎn)換為部分分時(shí)形式:?num=[7,24,24]num=7 24 24?den=[10,35,50,24]den=10 35 50 24?[R,P,H]=residue(num,den)R=-0.0071-0.2939i-0.0071+0.2939i0.7141P=-1.2973+0.9838i-1.2973-0.9838i-0.9053H=[]4）部分分式形式為:"2.25 -5-1.25-0.5''42.25-4.25-1.25-0.252(2)X=0.25-0.5-1.25一1X+2?U1.25-1.75-0.25-0.750y=[0202]X解:1）狀態(tài)方程轉(zhuǎn)換為傳遞函數(shù)為:?A=[2.25-5-1.25-0.5225-4.25-1.25-0.25;0.25-0.5-1.25-1;1.25-1.75-0.25-0.75]A=2.2500-5.0000-1.2500-0.50002.2500-4.2500-1.2500-0.25000.2500-0.5000-1.2500-1.00001.2500-1.7500-0.2500-0.7500?B=[4;2;2;〇]B=4220?C=[0202]C=0 2 0 2?D=0D=0?[num,den]=ss2tf(A,B,C,D)num=04.000014.000022.000015.0000den=1.00004.00006.25005.25002.2500傳遞函數(shù)為:2)狀態(tài)方程轉(zhuǎn)換成零極點(diǎn):?A=[2.25-5-1.25-0.5;2.25-4.25-1.25-0.25;0.25-0.5-1.25-1;1.25-1.75-0.25-0.75]A=2.2500-5.0000-1.2500-0.50002.2500-4.2500-1.2500-0.25000.2500-0.5000-1.2500-1.00001.2500-1.7500-0.2500-0.7500?B=[4;2;2;0]B=4220?C=[0202]C=0 2 0 2?D=0D=0?[Z,RK]=ss2zp(A,B,C,D)Z=-1.0000+1.2247i-1.0000-1.2247i-1.5000P=-0.5000+0.8660i-0.5000-0.8660i-1.5000-1.5000K=4.0000零極點(diǎn)增益方程為:3)轉(zhuǎn)換成部分分式形式:?num=[04142215]num=0 4 14 22 15?den=[l46.255.252.25]den=1.0000 4.0000 6.2500 5.2500 2.2500?[RPH]=residue(num,den)4.0000-0.0000-0.0000-2.3094i-0.0000+2.3094iP=-1.5000-1.5000-0.5000+0.8660i-0.5000-0.8660iH=[]部分分式形式的方程為:2-3用毆拉法求下列系統(tǒng)的輸出響應(yīng)y(。在04,W1上,厶=0.1時(shí)的數(shù)值解。y=-2y,y(0)=1要求保留4位小數(shù),并將結(jié)果以圖形的方式與真解y(r)=e-”比較。t=0:0.1:l;h=0.1;y(1)=1；fori=l：10y(i+1)=y(i)+h*(-2*y(i))；endplot(t,y,*r')holdonm=exp(-2*t)plot(t,m,?bo')2-5用四階龍格一庫(kù)塔梯形法求解2-3的數(shù)值解,并通過(guò)與真值及毆拉法的比較,分析其精度。h=0.1；fori=l：10kl=-2*y(i)k2=-2*(y(i)+kl*h/2)k3=-2*(y(i)+k2*h/2)k4=-2*(y(i)+h*k3)y(i+1)=y(i)+(kl+2*k2+2*k3+k4)*h/6endplot(t,y,?o1)holdonm=exp(-2*t)plot(t,m,,r*')lea=y-mplot(t,lea,1g')holdoff4-2設(shè)典型閉環(huán)結(jié)構(gòu)控制系統(tǒng)如下圖所示,當(dāng)階躍輸入幅值/?=20時(shí),用sp4_l.m求取輸出y(t)的響應(yīng)。解K=：La=[154204.2213.863.5];b=[18750001562000];X0=[0,0,0,01;V=0.002;n=4；T0=0;Tf=10;h=0.01;R=20;b=b/a(1)；a=a/a(1)；A=a(2：n+l)；A=[rot90(rot90(eye(n-1,n)))；-fliplr(A)];B=[zeros(1,n-1),1]'；ml=length(b)；C=[fliplr(b),zeros(l,n-ml)]；Ab=A-B*C*V;X=X0'；y=0；t=T0;N=round((Tf-TO)/h);fori=l：NKl=Ab*X+B*R;K2=Ab*(X+h*Kl/2)+B*R;K3=Ab*(X+h*K2/2)+B*R;K4=Ab*(X+h*K3)+B*R;X=X+h*(K1+2*K2+2*K3+K4)/6;y=[y,c*x];t=[t,t(i)+h];end[t?,y']plot(t,y)

