Help with formulating conditional logic.

3 visualizzazioni (ultimi 30 giorni)
Jeffrey Lewis
Jeffrey Lewis il 4 Nov 2022
Commentato: Sam Chak il 4 Nov 2022
I am writing a stability and control code (for a class assignment) that takes into account 3 different airplane conditions; Climb data, Cruise data, and Approach data. I don't want to change variables for each condition, rather I have captured all of the data for each condition in the code with differing data for each condition.
Ultimately, I would like to output the transfer functions for each condition. I am not very savy with MATLAB and would love some help in finding the best way to formulate this logic.
The code:
clc
clear all
g = 32.174
theta1 = 0
%Cessna design parameters
S = 174 %Planform Area (ft^2)
c = 4.9 %Chord length (ft)
b = 36.0 %Wing span (ft)
%%%%%%%%%%%%%%%%Flight Conditions%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Climb Flight Condition
altitude = 0
M = 0.120
U_1 = 133.5
q_bar = 21.2
c_frac = 26.2
a_1 = 5.4
%Cruise Flight Condition
h = 5000 %Altitude (ft)
M = 0.201 %Mach Number
U_1 = 220.1 %TAS (ft/s)
q_bar = 49.6 %Dynamic Pressure (lbs/ft^2)
c_frac = 26.4 %CG Location
a_1 = 0 %Angle of Attack (Deg)
%Approach Flight Condition
h = 0
M = 0.096
U_1 = 107.1
q_bar = 13.6
c_frac = 26.4
a_1 = 4
%%%%%%%%%%%%%%%%Mass Data For All Flight Conditions%%%%%%%%%%%%%%%%%%%%%%
%Mass Data in Climb, Cruise, and Approach Conditions
W = 2650 %Weight (lbs)
m = W/g %Mass
I_xx_B = 948 %Moment of Inertia along the X-axis (slug-ft^2)
I_yy_B = 1346 %Moment of Inertia along the Y-axis (slug-ft^2)
I_zz_B = 1967 %Moment of Inertia along the Z-axis (slug-ft^2)
I_xz_B = 0 %Moment of Inertia along the XZ plane (slug-ft^2)
%%%%%%%%%%%%%%%%%%%%%%%Longitudinal Control and Hinge Momoment $$$$$$$$$
%Climb Longitudinal Control and Hinge Moment Derivatives
Ch_a = -0.0545
Ch_del_e = -0.594
%Cruise Longitudinal Control and Hinge Moment Derivatives
Ch_a = -0.0584
Ch_del_e = -0.585
%Approach Longitudinal Control and Hinge Moment Derivatives
Ch_a = -0.0549
Ch_del_e = -0.594
%%%%%%%%%%%%%%%%%%%Lateral-Directional Stability%%%%%%%%%%%%%%%%%%%%
%Climb Lateral-Directional Stabillity Derivatives
Cl_B = -0.0895
Cl_p = -0.487
Cl_r = 0.1869
Cy_B = -0.404
Cy_p = -0.145
Cy_r = 0.267
Cn_B = 0.0907
Cn_TB = 0
Cn_p = -0.0649
Cn_r = -0.1199
%Cruise Lateral-Directional Stability Derivatives
Cl_B = -0.0923
Cl_p = -0.484
Cl_r = 0.0798
Cy_B = -0.393
Cy_p = -0.075
Cy_r = 0.214
Cn_B = 0.0587
Cn_TB = 0
Cn_p = -0.0278
Cn_r = -0.0937
%Approach Lateral-Directional Stability Derivatives
Cl_B = -0.0969
Cl_p = -0.494
Cl_r = 0.2039
Cy_B = -0.303
Cy_p = -0.213
Cy_r = 0.201
Cn_B = 0.0701
Cn_TB = 0
Cn_p = -0.0960
Cn_r = -0.1151
%%%%%%%%%%%%%%%%%%%%Lateral-Directional Control and Hing Moment%%%%%%%%%
%Climb Lateral-Directional Control and Hinge Moment Derivatives
Cl_dela = 0.229
Cl_delr = 0.0147
Cy_dela = 0
Cy_delr = 0.187
Cn_dela = -0.0504
Cn_delr = -0.0805
Ch_aa = 0
Ch_dela = -0.369
Ch_Br = 0.0819
Ch_delr = -0.579
%Cruise Lateral-Directional Control and Hinge Moment Derivatives
Cl_dela = 0.229
Cl_delr = 0.0147
Cy_dela = 0
Cy_delr = 0.187
Cn_dela = -0.0216
Cn_delr = -0.0645
Ch_aa = 0
Ch_dela = -0.363
Ch_Br = 0.0819
Ch_delr = -0.567
%Approach Lateral-Directional Control and Hinge moment Derivatives
Cl_dela = 0.229
Cl_delr = 0.0147
Cy_dela = 0
Cy_delr = 0.187
Cn_dela = -0.0504
Cn_delr = -0.0805
Ch_aa = 0
Ch_dela = -0.369
Ch_Br = 0.0819
Ch_delr = -0.579
%Lateral-Directional Dimensional Stability Derivatives
YB = (q_bar*S*Cy_B)/m
Yp = (S*b*Cy_p)/(2*m*U_1)
Yr = (q_bar*S*b*Cy_r)/(2*m*U_1)
Y_dela = (q_bar*S*Cy_dela)/m
Y_delr = (q_bar*S*Cy_delr)/m
LB = (q_bar*S*b*Cl_B)/I_xx_B
Lp = (q_bar*S*(b^2)*Cl_p)/(2*I_xx_B*U_1)
Lr = (q_bar*S*(b^2)*Cl_r)/(2*I_xx_B*U_1)
L_dela = (q_bar*S*b*Cl_dela)/I_xx_B
L_delr = (q_bar*S*b*Cl_delr)/I_xx_B
NB = (q_bar*S*b*Cn_B)/I_zz_B
NT_B = (q_bar*S*b*Cn_TB)/I_zz_B
Np = (q_bar*S*(b^2)*Cn_p)/(2*I_zz_B*U_1)
Nr = (q_bar*S*(b^2)*Cn_r)/(2*I_zz_B*U_1)
N_dela = (q_bar*S*b*Cn_dela)/I_zz_B
N_delr = (q_bar*S*b*Cn_delr)/I_zz_B
%Perturbed Lateral-Directional Equations of Motion
A_1 = I_xz/I_xx_B
B_1 = I_xz/I_zz_B
%Denominator Polynomial
A2 = U_1(1-A_1*B_1)
B2 = -YB*(1-A_1*B_1)-U_1*(Lp+Nr+A_1*Np+B_1*Lr)
C2 = U_1*(Lp*Nr-Lr*Np)+YB*(Nr+Lp+A_1*Np+B_1*Lr)-Yp*(LB+NB*A_1+NT_B*A_1)...
+U_1*(LB*B_1+NB+NT_B)-Yr*(LB*B_1+NB+NT_B)
D2 = -YB*(Lp*Nr-Lr*Np)+Yp*(LB*Nr-NB*Lr-NT_B*Lr)-g*cos(theta1)...
