Example 15
INERTIA = [3629 0 0 0 0 0;
0 3629 0 0 0 0;
0 0 3629 0 0 0;
0 0 0 3966 0 -1695;
0 0 0 0 14684 0;
0 0 0 -1695 0 12541];
FORCE = [-0.58; 92.68; 0; 1343.86; 8.41; -2780.4]
ACCELERATIONS = inv(INERTIA) * FORCE
VELOCITIES = ACCELERATIONS * 0.1
pause;
UH1H_A=[-0.0340 0.0041 0.0788 -0.3332 0.5267 -0.0917;
0.0020 -0.1534 -0.0115 -0.5926 -0.3763 0.5423;
0.0571 -0.0242 -0.9464 -0.7223 -0.8209 0.6116;
0.0012 -0.0556 -0.0324 -1.1435 -0.7824 0.3434;
0.0131 0.0017 -0.0142 0.1967 -0.6126 0.0192;
-0.0026 0.1212 -0.0527 -0.1555 -0.1171 -1.4981]
[VA,DA] = eig(UH1H_A)
UH1H_AA=[-0.0334 0.0040 -0.3233 0.5098 -0.0745 0
-0.0334 0.0040 0.0765 -0.3233 0.5098 -0.0745
0.0464 -0.0148 -0.8352 -0.7091 -0.6259 0.5153
0.0009 -0.0546 -0.0283 -0.9634 -0.5262 0.3371
0.0093 0.0012 -0.0101 0.1931 -0.4365 0.0137
-0.0009 0.1835 -0.0413 -0.1347 -0.1275 -0.9830]
[VAA,DAA] = eig(UH1H_AA)
UH1H_AABAR = inv(VAA) * UH1H_AA * VAA;
UH1H_ABAR = inv(VA) * UH1H_A * VA;
UH1H_B=[0.1141 0.0849 -0.0025 -0.0096;
-0.0179 0.0090 0.1054 0.2692;
-1.4946 0.4712 -0.0051 -0.0130;
-0.0248 0.0227 0.2200 0.2295;
-0.0001 -0.0683 0.0008 -0.0036;
0.0746 0.0290 0.0305 -0.6475]
UH1H_BBAR = inv(VA) * UH1H_B
C = [0.0000 0.0000 0.0000 0.0000 0.0000 0.0000];
D = [0.0000 0.0000 0.0000 0.0000];
T = [0:0.1:180];
U = [repmat(0,1,length(T));
repmat(0,1,length(T));
repmat(0,1,length(T));
repmat(0,1,length(T))];
X_0 = VELOCITIES
[Y,X]=lsim(UH1H_AA,UH1H_B,C,D,U,T,X_0);
x_dist = cumtrapz(T,X(:,1));
y_dist = cumtrapz(T,X(:,2));
z_dist = cumtrapz(T,X(:,3));
phi = cumtrapz(T,X(:,4));
the = cumtrapz(T,X(:,5));
psi = cumtrapz(T,X(:,6));
plot(T,X(:,1))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Forward velocity')
title('Figure 1: Variation of forward velocity with time')
print figure1.ps;
plot(T,X(:,2))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Sideward velocity')
title('Figure 3: Variation of Sideward velocity with time')
print;
plot(T,X(:,3))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Vertical velocity')
title('Figure 5: Variation of Vertical velocity with time')
print;
plot(T,X(:,4))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Roll Rate')
title('Figure 7: Variation of Roll Rate with time')
print;
plot(T,X(:,5))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Pitch Rate')
title('Figure 9: Variation of Pitch Rate with time')
print;
plot(T,X(:,6))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Yaw Rate')
title('Figure 11: Variation of Yaw Rate with time')
print;
plot(T,psi)
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Yaw Angle')
title('Figure 12: Variation of Yaw angle with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0',2)
plot(T,U(1,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Collective')
title('Figure 13: Variation of Collective with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0',2)
plot(T,U(2,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Longitudinal Cyclic')
title('Figure 14: Variation of Longitudinal Cyclic with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0',2)
plot(T,U(3,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Lateral Cyclic')
title('Figure 15: Variation of Lateral Cyclic with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0',2)
plot(T,U(4,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Pedals')
title('Figure 16: Variation of Pedals with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0',2)
k=0.4;
WEIGHT=[1.0 0.0 0.0 0.0 0.0 0.0;
0.0 1.0 0.0 0.0 0.0 0.0;
0.0 0.0 1.0 0.0 0.0 0.0;
0.0 0.0 0.0 1.0 0.0 0.0;
0.0 0.0 0.0 0.0 1.0 0.0;
0.0 0.0 0.0 0.0 0.0 3.0]
UH1H_Astar = UH1H_ABAR - k * WEIGHT * UH1H_BBAR * UH1H_BBAR';
[Ystar,Xstar]=lsim(UH1H_Astar,UH1H_BBAR,C,D,U,T,X_0);
Xstart = VA * Xstar';
Xstart = Xstart';
x_diststart = cumtrapz(T,Xstart(:,1));
y_diststart = cumtrapz(T,Xstart(:,2));
z_diststart = cumtrapz(T,Xstart(:,3));
phistart = cumtrapz(T,Xstart(:,4));
thestart = cumtrapz(T,Xstart(:,5));
psistart = cumtrapz(T,Xstart(:,6));
plot(T,Xstart(:,1))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Forward velocity')
title('Figure 17: Variation of controlled forward velocity with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print;
