lecture4 - % % B747 longitudinal dynamics % AA271a % B747...

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% % B747 longitudinal dynamics % AA271a % B747 at Mach 0.8, 40,000ft, level-flight % From Etkin and Reid page 166 % if 1 % metric Xu=-1.982e3;Xw=4.025e3; Zu=-2.595e4;Zw=-9.030e4;Zq=-4.524e5;Zwd=1.909e3; Mu=1.593e4;Mw=-1.563e5;Mq=-1.521e7;Mwd=-1.702e4; g=9.81;theta0=0;S=511;cbar=8.324; U0=235.9;Iyy=.449e8;m=2.83176e6/g;cbar=8.324;rho=0.3045; Xdp=.3*m*g;Zdp=0;Mdp=0; Xde=-3.818e-6*(1/2*rho*U0^2*S);Zde=-0.3648*(1/2*rho*U0^2*S); Mde=-1.444*(1/2*rho*U0^2*S*cbar); else %english Xu=-1.358e2;Xw=2.758e2;cbar=27.31; Zu=-1.778e3;Zw=-6.188e3;Zq=-1.017e5;Zwd=1.308e2; Mu=3.581e3;Mw=-3.515e4;Mq=-1.122e7;Mwd=-3.826e3; g=32.2;U0=774;Iyy=.331e8;m=636636/g;cbar=27.31;rho=0.0005909; theta0=0;S=5500; Xdp=.3*m*g;Zdp=0;Mdp=0; Xde=-3.818e-6*(1/2*rho*U0^2*S);Zde=-0.3648*(1/2*rho*U0^2*S); Mde=-1.444*(1/2*rho*U0^2*S*cbar); end A=[Xu/m Xw/m 0 -g*cos(theta0);[Zu Zw Zq+m*U0 -m*g*sin(theta0)]/(m-Zwd); [Mu+Zu*Mwd/(m-Zwd) Mw+Zw*Mwd/(m-Zwd) Mq+(Zq+m*U0)*Mwd/(m-Zwd) . .. -m*g*sin(theta0)*Mwd/(m-Zwd)]/Iyy; [ 0 0 1 0]]; B=[Xde/m Xdp/m;Zde/(m-Zwd) Zdp/(m-Zwd);(Mde+Zde*Mwd/(m-Zwd))/Iyy . .. (Mdp+Zdp*Mwd/(m-Zwd))/Iyy;0 0]; C=[eye(3,4)]; wsp=sqrt(-U0*Mw/Iyy) zetasp=-Mq/2*sqrt(-1/U0/Mw/Iyy) wsp=sqrt(Zw*Mq/m/Iyy-U0*Mw/Iyy) zetasp=-(Zw/m+Mq/Iyy+Mwd/Iyy*U0)/2/wsp [V,ev]=eig(A);ev=diag(ev);D=V; %rifd(ev) % nondimensionalization of the eigenvetors V(1,:)=V(1,:)/U0; V(2,:)=V(2,:)/U0; V(3,:)=V(3,:)/(2*U0/cbar); for i=1:4 V(:,i)=V(:,i)/V(4,i); end figure(3) subplot(221) polar(phase(V(:,1)),abs(V(:,1))) axis('square') xlabel(num2str(abs(ev(1)))) subplot(222)
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polar(phase(V(:,3)),abs(V(:,3))) axis('square') xlabel(num2str(abs(ev(3)))) % % initial condition response using the original EVectors % as the the IC % sys=ss(A,zeros(size(A,1),1),eye(3,4),zeros(3,1)); [y1,t1,x1]=initial(sys,real(D(:,1))); [y3,t3,x3]=initial(sys,real(D(:,3))); subplot(223) plot(t1,y1(:,1),'-',t1,y1(:,2),'--',t1,y1(:,3),'-.') ylabel('Perturbation States u,w,q');xlabel('time (sec)');axis([0 15 -1 .5])
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lecture4 - % % B747 longitudinal dynamics % AA271a % B747...

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