*(LB+NB*A_1+NT_B*A_1)+U_1*(LB*Np-NB*Lp-NT_B*Lp)-Yr*(LB*Np-NB*Lp-NT_B*Lp)
E2 = g*cos(theta1)*(LB*Nr-NB*Lr-NT_B*Lr)
D_2 = [A2 B2 C2 D2 E2]
%Numerator Polynomial
AB = Y_dela*(1-A_1*B_1)+Y_delr*(1-A_1*B_1)
BB = -Y_dela*(Nr+Lp+A_1*Np+B_1*Lr)-Y_delr*(Nr+Lp+A_1*Np+B_1*Lr)+Yp*(L_dela+N_dela*A_1)+Yp*(L_delr+N_delr*A_1)...
+Yr*(L_dela*B_1+N_dela)+Yr*(L_delr*B_1+N_delr)-U_1*(L_dela*B_1+N_dela)...
+U_1*(L_delr*B_1+N_delr)
CB = Y_dela*(Lp*Nr-Np*Lr)+Y_delr*(Lp*Nr-Np*Lr)+Yp*(N_dela*Lr-L_dela*Nr)+Yp*(N_delr*Lr-L_delr*Nr)...
+g*cos(theta1)*(L_dela+N_dela*A_1)+g*cos(theta1)*(L_delr+N_delr*A_1)...
+Yr*(L_dela*Np-N_dela*Lp)+Yr*(L_delr*Np-N_delr*Lp)+U_1*(L_dela*Np-N_dela*Lp)+U_1*(L_delr*Np-N_delr*Lp)
DB = g*cos(theta1)*(N_dela*Lr-L_dela*Nr)+g*cos(theta1)*(N_delr*Lr-L_delr*Nr)
N_B = [AB BB CB DB]
%Transfer Function
sys = tf(N_B,D_2)
damp(sys)

Accedi per rispondere a questa domanda.

Risposta accettata

Sam Chak
Sam Chak il 4 Nov 2022
Ran in:
Hi @Jeffrey Lewis
There are a few ways to do it. But since you have written the data into the code, I think probably the simplest way is to write a function file for eash flight condition, and then call the specific function. The example is shown below:
1. Calling climbsys
climbsys
Climb_sys = 8.375 s^3 - 200.8 s^2 - 1.251e04 s + 195.1 ------------------------------------------------ 133.5 s^4 + 1392 s^3 + 2612 s^2 + 9028 s - 255.2 Continuous-time transfer function. Pole Damping Frequency Time Constant (rad/seconds) (seconds) 2.80e-02 -1.00e+00 2.80e-02 -3.57e+01 -6.80e-01 + 2.65e+00i 2.48e-01 2.74e+00 1.47e+00 -6.80e-01 - 2.65e+00i 2.48e-01 2.74e+00 1.47e+00 -9.09e+00 1.00e+00 9.09e+00 1.10e-01
2. Calling cruisesys
cruisesys
Cruise_sys = 19.59 s^3 - 1240 s^2 - 4.263e04 s + 2174 -------------------------------------------------- 220.1 s^4 + 3163 s^3 + 6232 s^2 + 3.028e04 s + 540 Continuous-time transfer function. Pole Damping Frequency Time Constant (rad/seconds) (seconds) -1.79e-02 1.00e+00 1.79e-02 5.59e+01 -6.74e-01 + 3.18e+00i 2.08e-01 3.25e+00 1.48e+00 -6.74e-01 - 3.18e+00i 2.08e-01 3.25e+00 1.48e+00 -1.30e+01 1.00e+00 1.30e+01 7.69e-02
3. Calling approachsys
approachsys
Approach_sys = 5.373 s^3 - 102.2 s^2 - 5475 s + 28.61 ------------------------------------------------- 107.1 s^4 + 897.5 s^3 + 1294 s^2 + 3403 s - 66.09 Continuous-time transfer function. Pole Damping Frequency Time Constant (rad/seconds) (seconds) 1.93e-02 -1.00e+00 1.93e-02 -5.19e+01 -5.37e-01 + 2.02e+00i 2.57e-01 2.09e+00 1.86e+00 -5.37e-01 - 2.02e+00i 2.57e-01 2.09e+00 1.86e+00 -7.32e+00 1.00e+00 7.32e+00 1.37e-01
function climbsys
g = 32.174;
theta1 = 0;
% Cessna design parameters
S = 174; % Planform Area (ft^2)
c = 4.9; % Chord length (ft)
b = 36.0; % Wing span (ft)
%%%%%%%%%%%%%%%%Flight Conditions%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Climb Flight Condition
altitude = 0;
M = 0.120;
U_1 = 133.5;
q_bar = 21.2;
c_frac = 26.2;
a_1 = 5.4;
% % Cruise Flight Condition
% h = 5000; % Altitude (ft)
% M = 0.201; % Mach Number
% U_1 = 220.1; % TAS (ft/s)
% q_bar = 49.6; % Dynamic Pressure (lbs/ft^2)
% c_frac = 26.4; % CG Location
% a_1 = 0; % Angle of Attack (Deg)
%
% % Approach Flight Condition
% h = 0;
% M = 0.096;
% U_1 = 107.1;
% q_bar = 13.6;
% c_frac = 26.4;
% a_1 = 4;
%%%%%%%%%%%%%%%%Mass Data For All Flight Conditions%%%%%%%%%%%%%%%%%%%%%%
% Mass Data in Climb, Cruise, and Approach Conditions
W = 2650; % Weight (lbs)
m = W/g; % Mass
I_xx_B = 948; % Moment of Inertia along the X-axis (slug-ft^2)
I_yy_B = 1346; % Moment of Inertia along the Y-axis (slug-ft^2)
I_zz_B = 1967; % Moment of Inertia along the Z-axis (slug-ft^2)
I_xz_B = 0; % Moment of Inertia along the XZ plane (slug-ft^2)
%%%%%%%%%%%%%%%%%%%%%%%Longitudinal Control and Hinge Momoment $$$$$$$$$
% Climb Longitudinal Control and Hinge Moment Derivatives
Ch_a = -0.0545;
Ch_del_e = -0.594;
% % Cruise Longitudinal Control and Hinge Moment Derivatives
% Ch_a = -0.0584;
% Ch_del_e = -0.585;
%
% % Approach Longitudinal Control and Hinge Moment Derivatives
% Ch_a = -0.0549;
% Ch_del_e = -0.594;
%%%%%%%%%%%%%%%%%%%Lateral-Directional Stability%%%%%%%%%%%%%%%%%%%%
% Climb Lateral-Directional Stabillity Derivatives
Cl_B = -0.0895;
Cl_p = -0.487;
Cl_r = 0.1869;
Cy_B = -0.404;
Cy_p = -0.145;
Cy_r = 0.267;
Cn_B = 0.0907;
Cn_TB = 0;
Cn_p = -0.0649;
Cn_r = -0.1199;
% % Cruise Lateral-Directional Stability Derivatives
% Cl_B = -0.0923;
% Cl_p = -0.484;
% Cl_r = 0.0798;
% Cy_B = -0.393;
% Cy_p = -0.075;
% Cy_r = 0.214;
% Cn_B = 0.0587;