plot(T,x_diststart)
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Horizontal Distance')
title('Figure 18: Variation of controlled forward distance with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print;
plot(T,Xstart(:,2))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Sideward Velocity')
title('Figure 19: Variation of Controlled Sideward Velocity with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print;
plot(T,y_diststart)
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Sideward Distance')
title('Figure 20: Variation of Controlled Sideward distance with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print;
plot(T,Xstart(:,3))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Vertical velocity')
title('Figure 21: Variation of Controlled Vertical velocity with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print;
plot(T,z_diststart)
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Vertical Distance')
title('Figure 22: Variation of Controlled Vertical distance with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,Xstart(:,4))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Roll Rate')
title('Figure 23: Variation of Controlled Roll Rate with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,phistart)
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Roll Angle')
title('Figure 24: Variation of Controlled Roll Angle with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,Xstart(:,5))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Pitch Rate')
legend('UH-1H: Normal Landing',1)
title('Figure 25: Variation of Controlled Pitch Rate with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,thestart)
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Pitch Angle')
title('Figure 26: Variation of Controlled Pitch angle with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,Xstart(:,6))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Yaw Rate')
title('Figure 27: Variation of Controlled Yaw Rate with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,psistart)
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Controlled Yaw Angle')
title('Figure 28: Variation of Controlled Yaw angle with time')
legend('UH-1H: Controlled Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,U(1,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Collective')
title('Figure 29: Variation of Collective with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,U(2,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Longitudinal Cyclic')
title('Figure 30: Variation of Longitudinal Cyclic with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,U(3,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Lateral Cyclic')
title('Figure 31: Variation of Lateral Cyclic with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,U(4,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Pedals')
title('Figure 32: Variation of Pedals with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0.40',2)
print;
plot(x_diststart,z_diststart)
grid on
axis auto;
xlabel('Forward Distance in feet')
ylabel('Vertical Distance in feet')
title('Figure 33: Variation of Vertical Distance with Forward Distance')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0.40',2)
print;
uf = -k * UH1H_BBAR' * Xstart';
plot(T,uf(1,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Collective')
title('Figure 34: Variation of Collective with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,uf(2,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Long. Cyc.')
title('Figure 35: Variation of Long. Cyc. with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,uf(3,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Late. Cyc.')
title('Figure 36: Variation of Late. Cyc. with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0.40',2)
print
plot(T,uf(4,:))
grid on
axis auto;
xlabel('Time in seconds')
ylabel('Pedals')
title('Figure 37: Variation of Pedals with time')
legend('UH-1H: Normal Landing','-0.4 0 0 0','k=0.40',2)
print
Example
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