例1
%绘图
subplot(2,2,1);
t=0:0.01:2;y=sin(2*pi*t);plot(t,y); subplot(2,2,2); t=0:0.01:2;plot(t,exp(-t),t,exp(-2*t),t,exp(-3*t)); axis([0 2 -0.2 1.2])
subplot(2,2,3); x=[0 1 1 1 2 2 2 3 4];y=[0 0 1 2 2 1 0 0 0]; plot(x,y);axis([0 4 -0.5 3]) subplot(2,2,4); x=0:0.01:2*pi;plot(sin(x),cos(x)); axis([-1.2 1.2 -1.2 1.2]);axis equal
例2-17
num1=[10];den1=[1 1];num2=[1];den2=[2 0.5];num3=[540];den3=[1]; >> num4=[0.1];den4=[1];[na,da]=series(num1,den1,num2,den2);
[nb,db]=feedback(na,da,num4,den4,-1);[nc,dc]=series(num3,den3,nb,db); [num,den]=cloop(nc,dc,-1);printsys(num,den)
例3-1
r=2;numo=8;deno=[1,3,0];numh=1;denh=1;
[num,den]=feedback(numo,deno,numh,denh);[A,b,C,d]=tf2ss(num,den); Tf=input('Tf=');h=input('h='); x=[zeros(length(A),1)];y=0;t=0; for i=1:Tf/h K1=A*x+b*r;
K2=A*(x+h*K1/2)+b*r; K3=A*(x+h*K2/2)+b*r; K4=A*(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 plot(t,y)
例4-1
R=10;P=[0.1 1 0.5 1 1 1;0 1 1 0 0 0;2 1 2 0 0 0;10 1 10 0 0 0]; W=[0 0 0 -1;1 0 0 0;0 1 0 0;0 0 1 0]; W0=[1;0;0;0];Wc=[0 0 0 1];
Tf\\input('仿真时间Tf=');T=input('计算步长h=');
A=P(:,1);B=P(:,2);C=P(:,3);D=P(:,4);FZ=P(:,5);S=P(:,6); n=length(A); for i=1:n if(A(i)~=0) if(B(i)==0)
E(i)=0;F(i)=0;G(i)=0;H(i)=0;
L(i)=(C(i)+D(i)/T)/A(i);Q(i)=-D(i)/(A(i)*T); else
E(i)=exp(-A(i)*T/B(i));
F(i)=(D(i)/B(i)-C(i)/A(i))*((1-E(i))*B(i)/(A(i)*T)-1);
G(i)=(D(i)/B(i)-C(i)/A(i))*(1+(E(i)-1)*(1+B(i)/(A(i)*T))); H(i)=1;L(i)=D(i)/B(i);Q(i)=0; end else
if(B(i)~=0)
E(i)=1;F(i)=0.5*C(i)*T/B(i);G(i)=F(i); H(i)=1;L(i)=D(i)/B(i);Q(i)=0; else
disp('A(i)=B(i)=0'); end end end
x=[zeros(length(A),1)];x0=x;z=x; u=[zeros(length(A),1)];u0=u; y=[zeros(length(Wc(:,1)),1)];t=0; for j=1:Tf/T
u1=u;u=W*x+W0*R; for i=i:n if(FZ(i)~=0)
if(FZ(i)==1) u(i)=saturation(u(i),S(i));end if(FZ(i)==2) u(i)=deadzone(u(i),S(i));end
if(FZ(i)==3) [u(i),u0(i)]=backlash(u0(i),u(i),u1(i),S(i));end if(FZ(i)==4) u(i)=sign1(u(i),S(i));end end end x1=x; for i=1:n
z(i)=E(i)*z(i)+F(i)*u(i)+G(i)*u1(i);
x(i)=H(i)*z(i)+L(i)*u(i)+Q(i)*u1(i); end
for i=1:n if(FZ(i)~=0)
if(FZ(i)==5) x(i)=saturation(x(i),S(i));end if(FZ(i)==6) x(i)=deadzone(x(i),S(i));end
if(FZ(i)==7) [x(i),x0(i)]=backlash(x0(i),x(i),x1(i),S(i));end if(FZ(i)==8) x(i)=sign1(x(i),S(i));end end end
y=[y,Wc*x];t=[t,t(j)+T]; end plot(t,y)
例5-1 有问题注意
R=1;
Gr=[2.72 -1];Fr=[0.717]; P=[0 1 1 0 0 0;1 1 1 0 0 0];
W=[0 0;1 0];W0=[1;0];Wc=[0 1];
Tf=input('仿真时间Tf=');Tm=input('采样周期Tm=');T=input('计算步长h='); A=P(:,1);B=P(:,2);C=P(:,3);D=P(:,4);FZ=P(:,5);S=P(:,6); n=length(A);n1=length(Fr);m1=length(Gr); for i=1:n if(A(i)~=0) if(B(i)==0)
E(i)=0;F(i)=0;G(i)=0;H(i)=0;
L(i)=(C(i)+D(i)/T)/A(i);Q(i)=-D(i)/(A(i)*T); else
E(i)=exp(-A(i)*T/B(i));
F(i)=(D(i)/B(i)-C(i)/A(i))*((1-E(i))*B(i)/(A(i)*T)-1);
G(i)=(D(i)/B(i)-C(i)/A(i))*(1+(E(i)-1)*(1+B(i)/(A(i)*T))); H(i)=1;L(i)=D(i)/B(i);Q(i)=0; end else
if(B(i)~=0)
E(i)=1;F(i)=0.5*C(i)*T/B(i);G(i)=F(i); H(i)=1;L(i)=D(i)/B(i);Q(i)=0; else
disp('A(i)=B(i)=0'); end end end
x=[zeros(length(A),1)];x0=x;z=x; u=[zeros(length(A),1)];u0=u; y=[zeros(length(Wc(:,1)),1)];
t=0;Ur=[zeros(n1,1)];Er=[zeros(m1,1)]; for ij=0:Tf/Tm;
e=R-x(n);Er=[e;Er(1:m1-1)];
ur=-Fr*Ur+Gr*Er;Ur=[ur;Ur(1:n1-1)]; for j=1:Tm/T
u1=u;u=W*x+W0*ur; for i=i:n if(FZ(i)~=0)
if(FZ(i)==1) u(i)=saturation(u(i),S(i));end if(FZ(i)==2) u(i)=deadzone(u(i),S(i));end
if(FZ(i)==3) [u(i),u0(i)]=backlash(u0(i),u(i),u1(i),S(i));end if(FZ(i)==4) u(i)=sign1(u(i),S(i));end end end x1=x; for i=1:n
z(i)=E(i)*z(i)+F(i)*u(i)+G(i)*u1(i); x(i)=H(i)*z(i)+L(i)*u(i)+Q(i)*u1(i); end
for i=1:n if(FZ(i)~=0)
if(FZ(i)==5) x(i)=saturation(x(i),S(i));end if(FZ(i)==6) x(i)=deadzone(x(i),S(i));end
if(FZ(i)==7) [x(i),x0(i)]=backlash(x0(i),x(i),x1(i),S(i));end if(FZ(i)==8) x(i)=sign1(x(i),S(i));end end end
y=[y,Wc*x];t=[t,t(j)+T]; end plot(t,y)
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