% Cn_TB = 0;
% Cn_p = -0.0278;
% Cn_r = -0.0937;
%
% % Approach Lateral-Directional Stability Derivatives
% Cl_B = -0.0969;
% Cl_p = -0.494;
% Cl_r = 0.2039;
% Cy_B = -0.303;
% Cy_p = -0.213;
% Cy_r = 0.201;
% Cn_B = 0.0701;
% Cn_TB = 0;
% Cn_p = -0.0960;
% Cn_r = -0.1151;
%%%%%%%%%%%%%%%%%%%%Lateral-Directional Control and Hing Moment%%%%%%%%%
% Climb Lateral-Directional Control and Hinge Moment Derivatives
Cl_dela = 0.229;
Cl_delr = 0.0147;
Cy_dela = 0;
Cy_delr = 0.187;
Cn_dela = -0.0504;
Cn_delr = -0.0805;
Ch_aa = 0;
Ch_dela = -0.369;
Ch_Br = 0.0819;
Ch_delr = -0.579;
% % Cruise Lateral-Directional Control and Hinge Moment Derivatives
% Cl_dela = 0.229;
% Cl_delr = 0.0147;
% Cy_dela = 0;
% Cy_delr = 0.187;
% Cn_dela = -0.0216;
% Cn_delr = -0.0645;
% Ch_aa = 0;
% Ch_dela = -0.363;
% Ch_Br = 0.0819;
% Ch_delr = -0.567;
%
% % Approach Lateral-Directional Control and Hinge moment Derivatives
% Cl_dela = 0.229;
% Cl_delr = 0.0147;
% Cy_dela = 0;
% Cy_delr = 0.187;
% Cn_dela = -0.0504;
% Cn_delr = -0.0805;
% Ch_aa = 0;
% Ch_dela = -0.369;
% Ch_Br = 0.0819;
% Ch_delr = -0.579;
% Lateral-Directional Dimensional Stability Derivatives
YB = (q_bar*S*Cy_B)/m;
Yp = (S*b*Cy_p)/(2*m*U_1);
Yr = (q_bar*S*b*Cy_r)/(2*m*U_1);
Y_dela = (q_bar*S*Cy_dela)/m;
Y_delr = (q_bar*S*Cy_delr)/m;
LB = (q_bar*S*b*Cl_B)/I_xx_B;
Lp = (q_bar*S*(b^2)*Cl_p)/(2*I_xx_B*U_1);
Lr = (q_bar*S*(b^2)*Cl_r)/(2*I_xx_B*U_1);
L_dela = (q_bar*S*b*Cl_dela)/I_xx_B;
L_delr = (q_bar*S*b*Cl_delr)/I_xx_B;
NB = (q_bar*S*b*Cn_B)/I_zz_B;
NT_B = (q_bar*S*b*Cn_TB)/I_zz_B;
Np = (q_bar*S*(b^2)*Cn_p)/(2*I_zz_B*U_1);
Nr = (q_bar*S*(b^2)*Cn_r)/(2*I_zz_B*U_1);
N_dela = (q_bar*S*b*Cn_dela)/I_zz_B;
N_delr = (q_bar*S*b*Cn_delr)/I_zz_B;
% Perturbed Lateral-Directional Equations of Motion
A_1 = I_xz_B/I_xx_B;
B_1 = I_xz_B/I_zz_B;
% Numerator Polynomial
AB = Y_dela*(1 - A_1*B_1) + Y_delr*(1 - A_1*B_1);
BB = - Y_dela*(Nr + Lp + A_1*Np + B_1*Lr) - Y_delr*(Nr + Lp + A_1*Np + B_1*Lr) + Yp*(L_dela + N_dela*A_1) + Yp*(L_delr + N_delr*A_1) + Yr*(L_dela*B_1 + N_dela) + Yr*(L_delr*B_1 + N_delr) - U_1*(L_dela*B_1 + N_dela) + U_1*(L_delr*B_1 + N_delr);
CB = Y_dela*(Lp*Nr - Np*Lr) + Y_delr*(Lp*Nr - Np*Lr) + Yp*(N_dela*Lr - L_dela*Nr) + Yp*(N_delr*Lr - L_delr*Nr) + g*cos(theta1)*(L_dela + N_dela*A_1) + g*cos(theta1)*(L_delr + N_delr*A_1) + Yr*(L_dela*Np - N_dela*Lp) + Yr*(L_delr*Np - N_delr*Lp) + U_1*(L_dela*Np - N_dela*Lp) + U_1*(L_delr*Np - N_delr*Lp);
DB = g*cos(theta1)*(N_dela*Lr-L_dela*Nr)+g*cos(theta1)*(N_delr*Lr-L_delr*Nr);
N_B = [AB BB CB DB];
% Denominator Polynomial
A2 = U_1*(1 - A_1*B_1);
B2 = - YB*(1 - A_1*B_1) - U_1*(Lp + Nr + A_1*Np + B_1*Lr);
C2 = U_1*(Lp*Nr - Lr*Np) + YB*(Nr + Lp + A_1*Np + B_1*Lr) - Yp*(LB + NB*A_1 + NT_B*A_1) + U_1*(LB*B_1 + NB + NT_B) - Yr*(LB*B_1 + NB + NT_B);
D2 = - YB*(Lp*Nr - Lr*Np) + Yp*(LB*Nr - NB*Lr - NT_B*Lr) - g*cos(theta1)*(LB + NB*A_1 + NT_B*A_1) + U_1*(LB*Np - NB*Lp - NT_B*Lp) - Yr*(LB*Np - NB*Lp - NT_B*Lp);
E2 = g*cos(theta1)*(LB*Nr - NB*Lr - NT_B*Lr);
D_2 = [A2 B2 C2 D2 E2];
% Transfer Function
Climb_sys = tf(N_B, D_2)
damp(Climb_sys)
step(Climb_sys)
end
function cruisesys
g = 32.174;
theta1 = 0;
% Cessna design parameters
S = 174; % Planform Area (ft^2)
c = 4.9; % Chord length (ft)
b = 36.0; % Wing span (ft)
%%%%%%%%%%%%%%%%Flight Conditions%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % Climb Flight Condition
% altitude = 0;
% M = 0.120;
% U_1 = 133.5;
% q_bar = 21.2;
% c_frac = 26.2;
% a_1 = 5.4;
% Cruise Flight Condition
h = 5000; % Altitude (ft)
M = 0.201; % Mach Number
U_1 = 220.1; % TAS (ft/s)
q_bar = 49.6; % Dynamic Pressure (lbs/ft^2)
c_frac = 26.4; % CG Location
a_1 = 0; % Angle of Attack (Deg)
% % Approach Flight Condition
% h = 0;
% M = 0.096;
% U_1 = 107.1;
% q_bar = 13.6;
% c_frac = 26.4;
% a_1 = 4;
%%%%%%%%%%%%%%%%Mass Data For All Flight Conditions%%%%%%%%%%%%%%%%%%%%%%
% Mass Data in Climb, Cruise, and Approach Conditions
W = 2650; % Weight (lbs)
m = W/g; % Mass
I_xx_B = 948; % Moment of Inertia along the X-axis (slug-ft^2)
I_yy_B = 1346; % Moment of Inertia along the Y-axis (slug-ft^2)
I_zz_B = 1967; % Moment of Inertia along the Z-axis (slug-ft^2)
I_xz_B = 0; % Moment of Inertia along the XZ plane (slug-ft^2)
%%%%%%%%%%%%%%%%%%%%%%%Longitudinal Control and Hinge Momoment $$$$$$$$$
% % Climb Longitudinal Control and Hinge Moment Derivatives
% Ch_a = -0.0545;
% Ch_del_e = -0.594;
% Cruise Longitudinal Control and Hinge Moment Derivatives
Ch_a = -0.0584;
Ch_del_e = -0.585;
