Fa2004 16.33312-11 Wind code 1 Gust modeling 16.333,Fa112004 Z Jonathan P. Ho 5Xu=-1.982e3;Xw=4.025e3;zu=-2.59504;zw-9.030e4;Zq=-4.5245;Zwd=1.909e GMhu=1.593e4;Mw=-1.563e5;Mqm-1.521e7;Mwdm-1.702e4; sg=9.81; theta0=0;s=511;cbar=8.324 9U0=235.9;Iyy.449e8;m=2.83176e6/g;cbar=8.324;rho=0.3045; 10 Xdp* 3*m*g: Zdp=0; Mdp=0; 11Xde=-3.818e-6*(1/2*rho*U0-2*s);zde=-0.3648*(1/2*rho*Uo^2*s) 12Mde=-1.444*(1/2*rho*Uo-2*S*cbar) 4Ehat=[m000;0m-Zwd00;0- Mwd Iyy0;0001; 15 Ahat= [Xu Xw o -mg*cos(theta); [Zu Zw Za+m*UO -m*g*sin(theto)] Mu Mw Mq0;[0010]; form the gust input matrix Bwhat=[-Xu -Xw 0; -Zu -Zw 0;-Mu -Mw -Mq: 00 0]: 22 Z add height state 23 Ehat (5, 5)=1: \dot h state not couple 5)=0; Ahat (5, [1: 41)=[0 -1 0 UO]: add height state (5, 3)=0: % no input 28 form the odel 29 %e \dot x A x hat B u_controls \hat B_w Adot 32 A=inv(Ehat)* 33 B=inv(Ehat)* 34 Bw=inv (ehat) 4 assume that w_g=g-g 3s"ug·(du/dh)h 40dudh=[0.08.15.2] 1)*[00001]*du_dh(1) ,1)*[00001]*duah(2) 1)*[00001]*dudh(3); 46 evl=eig(A1): ev2=eig(A2): ev 3=eig(A3); ev4=eig(A4) plot(Levi ev2 ev3 ev4],x' as [ev1 ev2 ev3 ev4]Fall 2004 16.333 12–11 Wind Code 1 % Gust modeling 2 % 16.333, Fall 2004 3 % Jonathan P. How 4 5 Xu=­1.982e3;Xw=4.025e3;Zu=­2.595e4;Zw=­9.030e4;Zq=­4.524e5;Zwd=1.909e3; 6 Mu=1.593e4;Mw=­1.563e5;Mq=­1.521e7;Mwd=­1.702e4; 7 % 8 g=9.81;theta0=0;S=511;cbar=8.324; 9 U0=235.9;Iyy=.449e8;m=2.83176e6/g;cbar=8.324;rho=0.3045; 10 Xdp=.3*m*g;Zdp=0;Mdp=0; 11 Xde=­3.818e­6*(1/2*rho*U0^2*S);Zde=­0.3648*(1/2*rho*U0^2*S); 12 Mde=­1.444*(1/2*rho*U0^2*S*cbar);; 13 % 14 Ehat=[m 0 0 0;0 m­Zwd 0 0;0 ­Mwd Iyy 0;0 0 0 1]; 15 Ahat=[Xu Xw 0 ­m*g*cos(theta0);[Zu Zw Zq+m*U0 ­m*g*sin(theta0)]; 16 [Mu Mw Mq 0];[ 0 0 1 0]]; 17 Bhat=[Xde Xdp;Zde Zdp;Mde Mdp;0 0]; 18 % 19 % form the gust input matrix 20 Bwhat=[­Xu ­Xw 0;­Zu ­Zw 0;­Mu ­Mw ­Mq; 0 0 0]; 21 % 22 % add height state 23 Ehat(5,5)=1; % \dot h state not coupled 24 Ahat(5,5)=0;Ahat(5,[1:4])=[0 ­1 0 U0]; % add height state 25 Bhat(5,2)=0; % noinput 26 Bwhat(5,3)=0; % no input 27 28 % form the full model 29 % E \dot x = \hat A x + \hat B u_controls + 30 % ==> \dot x = A x + B u_controls + B_w w 31 % 32 A=inv(Ehat)*Ahat; 33 B=inv(Ehat)*Bhat; 34 Bw=inv(Ehat)*Bwhat; 35 % 36 % set u_controls=0 37 % assume that w_g=q_g=0 and 38 % u_g = (du/dh) h 39 % 40 du_dh=[0 .08 .15 .2]; 41 A1=A+Bw(:,1)*[0 0 0 0 1]*du_dh(1); 42 A2=A+Bw(:,1)*[0 0 0 0 1]*du_dh(2); 43 A3=A+Bw(:,1)*[0 0 0 0 1]*du_dh(3); 44 A4=A+Bw(:,1)*[0 0 0 0 1]*du_dh(4); 45 \hat B_w w 46 ev1=eig(A1);ev2=eig(A2);ev3=eig(A3);ev4=eig(A4); 47 plot([ev1 ev2 ev3 ev4],’x’) 48 [ev1 ev2 ev3 ev4]