4-5下圖中,若各環(huán)節(jié)傳遞函數(shù)已知為:G（s）=]4-5下圖中,若各環(huán)節(jié)傳遞函數(shù)已知為:G（s）=]1+0.015G[(s)=1+0.155 0.21 0.1 「（ヽG式s）=繭ナ'G，（s）=時(shí)7，G5（s）=雨而，G6（5）=1+0.1750.08550.0044/ロ ,[旦1+0.015G7（5）=0.212；試列寫(xiě)鏈接矩陣W、w。和非零元素陣Wu,將程序sp4一2完善后,應(yīng)用此程序求輸出九的響應(yīng)曲線(xiàn)。解:解:P=[1,0.01,1,0;0,0.085,1,0.17;0,0.051,1,0.15;1,0.15,0.21,0;1,0.01,0.1,0;l,0.01,0.0044,0];W=[000000;10000-l;0100-10/001-0.21200/000100/000100]/W0=[l/0/0/0/0/0]/n=6/Y0=l/Yt0=[000000]/h=0.01/Ll=10/T0=0/Tf=20/nout=4/A=diag(P(:,1))/B=diag(P(:,2));C=diag(P(：,3))/D=diag(P(:,4))；Q=B-D*W/Qn=inv(Q)/R=C*W-A/V1=C*WO/Ab=Qn*R/bl=Qn*Vl/Y=YtO'/y=Y(nout)/t=T0/N=round(Tf-TO)/(h*Ll)/fori=l：Nforj=1:LI/Kl=Ab*Y+bl*Y0K2=Ab*(Y+h*Kl/2)+bl*Y0K3=Ab*(Y+h*K2/2)+bl*Y0K4=Ab*(Y+h*K3)+bl*Y0Y=Y+h*(K1+2*K2+2*K3+K4)/6/endy=[y,Y(nout)]/t=[t,t(i)+h*Ll]/end[f,y']plot(t,y)4-7用離散相似法仿真程序sp4_3.m重求上題輸出H的數(shù)據(jù)與曲線(xiàn),并與四階龍格一庫(kù)塔法比較精度。P=[1,0.01,1,0;0,0.085,1,0.17;0,0.051,1,0.15;1,0.15,0.21,0;1,0.01z0.1,0;1,0.01,0.0044,0];W=[000000;10000-1;0100-10;001-0.21200;000100;000100];W0=[l;0;0;0;0;0];n=6;Y0=l;Yt0=[000000];h=0.01；Ll=10;T0=0;Tf=40;nout=5；A=diag(P(：,1))；B=diag(P(：,2))；C=diag(P(：,3))；D=diag(P(：,4))；fori=l：6if(A(i,i)==0);FI(i,i)=l;FIM(i,i)=h*C(i,i)/B(i,i)；FIJ(i,i)=h*h*C(i,i)/B(i,i)/2；FIC(i,i)=l;FID(i,i)=0;if(D(i,i)=0)；FID(i,i)=D(i,i)/B(i,i)；elseendelseFI(i,i)=exp(-h*A(i,i)/B(izi))；FIM(i,i)=(l-FI(iri))*C(i,i)/A(i,i);FIJ(i,i)=h*C(i,i)/A(i/i)-FIM(i,i)*B(i,i)/A(i,i)；FIC(i,i)=l;FID(i,i)=0；if(D(i,i)-=0);F1C(i,i)=C(i,i)/D(i,i)-A(i,i)/B(i,i);FlD(i/i)=D(i,i)/B(i,i)；elseendendendY=zeros(6,1)；X=Y；y=0；Uk=zeros(6,1)；Ub=Uk；t=T0:h*Ll:Tf;N=length(t);fork=l：N-1for1=1：LIUb=Uk;Uk=W*Y+W0*Y0;Udot=(Uk-Ub)/h；Uf=2*Uk-Ub;X=FI'*X+FIM'*Uk+FIJ?*Udot;Y=FIC'*X+FID'*Uf;endy=[y,Y(nout)]；endplot(t,y,'r*1)holdonQ=B-D*W;Qn=inv(Q);R=C*W-A;V1=C*WO；Ab=Qn*R；bl=Qn*Vl;Y=YtO'；y=Y(nout);t=T0；N=round(Tf-T0)/(h*Ll);fori=l：Nforj=1：LI;Kl=Ab*Y+bl*Y0K2=Ab*(Y+h*Kl/2)+bl*Y0K3=Ab*(Y+h*K2/2)+bl*Y0K4=Ab*(Y+h*K3)+bl*Y0Y=Y+h*(K1+2*K2+2*K3+K4)/6;endy=[y,Y(nout)]；t=[t,t(i)+h*Ll]；end[f,y']plot(t,y)P=[1,0.01,1,0;〇,0.085,1,0.17;。