How to maintain eigenvalues sequence

1 次查看（过去 30 天）

显示更早的评论

준호 2023-12-2

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2056594-how-to-maintain-eigenvalues-sequence

编辑： Anusha Sridharan 2023-12-5

在 MATLAB Online 中打开

Hello,

I have to draw root-locus for longitudinal motion; Short Period Mode and Phugoid Mode. Here is a code

%% Dynamics
Vp = 111.174
A_lon = [-0.0283  0.3139 -11.0665 -32.0344;
    -0.4204 -1.5452 108.6931 -3.2616; 
    0.0205 -0.2011 -3.5080   0; 
    0       0       1        0]
B_lon = [0.0115 0.1150;
    -0.2185 0;
    -0.3591 0;
    0      0]
C_lon = [1  0 0 0;
    0 -1 0 Vp]
%% LQR Servo Design
A_servo = [A_lon zeros(4,2);
    -C_lon zeros(2,2)]
B_servo = [B_lon ; zeros(2,2)]
n = 100; a = logspace(-2,2,n);
for i = 1:n
    Q = a(i)*[1 0   0   0     0 0;
        0 1   0  -Vp      0 0;
        0 0   0  0          0 0;
        0 -Vp 0 power(Vp,2) 0 0;
        0 0   0   0         1 0;
        0 0   0   0         0 1];
    R = eye(2);
    
    [K,S,P] = lqr(A_servo,B_servo,Q,R);
    p_cl = P;
    cl_sh(i,1) = p_cl(5); cl_sh(i,2) = p_cl(6);
    cl_ph(i,1) = p_cl(3); cl_ph(i,2) = p_cl(4);
end
%% Plot
figure;
plot(real(cl_sh(:,1)), imag(cl_sh(:,1)), '+', real(cl_sh(:,2)), imag(cl_sh(:,2)), 'x', MarkerSize=5);
title("Root Locus of Short Period Mode")
xlabel("real")
ylabel("imag")
grid on;
figure;
plot(real(cl_ph(:,1)), imag(cl_ph(:,1)), '+', real(cl_ph(:,2)), imag(cl_ph(:,2)), 'x', MarkerSize=5)
title("Root Locus of Phugoid Mode")
xlabel("real")
ylabel("imag")
grid on;

When the code is executed, the sequence of eigenvalues is misaligned from some point in the iteration statement and the point was depended on weight of Q, R matrix. So when the sequence of eigenvalues is out of order from a certain point in time like this, how should we modify the code to solve it?