ac3 - % % B747 lateral dynamics % Reid 188 clear all % %...

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% % B747 lateral dynamics % Reid 188 clear all % % metric Yv=-1.61e4;Yp=0;Yr=0; Lv=-3.062e5;Lp=-1.076e7;Lr=9.925e6; Nv=2.131e5;Np=-1.33e6;Nr=-8.934e6; g=9.81;theta0=0;S=511;cbar=8.324;b=59.64; U0=235.9; m=2.83176e6/g;cbar=8.324;rho=0.3045; Iyy=.449e8;Ixx=.247e8;Izz=.673e8;Ixz=-.212e7; % nondimensional control derivatives % reid page 207 % Cyda=0;Cydr=.1146; Clda=-1.368e-2;Cldr=6.976e-3; Cnda=-1.973e-4;Cndr=-.1257; QdS=1/2*rho*U0^2*S; Yda=QdS*Cyda;Ydr=QdS*Cydr;Lda=QdS*b*Clda;Ldr=QdS*b*Cldr; Nda=QdS*b*Cnda;Ndr=QdS*b*Cndr; Ixxp=(Ixx*Izz-Ixz^2)/Izz; Izzp=(Ixx*Izz-Ixz^2)/Ixx; Ixzp=Ixz/(Ixx*Izz-Ixz^2); % reid 289 % full lateral derivatives % state x=[v p r phi] % Alat=[Yv/m Yp/m (Yr/m-U0) g*cos(theta0); (Lv/Ixxp + Ixzp*Nv) (Lp/Ixxp + Ixzp*Np) (Lr/Ixxp + Ixzp*Nr) 0; (Ixzp*Lv + Nv/Izzp) (Ixzp*Lp + Np/Izzp) (Ixzp*Lr + Nr/Izzp) 0; 0 1 tan(theta0) 0]; Blat=[1/m 0 0;0 1/Ixxp Ixzp;0 Ixzp 1/Izzp;0 0 0]*[Yda Ydr;Lda Ldr;Nda Ndr]; % Model from rudder to r G_dr_r=ss(Alat,Blat(:,2),[0 0 1 0],0); % % rudder servo 3.33/(s+3.33) Hr=tf(3.33,[1 3.33]); % % expected control gain Kr=-1.6; tf(G_dr_r*Hr) figure(4);clf set(gcf,'DefaultLineLineWidth',2) set(gcf,'DefaultlineMarkerSize',18) pzmap(sign(Kr)*G_dr_r*Hr); hh=get(gcf,'children');hhh=get(hh(1),'children') set(hhh(1),'MarkerSize',18);set(hhh(1),'LineWidth',2) set(hhh(2),'MarkerSize',18);set(hhh(2),'LineWidth',2) axis([-3.75 .25 -2 2]) title('Lateral autopilot: r to rudder','FontSize',12) print -depsc lat_1;jpdf('lat_1') figure(1);clf
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set(gcf,'DefaultLineLineWidth',2) set(gcf,'DefaultlineMarkerSize',18) rlocus(G_dr_r*Hr); % note positive sign used here sgrid([.25 .5 .75],[.25 .5 1]) axis([-2 2 -2 2]) title('Lateral autopilot: r to \delta_r with k>0 ','FontSize',16) print -depsc lat_2a;jpdf('lat_2a') figure(1);clf set(gcf,'DefaultLineLineWidth',2) set(gcf,'DefaultlineMarkerSize',18) rlocus(sign(Kr)*G_dr_r*Hr); % note negative sign used here rr=rlocus(G_dr_r*Hr,Kr); hold on; plot(rr+eps*j,'rd','MarkerFace','r');hold off hh=get(1,'children');hhh=get(hh(1),'children') set(hhh(1),'MarkerSize',18);set(hhh(1),'LineWidth',2) set(hhh(2),'MarkerSize',18);set(hhh(2),'LineWidth',2) sgrid([.25 .5 .75],[.25 .5 1]) axis([-3.75 .25 -2 2]) title('Lateral autopilot: r to \delta_r with k<0 ','FontSize',16)
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This note was uploaded on 11/07/2011 for the course AERO 16.333 taught by Professor Alexandremegretski during the Fall '04 term at MIT.

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ac3 - % % B747 lateral dynamics % Reid 188 clear all % %...

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