Aircraft pitch angle response to elevator inputs
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Is it possible to form a simulink block diagram based upon the image below. The code below are the equations for the given variables, where delta eta is the elevator input.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1574012/image.jpeg)
% short period
% constant variables
rho = 0.905;
S = 64.8;
c = 2.51;
a = 5.3;
h_n = 0.63;
h_fwd = 0.18;
h_ac = 0.27;
I_yy = 136182.4308;
V_bar_t = 0.72;
a_1 = 4.33;
a_2 = 2.16;
a_3 = 0.47;
DWG = 0.4;
d_T = 11.2259;
V_cruise = 138.283;
% damping ratio
zeta = sqrt((rho*S*c)/(8*(h_n-h_fwd)*a*I_yy))*(V_bar_t*a_1*d_T);
% natural frequency
omega_n_cruise = V_cruise*sqrt(((rho*S*c*a*(h_n-h_fwd))/(2*I_yy)));
% damped frequency
omega_d_cruise = omega_n_cruise*sqrt(1-(zeta^2));
% elevator sensitivity
k_eta = -(V_bar_t*a_2)/((h_n - h_fwd)*a);
% change in pitching moment
delta_C_M = ((h_fwd - h_ac)*delta_C_L) - (V_bar_t*delta_C_L_T);
% change in lift coefficient
delta_C_L = a*delta_theta;
% change in tail lift coefficient
delta_C_L_T = a_1*delta_alpha_T + a_2*delta_eta;
% based on the following relationships
delta_alpha = delta_theta;
delta_beta = 0;
% change in angle of attack
delta_alpha_T = (delta_theta(1-DWG)) + ((q*d_T)/V_cruise);
% angle of attack
alpha_T = (alpha(1-DWG)) + psi_T;
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Answers (1)
Sam Chak
on 21 Dec 2023
If all the equations are correct, you can use the MATLAB Function block to enter each equation.
For an example, refer to:
Nevertheless, I recommend simulating the aircraft pitch dynamics in MATLAB before constructing the blocks in Simulink. By the way, I don't see the aircraft pitch dynamics in your code. Don't miss it.
3 Comments
Sam Chak
on 21 Dec 2023
The 2nd-order differential equation of the pitch dynamics that you posted is linear. Thus, you can use a single state-space block to represent that system. The values for the parameters
, ζ, and
can be calculated by hand or computed in MATLAB.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1574197/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1574202/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1574207/image.png)
Please write out the state-space model. This should be covered in the Aircraft course.
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