How to add trim values on to a linear models output?

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Daniel Jackson
Daniel Jackson 2024-3-21
回答： Nipun 2024-6-11
I am comparing a nonlinear model to a linear model, a short elevator input over 10s is used for the input for both the linear and non linear models. And as linear models are defined by deltas around an operating point I was wondering how I would go about adding trim values to the linear model output.
%% Set aircraft parameters
m = 18000;
S = 64.8;
rho = 0.905;
g = 9.81;
a1 = 4.33;
a2 = 2.16;
a3 = 0.47;
b1 = -0.11;
b2 = -0.64;
DWG = 0.4;
S_T = 10.7;
l_T = 11;
c = 2.51;
h_fwd = 0.18; % 0.1 - 0.3
h_aft = 0.66; % 0.6 - 0.7
psi_T = -5.5 * pi / 180;
I_yy = 136182.4308;
I_xx = 236000;
I_zz = 355000;
I_xz = 0;
% Set Aero parameters
a = 5.3;
h_AC = 0.27;
C_L_Max = 1.2;
C_M_0 = -0.06;
% Set CG
h = h_fwd;
% Calculate intermediate groups
V_T = S_T * l_T / (S * c);
d_T = l_T - (h-h_AC)*c;
h_n = h_AC + V_T * (a1/a)*(1-DWG);
% Calculate speed parameters
V_Stall = sqrt(2*m*g/(rho * S * C_L_Max)) * 1.94;
V_Max = 336;
V_C = 268.8;
V_1 = 210;
V_2 = 315;
C_L_Cruise = 2 * m * g / ((V_C/1.94)^2 * S * rho);
C_L_VMax = 2 * m * g / ((V_Max/1.94)^2 * S * rho);
% Set Speed
V = V_C/1.94;
% Drag parameters
C_D_0 = 0.011;
k = 0.041263048;
% Set thrust derivative
dEpsdT = 300;
%% Run 3DoF model
eta_step = -5;
eta_step_t = 0.5;
A = [-0.00787490219865814,0.0914386059970311,-8.15800578286344,-9.80848204812432;
-0.0705390429309272,-1.20661074126797,138.553434891686,0.172568561106160;
0.0103919494442555,-0.176494149311203,-2.63846804739098,0;
0,0,1,0];
B = [0.016666666666667,0;0,0;0,-16.272914167767752;0,0];
C = [1,0,0,0;
0,1,0,0;
0,0,1,0;
0,0,0,1;
0.998271075633783,0.0587780534943110,0,0;
0.000423493150696744,-0.00719249682384279,0,1];
D_0 = [0,0;0,0;0,0;0,0;0,0;0,0];
The linear model has been constructed by trimming the non linear model and using its matrix outputs. Attached is the simulink model and MATLAB code.

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回答（1 个）

Nipun
Nipun 2024-6-11
Hi Daniel,
I understand that you are trying to compare a nonlinear model to a linear model and need to add trim values to the linear model output. Here is how you may do it:
% Define the trim values (assumed example values, update as needed)
trim_values = [trim_x1, trim_x2, trim_x3, trim_x4]; % Replace with actual trim values
% Set up your linear model response
linear_response = lsim(A, B, C, D_0, input_signal, t);
% Add trim values to the linear model output
linear_response_trimmed = linear_response + trim_values;
% Plot to compare
figure;
plot(t, nonlinear_response, 'r', t, linear_response_trimmed, 'b');
legend('Nonlinear Model', 'Linear Model with Trim');
xlabel('Time (s)');
ylabel('Response');
title('Comparison of Nonlinear and Linear Models');
Refer to the following MathWorks documentation for more information for plotting dynamic system reponse: https://www.mathworks.com/help/control/ref/lsim.html
Hope this helps.
Regards,
Nipun

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