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

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규연
규연 on 28 Mar 2024 at 11:10
Commented: 규연 on 28 Mar 2024 at 12:18
Ran in:
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
  1 Comment
규연
규연 on 28 Mar 2024 at 11:20
I don't know why, but L_lqr(9x1) matrix's components are all complex number.

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Accepted Answer

Sam Chak
Sam Chak on 28 Mar 2024 at 11:29
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.
  2 Comments
Sam Chak
Sam Chak on 28 Mar 2024 at 12:05
Ran in:
%% 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
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X = 2×2
2.0000 1.0000 1.0000 2.0000
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L = 2×1
-1.0000 -1.0000
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%% 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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K = 1×2
1.0000 2.0000
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L = 2×1
-1.0000 -1.0000
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규연
규연 on 28 Mar 2024 at 12:18
i think the system has the problem.
i'll try lqr controller for another system.
thank you!

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