% % Approach Longitudinal Control and Hinge Moment Derivatives
% Ch_a = -0.0549;
% Ch_del_e = -0.594;
%%%%%%%%%%%%%%%%%%%Lateral-Directional Stability%%%%%%%%%%%%%%%%%%%%
% % Climb Lateral-Directional Stabillity Derivatives
% Cl_B = -0.0895;
% Cl_p = -0.487;
% Cl_r = 0.1869;
% Cy_B = -0.404;
% Cy_p = -0.145;
% Cy_r = 0.267;
% Cn_B = 0.0907;
% Cn_TB = 0;
% Cn_p = -0.0649;
% Cn_r = -0.1199;
% Cruise Lateral-Directional Stability Derivatives
Cl_B = -0.0923;
Cl_p = -0.484;
Cl_r = 0.0798;
Cy_B = -0.393;
Cy_p = -0.075;
Cy_r = 0.214;
Cn_B = 0.0587;
Cn_TB = 0;
Cn_p = -0.0278;
Cn_r = -0.0937;
% % Approach Lateral-Directional Stability Derivatives
% Cl_B = -0.0969;
% Cl_p = -0.494;
% Cl_r = 0.2039;
% Cy_B = -0.303;
% Cy_p = -0.213;
% Cy_r = 0.201;
% Cn_B = 0.0701;
% Cn_TB = 0;
% Cn_p = -0.0960;
% Cn_r = -0.1151;
%%%%%%%%%%%%%%%%%%%%Lateral-Directional Control and Hing Moment%%%%%%%%%
% % Climb Lateral-Directional Control and Hinge Moment Derivatives
% Cl_dela = 0.229;
% Cl_delr = 0.0147;
% Cy_dela = 0;
% Cy_delr = 0.187;
% Cn_dela = -0.0504;
% Cn_delr = -0.0805;
% Ch_aa = 0;
% Ch_dela = -0.369;
% Ch_Br = 0.0819;
% Ch_delr = -0.579;
% Cruise Lateral-Directional Control and Hinge Moment Derivatives
Cl_dela = 0.229;
Cl_delr = 0.0147;
Cy_dela = 0;
Cy_delr = 0.187;
Cn_dela = -0.0216;
Cn_delr = -0.0645;
Ch_aa = 0;
Ch_dela = -0.363;
Ch_Br = 0.0819;
Ch_delr = -0.567;
% % Approach Lateral-Directional Control and Hinge moment Derivatives
% Cl_dela = 0.229;
% Cl_delr = 0.0147;
% Cy_dela = 0;
% Cy_delr = 0.187;
% Cn_dela = -0.0504;
% Cn_delr = -0.0805;
% Ch_aa = 0;
% Ch_dela = -0.369;
% Ch_Br = 0.0819;
% Ch_delr = -0.579;
% Lateral-Directional Dimensional Stability Derivatives
YB = (q_bar*S*Cy_B)/m;
Yp = (S*b*Cy_p)/(2*m*U_1);
Yr = (q_bar*S*b*Cy_r)/(2*m*U_1);
Y_dela = (q_bar*S*Cy_dela)/m;
Y_delr = (q_bar*S*Cy_delr)/m;
LB = (q_bar*S*b*Cl_B)/I_xx_B;
Lp = (q_bar*S*(b^2)*Cl_p)/(2*I_xx_B*U_1);
Lr = (q_bar*S*(b^2)*Cl_r)/(2*I_xx_B*U_1);
L_dela = (q_bar*S*b*Cl_dela)/I_xx_B;
L_delr = (q_bar*S*b*Cl_delr)/I_xx_B;
NB = (q_bar*S*b*Cn_B)/I_zz_B;
NT_B = (q_bar*S*b*Cn_TB)/I_zz_B;
Np = (q_bar*S*(b^2)*Cn_p)/(2*I_zz_B*U_1);
Nr = (q_bar*S*(b^2)*Cn_r)/(2*I_zz_B*U_1);
N_dela = (q_bar*S*b*Cn_dela)/I_zz_B;
N_delr = (q_bar*S*b*Cn_delr)/I_zz_B;
% Perturbed Lateral-Directional Equations of Motion
A_1 = I_xz_B/I_xx_B;
B_1 = I_xz_B/I_zz_B;
% Numerator Polynomial
AB = Y_dela*(1 - A_1*B_1) + Y_delr*(1 - A_1*B_1);
BB = - Y_dela*(Nr + Lp + A_1*Np + B_1*Lr) - Y_delr*(Nr + Lp + A_1*Np + B_1*Lr) + Yp*(L_dela + N_dela*A_1) + Yp*(L_delr + N_delr*A_1) + Yr*(L_dela*B_1 + N_dela) + Yr*(L_delr*B_1 + N_delr) - U_1*(L_dela*B_1 + N_dela) + U_1*(L_delr*B_1 + N_delr);
CB = Y_dela*(Lp*Nr - Np*Lr) + Y_delr*(Lp*Nr - Np*Lr) + Yp*(N_dela*Lr - L_dela*Nr) + Yp*(N_delr*Lr - L_delr*Nr) + g*cos(theta1)*(L_dela + N_dela*A_1) + g*cos(theta1)*(L_delr + N_delr*A_1) + Yr*(L_dela*Np - N_dela*Lp) + Yr*(L_delr*Np - N_delr*Lp) + U_1*(L_dela*Np - N_dela*Lp) + U_1*(L_delr*Np - N_delr*Lp);
DB = g*cos(theta1)*(N_dela*Lr-L_dela*Nr)+g*cos(theta1)*(N_delr*Lr-L_delr*Nr);
N_B = [AB BB CB DB];
% Denominator Polynomial
A2 = U_1*(1 - A_1*B_1);
B2 = - YB*(1 - A_1*B_1) - U_1*(Lp + Nr + A_1*Np + B_1*Lr);
C2 = U_1*(Lp*Nr - Lr*Np) + YB*(Nr + Lp + A_1*Np + B_1*Lr) - Yp*(LB + NB*A_1 + NT_B*A_1) + U_1*(LB*B_1 + NB + NT_B) - Yr*(LB*B_1 + NB + NT_B);
D2 = - YB*(Lp*Nr - Lr*Np) + Yp*(LB*Nr - NB*Lr - NT_B*Lr) - g*cos(theta1)*(LB + NB*A_1 + NT_B*A_1) + U_1*(LB*Np - NB*Lp - NT_B*Lp) - Yr*(LB*Np - NB*Lp - NT_B*Lp);
E2 = g*cos(theta1)*(LB*Nr - NB*Lr - NT_B*Lr);
D_2 = [A2 B2 C2 D2 E2];
% Transfer Function
Cruise_sys = tf(N_B, D_2)
damp(Cruise_sys)
step(Cruise_sys)
end
function approachsys
g = 32.174;
theta1 = 0;
% Cessna design parameters
S = 174; % Planform Area (ft^2)
c = 4.9; % Chord length (ft)
b = 36.0; % Wing span (ft)
%%%%%%%%%%%%%%%%Flight Conditions%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % Climb Flight Condition
% altitude = 0;
% M = 0.120;
% U_1 = 133.5;
% q_bar = 21.2;
% c_frac = 26.2;
% a_1 = 5.4;
%
% % Cruise Flight Condition
% h = 5000; % Altitude (ft)
% M = 0.201; % Mach Number
% U_1 = 220.1; % TAS (ft/s)
% q_bar = 49.6; % Dynamic Pressure (lbs/ft^2)
% c_frac = 26.4; % CG Location
% a_1 = 0; % Angle of Attack (Deg)
% Approach Flight Condition
h = 0;
M = 0.096;
U_1 = 107.1;
q_bar = 13.6;
c_frac = 26.4;
a_1 = 4;
%%%%%%%%%%%%%%%%Mass Data For All Flight Conditions%%%%%%%%%%%%%%%%%%%%%%
% Mass Data in Climb, Cruise, and Approach Conditions
W = 2650; % Weight (lbs)
m = W/g; % Mass
