function u = ctrl_operation_lqr(t, x, plant, ref)
% CTRL_OPERATION_LQR  Full-state feedback for operation mode.
%
%  u = -K * (x - x_op),   K from LQR on (A, B) at x_op.
%
%  Advantages over ctrl_operation (plain P on T_avg):
%    - Damps the fast neutronics and the slow thermal response jointly.
%    - Adds NO state (K is 1x10, feedback is memoryless).
%    - Closed-loop A_cl = A - B*K is trivially propagable for reachability.
%
%  Q/R are persistently cached on the first call.  If the caller mutates
%  plant after the first invocation, gains become stale — clear `persistent`
%  by restarting MATLAB.  That's a reach-analysis bookkeeping issue, not a
%  runtime one.
%
%  Weighting rationale:
%    Q diagonal:
%       n        -> 1          (power tracking matters)
%       C1..C6   -> 1e-3       (precursor deviations are informational)
%       T_f      -> 1e-2       (care about it but not as much as coolant)
%       T_c      -> 1e2        (primary objective)
%       T_cold   -> 1          (secondary but consequential)
%    R = 1e6    (discourage large rod movements — one Kp of |u| ~ 1e-3)
%
%  Inputs:
%    t, x, plant, ref - standard signature.  ref is unused; the setpoint
%                       is baked in as x_op.  If you want to track a
%                       different operating point, regenerate K there.

    persistent K x_op_cached

    if isempty(K)
        x_op_cached = pke_initial_conditions(plant);
        [A, B, ~] = pke_linearize(plant, x_op_cached, 0, plant.P0);

        Q = diag([1, ...
                  1e-3, 1e-3, 1e-3, 1e-3, 1e-3, 1e-3, ...
                  1e-2, 1e2, 1]);
        R = 1e6;

        % MATLAB's lqr requires Control System Toolbox.  Fall back to
        % icare (in base MATLAB from R2019a) if lqr is unavailable.
        try
            K = lqr(A, B, Q, R);
        catch
            [~, ~, K_ric] = icare(A, B, Q, R);
            K = K_ric;
        end
    end

    u = -K * (x - x_op_cached);

end