,0.051,1,0.15;1,〇.:15,0.21,0;!,0.01,0.1,0;l,0.01,0.0044,0];W=[000000/10000-1;0100-10/001-0.21200;000100;000100];W0=[l;0;0;0;0;0];n=6;Y0=l;YtO=[000000];h=0.01;Ll=10;T0=0;Tf=40;nout=5;A=diag(P(：,1))；B=diag(P(：,2))；C=diag(P(:,3))；D=diag(P(:,4));fori=l：6if(A(i,i)==0);FI(i,i)=l;FIM(i,i)=h*C(i,i)/B(i,i)；FIJ(i,i)=h*h*C(i,i)/B(i,i)/2；FIC(i,i)=l;FID(i,i)=0;if(D(i,i)=0)；FID(i,i)=D(i,i)/B(i,i);elseendelseFI(i,i)=exp(-h*A(i,i)/B(i,i));FIM(i,i)=(l-FI(i,i))*C(i,i)/A(i,i)；FIJ(i,i)=h*C(i,i)/A(i,i)-FIM(i,i)*B(i,i)/A(i,i);FIC(i,i)=l;FID(i,i)=0；if(D(i,i)?=0);FIC(i,i)=C(i,i)/D(i,i)-A(i,i)/B(i,i)；FID(i,i)=D(i,i)/B(i,i);elseendendendY=zeros(6,1)；X=Y；y=0；Uk=zeros(6,1)；Ub=Uk；t=T0：h*Ll：Tf；N=length(t)；fork=l：N-1for1=1：LIUb=Uk；Uk=W*Y+WO*YO;Udot=(Uk-Ub)/h；Uf=2*Uk-Ub;X=FI'*X+FIM'*Uk+FIJ1*Udot;Y=FIC*X+FID'*Uf;endy=[y,Y(nout)]；endplot(t,y,'r*')holdonQ=B-D*W;Qn=inv(Q);R=C*W-A;V1=C*WO;Ab=Qn*R；bl=Qn*Vl；Y=YtO'；y=Y(nout);t=T0；N=round(Tf-TO)/(h*Ll)；fori=l：Nforj=1:LI;Kl=Ab*Y+bl*YOK2=Ab*(Y+h*Kl/2)+bl*Y0K3=Ab*(Y+h*K2/2)+bl*Y0K4=Ab*(Y+h*K3)+bl*Y0Y=Y+h*(K1+2*K2+2*K3+K4)/6;endy=[y,Y(nout)]；t=[t,t(i)+h*Ll]；endIt',y']plot(t,y)

4-8求下圖非線(xiàn)性系統(tǒng)的輸出響應(yīng)y(t),并與無(wú)非線(xiàn)性環(huán)節(jié)情況進(jìn)行比較。r(t)=10r(t)=10%filename：satu.mfunctionUc=satu(Ur#SI)if(abs(Ur)>=S1)if(Ur>0)Uc=Sl;elseUc=-Sl；endelseUc=Ur；end%filename：dead.mfunctionUc=dead(Ur,SI)if(abs(Ur)>=S1if(Ur>0)Uc=Ur-Sl；elseUc=Ur+Sl；endelseUc=0；end%filename：bcaklash.mfunction[Uc,Ubb]=backlash(Urb,Ur,Ucb,SI)if(Ur>Urb)if((Ur-Sl)>=Ucb)Uc=Ur-Sl；elseUc=Ucb；endelseif(Ur<Urb)if((Ur+Sl)<=Ucb)Uc=Ur+Sl;elseUc=Ucb；endendUbb=Ur；P=[0.110.5l;01200;2110;10110]WIJ=[101;14-1;211;321;431]Z=[0000];S=[0000];h=0.01;Ll=30;n=4；T0=0;Tf=20;nout=4；Y0=10;sp4_4;plot(t*g.?)holdonZ=[4000]；S=[5000];sp4_4;plot(try,'r*)%filename：sp4_4.mA=diag(P(：,1))；B=diag(P(：,2))；C=diag(P(：,3))；D=diag(P(：,4))；m=length(WIJ(：,1))；W0=zeros(n,1)；W=zeros(n,n)；fork=l：mif(WIJ(k,2)==0);W0(WIJ(k,1))=WIJ(k,3);elseW(WIJ(k,l)rWIJ(k,2))=WIJ(k/3)；end；end；fori=l：nif(A(i,i)==O)；FIM(i,i)=h*C(i,i)/B(i,i);FIJ(i,i)=h*h*C(i,i)/B(i,i)/2；FIC(i,i)=l;FID(i,i)=0;if(D(i,i)~=0);FID(i,i)=D(i,i)/B(i,i)；elseendelseFI(i,i)=exp(-h*A(i,i)/B(i,