I_xx_B = 948; % Moment of Inertia along the X-axis (slug-ft^2)
I_yy_B = 1346; % Moment of Inertia along the Y-axis (slug-ft^2)
I_zz_B = 1967; % Moment of Inertia along the Z-axis (slug-ft^2)
I_xz_B = 0; % Moment of Inertia along the XZ plane (slug-ft^2)
%%%%%%%%%%%%%%%%%%%%%%%Longitudinal Control and Hinge Momoment $$$$$$$$$
% % Climb Longitudinal Control and Hinge Moment Derivatives
% Ch_a = -0.0545;
% Ch_del_e = -0.594;
%
% % Cruise Longitudinal Control and Hinge Moment Derivatives
% Ch_a = -0.0584;
% Ch_del_e = -0.585;
% Approach Longitudinal Control and Hinge Moment Derivatives
Ch_a = -0.0549;
Ch_del_e = -0.594;
%%%%%%%%%%%%%%%%%%%Lateral-Directional Stability%%%%%%%%%%%%%%%%%%%%
% % Climb Lateral-Directional Stabillity Derivatives
% Cl_B = -0.0895;
% Cl_p = -0.487;
% Cl_r = 0.1869;
% Cy_B = -0.404;
% Cy_p = -0.145;
% Cy_r = 0.267;
% Cn_B = 0.0907;
% Cn_TB = 0;
% Cn_p = -0.0649;
% Cn_r = -0.1199;
%
% % Cruise Lateral-Directional Stability Derivatives
% Cl_B = -0.0923;
% Cl_p = -0.484;
% Cl_r = 0.0798;
% Cy_B = -0.393;
% Cy_p = -0.075;
% Cy_r = 0.214;
% Cn_B = 0.0587;
% Cn_TB = 0;
% Cn_p = -0.0278;
% Cn_r = -0.0937;
% Approach Lateral-Directional Stability Derivatives
Cl_B = -0.0969;
Cl_p = -0.494;
Cl_r = 0.2039;
Cy_B = -0.303;
Cy_p = -0.213;
Cy_r = 0.201;
Cn_B = 0.0701;
Cn_TB = 0;
Cn_p = -0.0960;
Cn_r = -0.1151;
%%%%%%%%%%%%%%%%%%%%Lateral-Directional Control and Hing Moment%%%%%%%%%
% % Climb Lateral-Directional Control and Hinge Moment Derivatives
% Cl_dela = 0.229;
% Cl_delr = 0.0147;
% Cy_dela = 0;
% Cy_delr = 0.187;
% Cn_dela = -0.0504;
% Cn_delr = -0.0805;
% Ch_aa = 0;
% Ch_dela = -0.369;
% Ch_Br = 0.0819;
% Ch_delr = -0.579;
%
% % Cruise Lateral-Directional Control and Hinge Moment Derivatives
% Cl_dela = 0.229;
% Cl_delr = 0.0147;
% Cy_dela = 0;
% Cy_delr = 0.187;
% Cn_dela = -0.0216;
% Cn_delr = -0.0645;
% Ch_aa = 0;
% Ch_dela = -0.363;
% Ch_Br = 0.0819;
% Ch_delr = -0.567;
% Approach Lateral-Directional Control and Hinge moment Derivatives
Cl_dela = 0.229;
Cl_delr = 0.0147;
Cy_dela = 0;
Cy_delr = 0.187;
Cn_dela = -0.0504;
Cn_delr = -0.0805;
Ch_aa = 0;
Ch_dela = -0.369;
Ch_Br = 0.0819;
Ch_delr = -0.579;
% Lateral-Directional Dimensional Stability Derivatives
YB = (q_bar*S*Cy_B)/m;
Yp = (S*b*Cy_p)/(2*m*U_1);
Yr = (q_bar*S*b*Cy_r)/(2*m*U_1);
Y_dela = (q_bar*S*Cy_dela)/m;
Y_delr = (q_bar*S*Cy_delr)/m;
LB = (q_bar*S*b*Cl_B)/I_xx_B;
Lp = (q_bar*S*(b^2)*Cl_p)/(2*I_xx_B*U_1);
Lr = (q_bar*S*(b^2)*Cl_r)/(2*I_xx_B*U_1);
L_dela = (q_bar*S*b*Cl_dela)/I_xx_B;
L_delr = (q_bar*S*b*Cl_delr)/I_xx_B;
NB = (q_bar*S*b*Cn_B)/I_zz_B;
NT_B = (q_bar*S*b*Cn_TB)/I_zz_B;
Np = (q_bar*S*(b^2)*Cn_p)/(2*I_zz_B*U_1);
Nr = (q_bar*S*(b^2)*Cn_r)/(2*I_zz_B*U_1);
N_dela = (q_bar*S*b*Cn_dela)/I_zz_B;
N_delr = (q_bar*S*b*Cn_delr)/I_zz_B;
% Perturbed Lateral-Directional Equations of Motion
A_1 = I_xz_B/I_xx_B;
B_1 = I_xz_B/I_zz_B;
% Numerator Polynomial
AB = Y_dela*(1 - A_1*B_1) + Y_delr*(1 - A_1*B_1);
BB = - Y_dela*(Nr + Lp + A_1*Np + B_1*Lr) - Y_delr*(Nr + Lp + A_1*Np + B_1*Lr) + Yp*(L_dela + N_dela*A_1) + Yp*(L_delr + N_delr*A_1) + Yr*(L_dela*B_1 + N_dela) + Yr*(L_delr*B_1 + N_delr) - U_1*(L_dela*B_1 + N_dela) + U_1*(L_delr*B_1 + N_delr);
CB = Y_dela*(Lp*Nr - Np*Lr) + Y_delr*(Lp*Nr - Np*Lr) + Yp*(N_dela*Lr - L_dela*Nr) + Yp*(N_delr*Lr - L_delr*Nr) + g*cos(theta1)*(L_dela + N_dela*A_1) + g*cos(theta1)*(L_delr + N_delr*A_1) + Yr*(L_dela*Np - N_dela*Lp) + Yr*(L_delr*Np - N_delr*Lp) + U_1*(L_dela*Np - N_dela*Lp) + U_1*(L_delr*Np - N_delr*Lp);
DB = g*cos(theta1)*(N_dela*Lr-L_dela*Nr)+g*cos(theta1)*(N_delr*Lr-L_delr*Nr);
N_B = [AB BB CB DB];
% Denominator Polynomial
A2 = U_1*(1 - A_1*B_1);
B2 = - YB*(1 - A_1*B_1) - U_1*(Lp + Nr + A_1*Np + B_1*Lr);
C2 = U_1*(Lp*Nr - Lr*Np) + YB*(Nr + Lp + A_1*Np + B_1*Lr) - Yp*(LB + NB*A_1 + NT_B*A_1) + U_1*(LB*B_1 + NB + NT_B) - Yr*(LB*B_1 + NB + NT_B);
D2 = - YB*(Lp*Nr - Lr*Np) + Yp*(LB*Nr - NB*Lr - NT_B*Lr) - g*cos(theta1)*(LB + NB*A_1 + NT_B*A_1) + U_1*(LB*Np - NB*Lp - NT_B*Lp) - Yr*(LB*Np - NB*Lp - NT_B*Lp);
E2 = g*cos(theta1)*(LB*Nr - NB*Lr - NT_B*Lr);
D_2 = [A2 B2 C2 D2 E2];
% Transfer Function
Approach_sys = tf(N_B, D_2)
damp(Approach_sys)
step(Approach_sys)
end
  2 Commenti
Jeffrey Lewis
Jeffrey Lewis il 4 Nov 2022
This is the approach I was looking for, thank you! The only issue I am facing with this structure is I am not getting an output on my end. Is there anything extra I need to do at the end to call the functions or should I expect the out put to show my TF as you have displayed?
