d2997c2861
Fill out the DRC mode set with ctrl_shutdown (u = -5*beta), ctrl_scram (u = -8*beta), and ctrl_heatup (feedback-linearizing P on ramped T_avg reference, saturated u, no integrator). Add ctrl_operation_lqr as a full-state-feedback counterpart to ctrl_operation — K cached, closed-loop essentially perfect under the 100%->80% Q_sg step where plain P has ~5F overshoot. Add pke_linearize for numerical (A, B, B_w) Jacobians at any operating point; test_linearize confirms ~4e-4 rel err vs nonlinear sim for a 5% Q_sg step. Extend pke_solver with an optional x0 argument so each mode can start from a plausible IC. main_mode_sweep.m exercises all five modes back-to-back and saves the 4-panel plots. CLAUDE.md updated with model-validity-range note (trust region is ~+/-50C around operating point; true cold shutdown is out of scope for the linear feedback coefficients). Hacker-Split: build out control layer end-to-end for reachability. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
55 lines
2.1 KiB
Matlab
55 lines
2.1 KiB
Matlab
function [A, B, B_w, x_star, u_star, Q_star] = pke_linearize(plant, x_star, u_star, Q_star)
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% PKE_LINEARIZE Numerical Jacobians of the PKE+T/H RHS at an operating point.
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%
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% Computes (A, B, B_w) such that, for small perturbations dx, du, dw
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% around (x_star, u_star, Q_star):
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%
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% dx/dt ~ A*dx + B*du + B_w*dw, where w = Q_sg.
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%
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% Uses central finite differences. Step sizes are scaled to each
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% variable's magnitude; fall back to an absolute epsilon near zero.
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%
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% Inputs:
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% plant - parameter struct from pke_params()
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% x_star - (optional) 10x1 linearization point; default = operating x0
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% u_star - (optional) scalar control; default = 0
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% Q_star - (optional) scalar SG heat removal [W]; default = plant.P0
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%
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% Outputs:
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% A - 10x10 state Jacobian df/dx
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% B - 10x1 input Jacobian df/du
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% B_w - 10x1 disturbance Jacobian df/d(Q_sg)
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% x_star, u_star, Q_star - echoed back for the caller's records
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if nargin < 2 || isempty(x_star), x_star = pke_initial_conditions(plant); end
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if nargin < 3 || isempty(u_star), u_star = 0; end
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if nargin < 4 || isempty(Q_star), Q_star = plant.P0; end
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n = numel(x_star);
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eps_rel = 1e-6;
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eps_abs = 1e-8;
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% Wrap the RHS as a function of (x, u, w) with plant fixed.
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f = @(x, u, w) pke_th_rhs(0, x, plant, @(t) w, u);
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f0 = f(x_star, u_star, Q_star); %#ok<NASGU> % sanity slot
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% --- A: df/dx via central differences, column by column ---
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A = zeros(n, n);
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for k = 1:n
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h = max(eps_rel * abs(x_star(k)), eps_abs);
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xp = x_star; xp(k) = xp(k) + h;
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xm = x_star; xm(k) = xm(k) - h;
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A(:, k) = (f(xp, u_star, Q_star) - f(xm, u_star, Q_star)) / (2*h);
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end
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% --- B: df/du ---
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h = max(eps_rel * abs(u_star), eps_abs);
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B = (f(x_star, u_star + h, Q_star) - f(x_star, u_star - h, Q_star)) / (2*h);
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% --- B_w: df/dQ_sg ---
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h = max(eps_rel * abs(Q_star), 1.0); % Q_star ~ 1e9, abs floor at 1 W
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B_w = (f(x_star, u_star, Q_star + h) - f(x_star, u_star, Q_star - h)) / (2*h);
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end
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