icare function doesn't return the value for X_lqr, K_lqr.

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규연 2024-3-28

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2100091-icare-function-doesn-t-return-the-value-for-x_lqr-k_lqr

评论： 규연 2024-3-28

采纳的回答： Sam Chak

在 MATLAB Online 中打开

I using icare function for the lqr controller.

Alift is 9x9 matrix, Blift is 9x1 matrix, Q is 9x9 identity matrix, and R is 1.

Alift, Blift matrix is work well.

But it only return the L_lqr(9x1) matrix.

What is the problem?

Below is my code.

x_ref = [5 5]';
x_ref_lift = liftFtn(x_ref);
Unrecognized function or variable 'liftFtn'.
[X_lqr, K_lqr, L_lqr] = icare(Alift, Blift, Q, R);
for m = 1 : Nsim - 1
    u = -K_lqr * (xlift2(:, end) - x_ref_lift);
    xlift2 = [xlift2, Alift * xlift2(:, end) + Blift * u]; % Lifted dynamics
end

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규연 2024-3-28

I don't know why, but L_lqr(9x1) matrix's components are all complex number.

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Answer 1

Sam Chak 2024-3-28

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2100091-icare-function-doesn-t-return-the-value-for-x_lqr-k_lqr#answer_1432796

OP: I don't know why, but L_lqr(9x1) matrix's components are all complex number.

The description in icare() documentation says that the syntax "[X,K,L] = icare(A,B,Q,R,S,E,G)" computes the unique stabilizing solution X, state-feedback gain K, and the closed-loop eigenvalues L of the following continuous-time algebraic Riccati equation.

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Sam Chak 2024-3-28

在 MATLAB Online 中打开

%% Double Integrator system, x" = u
A    = [0 1;
        0 0];
B    = [0;
        1];
%% Settings to force the Controller for a critically-damped response, u = – 2·x' – x
Q    = diag([1 2]);
R    = 1;
%% Tuning by LQR method
[K, X, L] = lqr(A, B, Q, R)
K = 1×2
    1.0000    2.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
X = 2×2
    2.0000    1.0000
    1.0000    2.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
L = 2×1
   -1.0000
   -1.0000
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<mw-icon class=""></mw-icon>
%% Tuning by solving Continuous-time Algebraic Riccati Equations
[X, K, L] = icare(A, B, Q, R)
X = 2×2
    2.0000    1.0000
    1.0000    2.0000
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<mw-icon class=""></mw-icon>
K = 1×2
    1.0000    2.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
L = 2×1
   -1.0000
   -1.0000
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>