I have written code for a previous homework that only includes one flight condition and it still outputs the TF as you have shown but now that I have all three conditions in this function structure, MATLAB is not outputting anything.
clc
clear all
function climb_sys
g = 32.174;
theta1 = 0;
%Cessna design parameters
S = 174; %Planform Area (ft^2)
c = 4.9; %Chord length (ft)
b = 36.0; %Wing span (ft)
%%%%%%%%%%%%%%%%Flight Conditions%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Climb Flight Condition
altitude = 0;
M = 0.120;
U_1 = 133.5;
q_bar = 21.2;
c_frac = 26.2;
a_1 = 5.4;
%%%%%%%%%%%%%%%%Mass Data For All Flight Conditions%%%%%%%%%%%%%%%%%%%%%%
%Mass Data in Climb, Cruise, and Approach Conditions
W = 2650; %Weight (lbs)
m = W/g; %Mass
I_xx_B = 948; %Moment of Inertia along the X-axis (slug-ft^2)
I_yy_B = 1346; %Moment of Inertia along the Y-axis (slug-ft^2)
I_zz_B = 1967; %Moment of Inertia along the Z-axis (slug-ft^2)
I_xz_B = 0; %Moment of Inertia along the XZ plane (slug-ft^2)
%%%%%%%%%%%%%%%%%%%%%%%Longitudinal Control and Hinge Momoment $$$$$$$$$
%Climb Longitudinal Control and Hinge Moment Derivatives
Ch_a = -0.0545;
Ch_del_e = -0.594;
%%%%%%%%%%%%%%%%%%%Lateral-Directional Stability%%%%%%%%%%%%%%%%%%%%
%Climb Lateral-Directional Stabillity Derivatives
Cl_B = -0.0895;
Cl_p = -0.487;
Cl_r = 0.1869;
Cy_B = -0.404;
Cy_p = -0.145;
Cy_r = 0.267;
Cn_B = 0.0907;
Cn_TB = 0;
Cn_p = -0.0649;
Cn_r = -0.1199;
%%%%%%%%%%%%%%%%%%%%Lateral-Directional Control and Hing Moment%%%%%%%%%
%Climb Lateral-Directional Control and Hinge Moment Derivatives
Cl_dela = 0.229;
Cl_delr = 0.0147;
Cy_dela = 0;
Cy_delr = 0.187;
Cn_dela = -0.0504;
Cn_delr = -0.0805;
Ch_aa = 0;
Ch_dela = -0.369;
Ch_Br = 0.0819;
Ch_delr = -0.579;
%Lateral-Directional Dimensional Stability Derivatives
YB = (q_bar*S*Cy_B)/m;
Yp = (S*b*Cy_p)/(2*m*U_1);
Yr = (q_bar*S*b*Cy_r)/(2*m*U_1);
Y_dela = (q_bar*S*Cy_dela)/m;
Y_delr = (q_bar*S*Cy_delr)/m;
LB = (q_bar*S*b*Cl_B)/I_xx_B;
Lp = (q_bar*S*(b^2)*Cl_p)/(2*I_xx_B*U_1);
Lr = (q_bar*S*(b^2)*Cl_r)/(2*I_xx_B*U_1);
L_dela = (q_bar*S*b*Cl_dela)/I_xx_B;
L_delr = (q_bar*S*b*Cl_delr)/I_xx_B;
NB = (q_bar*S*b*Cn_B)/I_zz_B;
NT_B = (q_bar*S*b*Cn_TB)/I_zz_B;
Np = (q_bar*S*(b^2)*Cn_p)/(2*I_zz_B*U_1);
Nr = (q_bar*S*(b^2)*Cn_r)/(2*I_zz_B*U_1);
N_dela = (q_bar*S*b*Cn_dela)/I_zz_B;
N_delr = (q_bar*S*b*Cn_delr)/I_zz_B;
%Perturbed Lateral-Directional Equations of Motion
A_1 = I_xz/I_xx_B;
B_1 = I_xz/I_zz_B;
%Denominator Polynomial
A2 = U_1(1-A_1*B_1);
B2 = -YB*(1-A_1*B_1)-U_1*(Lp+Nr+A_1*Np+B_1*Lr);
C2 = U_1*(Lp*Nr-Lr*Np)+YB*(Nr+Lp+A_1*Np+B_1*Lr)-Yp*(LB+NB*A_1+NT_B*A_1)...
+U_1*(LB*B_1+NB+NT_B)-Yr*(LB*B_1+NB+NT_B);
D2 = -YB*(Lp*Nr-Lr*Np)+Yp*(LB*Nr-NB*Lr-NT_B*Lr)-g*cos(theta1)...
*(LB+NB*A_1+NT_B*A_1)+U_1*(LB*Np-NB*Lp-NT_B*Lp)-Yr*(LB*Np-NB*Lp-NT_B*Lp);
E2 = g*cos(theta1)*(LB*Nr-NB*Lr-NT_B*Lr);
D_2 = [A2 B2 C2 D2 E2];
%Numerator Polynomial
AB = Y_dela*(1-A_1*B_1)+Y_delr*(1-A_1*B_1);
BB = -Y_dela*(Nr+Lp+A_1*Np+B_1*Lr)-Y_delr*(Nr+Lp+A_1*Np+B_1*Lr)+Yp*(L_dela+N_dela*A_1)+Yp*(L_delr+N_delr*A_1)...
+Yr*(L_dela*B_1+N_dela)+Yr*(L_delr*B_1+N_delr)-U_1*(L_dela*B_1+N_dela)...
+U_1*(L_delr*B_1+N_delr);
CB = Y_dela*(Lp*Nr-Np*Lr)+Y_delr*(Lp*Nr-Np*Lr)+Yp*(N_dela*Lr-L_dela*Nr)+Yp*(N_delr*Lr-L_delr*Nr)...
+g*cos(theta1)*(L_dela+N_dela*A_1)+g*cos(theta1)*(L_delr+N_delr*A_1)...
+Yr*(L_dela*Np-N_dela*Lp)+Yr*(L_delr*Np-N_delr*Lp)+U_1*(L_dela*Np-N_dela*Lp)+U_1*(L_delr*Np-N_delr*Lp);
DB = g*cos(theta1)*(N_dela*Lr-L_dela*Nr)+g*cos(theta1)*(N_delr*Lr-L_delr*Nr);
N_B = [AB BB CB DB];
%Transfer Function
climb_sys = tf(N_B,D_2);
damp(climb_sys);
end
function cruise_sys
g = 32.174
theta1 = 0
%Cessna design parameters
S = 174 %Planform Area (ft^2)
c = 4.9 %Chord length (ft)
b = 36.0 %Wing span (ft)
%%%%%%%%%%%%%%%%Flight Conditions%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Cruise Flight Condition
h = 5000 %Altitude (ft)
M = 0.201 %Mach Number
U_1 = 220.1 %TAS (ft/s)
q_bar = 49.6 %Dynamic Pressure (lbs/ft^2)
c_frac = 26.4 %CG Location
a_1 = 0 %Angle of Attack (Deg)
%%%%%%%%%%%%%%%%Mass Data For All Flight Conditions%%%%%%%%%%%%%%%%%%%%%%
%Mass Data in Climb, Cruise, and Approach Conditions
W = 2650 %Weight (lbs)
m = W/g %Mass
I_xx_B = 948 %Moment of Inertia along the X-axis (slug-ft^2)
I_yy_B = 1346 %Moment of Inertia along the Y-axis (slug-ft^2)
I_zz_B = 1967 %Moment of Inertia along the Z-axis (slug-ft^2)
I_xz_B = 0 %Moment of Inertia along the XZ plane (slug-ft^2)
%%%%%%%%%%%%%%%%%%%%%%%Longitudinal Control and Hinge Momoment $$$$$$$$$
%Cruise Longitudinal Control and Hinge Moment Derivatives
Ch_a = -0.0584
Ch_del_e = -0.585
%%%%%%%%%%%%%%%%%%%Lateral-Directional Stability%%%%%%%%%%%%%%%%%%%%
%Cruise Lateral-Directional Stability Derivatives
Cl_B = -0.0923
Cl_p = -0.484
Cl_r = 0.0798
Cy_B = -0.393
Cy_p = -0.075
Cy_r = 0.214
Cn_B = 0.0587
Cn_TB = 0
Cn_p = -0.0278
Cn_r = -0.0937
%%%%%%%%%%%%%%%%%%%%Lateral-Directional Control and Hing Moment%%%%%%%%%
%Cruise Lateral-Directional Control and Hinge Moment Derivatives
Cl_dela = 0.229
Cl_delr = 0.0147
Cy_dela = 0
Cy_delr = 0.187
Cn_dela = -0.0216
Cn_delr = -0.0645
Ch_aa = 0
Ch_dela = -0.363
Ch_Br = 0.0819
Ch_delr = -0.567
%Lateral-Directional Dimensional Stability Derivatives
YB = (q_bar*S*Cy_B)/m
Yp = (S*b*Cy_p)/(2*m*U_1)
Yr = (q_bar*S*b*Cy_r)/(2*m*U_1)
Y_dela = (q_bar*S*Cy_dela)/m
Y_delr = (q_bar*S*Cy_delr)/m
LB = (q_bar*S*b*Cl_B)/I_xx_B
Lp = (q_bar*S*(b^2)*Cl_p)/(2*I_xx_B*U_1)
Lr = (q_bar*S*(b^2)*Cl_r)/(2*I_xx_B*U_1)
L_dela = (q_bar*S*b*Cl_dela)/I_xx_B
L_delr = (q_bar*S*b*Cl_delr)/I_xx_B
NB = (q_bar*S*b*Cn_B)/I_zz_B
NT_B = (q_bar*S*b*Cn_TB)/I_zz_B
Np = (q_bar*S*(b^2)*Cn_p)/(2*I_zz_B*U_1)
Nr = (q_bar*S*(b^2)*Cn_r)/(2*I_zz_B*U_1)
N_dela = (q_bar*S*b*Cn_dela)/I_zz_B
N_delr = (q_bar*S*b*Cn_delr)/I_zz_B
%Perturbed Lateral-Directional Equations of Motion
A_1 = I_xz/I_xx_B
B_1 = I_xz/I_zz_B
%Denominator Polynomial
A2 = U_1(1-A_1*B_1)
B2 = -YB*(1-A_1*B_1)-U_1*(Lp+Nr+A_1*Np+B_1*Lr)
C2 = U_1*(Lp*Nr-Lr*Np)+YB*(Nr+Lp+A_1*Np+B_1*Lr)-Yp*(LB+NB*A_1+NT_B*A_1)...
+U_1*(LB*B_1+NB+NT_B)-Yr*(LB*B_1+NB+NT_B)
D2 = -YB*(Lp*Nr-Lr*Np)+Yp*(LB*Nr-NB*Lr-NT_B*Lr)-g*cos(theta1)...
*(LB+NB*A_1+NT_B*A_1)+U_1*(LB*Np-NB*Lp-NT_B*Lp)-Yr*(LB*Np-NB*Lp-NT_B*Lp)
E2 = g*cos(theta1)*(LB*Nr-NB*Lr-NT_B*Lr)
D_2 = [A2 B2 C2 D2 E2]
%Numerator Polynomial
AB = Y_dela*(1-A_1*B_1)+Y_delr*(1-A_1*B_1)
BB = -Y_dela*(Nr+Lp+A_1*Np+B_1*Lr)-Y_delr*(Nr+Lp+A_1*Np+B_1*Lr)+Yp*(L_dela+N_dela*A_1)+Yp*(L_delr+N_delr*A_1)...
+Yr*(L_dela*B_1+N_dela)+Yr*(L_delr*B_1+N_delr)-U_1*(L_dela*B_1+N_dela)...
+U_1*(L_delr*B_1+N_delr)
CB = Y_dela*(Lp*Nr-Np*Lr)+Y_delr*(Lp*Nr-Np*Lr)+Yp*(N_dela*Lr-L_dela*Nr)+Yp*(N_delr*Lr-L_delr*Nr)...
+g*cos(theta1)*(L_dela+N_dela*A_1)+g*cos(theta1)*(L_delr+N_delr*A_1)...
+Yr*(L_dela*Np-N_dela*Lp)+Yr*(L_delr*Np-N_delr*Lp)+U_1*(L_dela*Np-N_dela*Lp)+U_1*(L_delr*Np-N_delr*Lp)
DB = g*cos(theta1)*(N_dela*Lr-L_dela*Nr)+g*cos(theta1)*(N_delr*Lr-L_delr*Nr)
N_B = [AB BB CB DB]
%Transfer Function
cruise_sys = tf(N_B,D_2)
damp(cruise_sys)
end
function approach_sys
g = 32.174
theta1 = 0
%Cessna design parameters
S = 174 %Planform Area (ft^2)
c = 4.9 %Chord length (ft)
b = 36.0 %Wing span (ft)
%%%%%%%%%%%%%%%%Flight Conditions%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Approach Flight Condition
h = 0
M = 0.096
U_1 = 107.1
q_bar = 13.6
c_frac = 26.4
a_1 = 4
%%%%%%%%%%%%%%%%Mass Data For All Flight Conditions%%%%%%%%%%%%%%%%%%%%%%
%Mass Data in Climb, Cruise, and Approach Conditions
W = 2650 %Weight (lbs)
m = W/g %Mass
I_xx_B = 948 %Moment of Inertia along the X-axis (slug-ft^2)
I_yy_B = 1346 %Moment of Inertia along the Y-axis (slug-ft^2)
I_zz_B = 1967 %Moment of Inertia along the Z-axis (slug-ft^2)
I_xz_B = 0 %Moment of Inertia along the XZ plane (slug-ft^2)
%%%%%%%%%%%%%%%%%%%%%%%Longitudinal Control and Hinge Momoment $$$$$$$$$
%Approach Longitudinal Control and Hinge Moment Derivatives
Ch_a = -0.0549
Ch_del_e = -0.594
%%%%%%%%%%%%%%%%%%%Lateral-Directional Stability%%%%%%%%%%%%%%%%%%%%
%Approach Lateral-Directional Stability Derivatives
Cl_B = -0.0969
Cl_p = -0.494
Cl_r = 0.2039
Cy_B = -0.303
Cy_p = -0.213
Cy_r = 0.201
Cn_B = 0.0701
Cn_TB = 0
Cn_p = -0.0960
Cn_r = -0.1151
%%%%%%%%%%%%%%%%%%%%Lateral-Directional Control and Hing Moment%%%%%%%%%
%Approach Lateral-Directional Control and Hinge moment Derivatives
Cl_dela = 0.229
Cl_delr = 0.0147
Cy_dela = 0
Cy_delr = 0.187
Cn_dela = -0.0504
Cn_delr = -0.0805
Ch_aa = 0
Ch_dela = -0.369
Ch_Br = 0.0819
Ch_delr = -0.579
%Lateral-Directional Dimensional Stability Derivatives
YB = (q_bar*S*Cy_B)/m
Yp = (S*b*Cy_p)/(2*m*U_1)
Yr = (q_bar*S*b*Cy_r)/(2*m*U_1)
Y_dela = (q_bar*S*Cy_dela)/m
Y_delr = (q_bar*S*Cy_delr)/m
LB = (q_bar*S*b*Cl_B)/I_xx_B
Lp = (q_bar*S*(b^2)*Cl_p)/(2*I_xx_B*U_1)
Lr = (q_bar*S*(b^2)*Cl_r)/(2*I_xx_B*U_1)
L_dela = (q_bar*S*b*Cl_dela)/I_xx_B
L_delr = (q_bar*S*b*Cl_delr)/I_xx_B
NB = (q_bar*S*b*Cn_B)/I_zz_B
NT_B = (q_bar*S*b*Cn_TB)/I_zz_B
Np = (q_bar*S*(b^2)*Cn_p)/(2*I_zz_B*U_1)
Nr = (q_bar*S*(b^2)*Cn_r)/(2*I_zz_B*U_1)
N_dela = (q_bar*S*b*Cn_dela)/I_zz_B
N_delr = (q_bar*S*b*Cn_delr)/I_zz_B
%Perturbed Lateral-Directional Equations of Motion
A_1 = I_xz/I_xx_B
B_1 = I_xz/I_zz_B
%Denominator Polynomial
A2 = U_1(1-A_1*B_1)
B2 = -YB*(1-A_1*B_1)-U_1*(Lp+Nr+A_1*Np+B_1*Lr)
C2 = U_1*(Lp*Nr-Lr*Np)+YB*(Nr+Lp+A_1*Np+B_1*Lr)-Yp*(LB+NB*A_1+NT_B*A_1)...
+U_1*(LB*B_1+NB+NT_B)-Yr*(LB*B_1+NB+NT_B)
D2 = -YB*(Lp*Nr-Lr*Np)+Yp*(LB*Nr-NB*Lr-NT_B*Lr)-g*cos(theta1)...
*(LB+NB*A_1+NT_B*A_1)+U_1*(LB*Np-NB*Lp-NT_B*Lp)-Yr*(LB*Np-NB*Lp-NT_B*Lp)
E2 = g*cos(theta1)*(LB*Nr-NB*Lr-NT_B*Lr)
D_2 = [A2 B2 C2 D2 E2]
%Numerator Polynomial
AB = Y_dela*(1-A_1*B_1)+Y_delr*(1-A_1*B_1)
BB = -Y_dela*(Nr+Lp+A_1*Np+B_1*Lr)-Y_delr*(Nr+Lp+A_1*Np+B_1*Lr)+Yp*(L_dela+N_dela*A_1)+Yp*(L_delr+N_delr*A_1)...
+Yr*(L_dela*B_1+N_dela)+Yr*(L_delr*B_1+N_delr)-U_1*(L_dela*B_1+N_dela)...
+U_1*(L_delr*B_1+N_delr)
CB = Y_dela*(Lp*Nr-Np*Lr)+Y_delr*(Lp*Nr-Np*Lr)+Yp*(N_dela*Lr-L_dela*Nr)+Yp*(N_delr*Lr-L_delr*Nr)...
+g*cos(theta1)*(L_dela+N_dela*A_1)+g*cos(theta1)*(L_delr+N_delr*A_1)...
+Yr*(L_dela*Np-N_dela*Lp)+Yr*(L_delr*Np-N_delr*Lp)+U_1*(L_dela*Np-N_dela*Lp)+U_1*(L_delr*Np-N_delr*Lp)
DB = g*cos(theta1)*(N_dela*Lr-L_dela*Nr)+g*cos(theta1)*(N_delr*Lr-L_delr*Nr)
N_B = [AB BB CB DB]
%Transfer Function
appoach_sys = tf(N_B,D_2)
damp(appoach_sys)
end
Sam Chak
Sam Chak il 4 Nov 2022
Hi @Jeffrey Lewis
I actually added the step function in the code to generate step response for each flight condition. Step response always start
https://www.mathworks.com/help/ident/ref/lti.step.html
You can also try the lsim(sys, u, t, x0) function for a more realistic simulated response data because you can design the the input signal u, and specify the initial condition x0. However, you must convert sys from transfer function into a state-space model (preferably in controllable canonical form)
https://www.mathworks.com/help/ident/ref/lti.lsim.html

Accedi per commentare.

Più risposte (0)

Categorie

Scopri di più su Unified Modeling in Help Center e File Exchange

Tag

Prodotti


Release

R2021a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by