72143bcff5
Earlier placeholder claimed ramp-rate limits weren't expressible as
state halfspaces without augmentation. That was wrong: dT_c/dt is
linear in (T_f, T_c, T_cold) directly from pke_th_rhs (no neutronics
coupling), so |dT_c/dt| <= r_max is two clean halfspaces over x.
Coefficients from pke_params:
a_f = hA / (M_c*c_c) = +0.4587 /s
a_c = -(hA + 2*W*c_c)/(M_c*c_c) = -0.9587 /s
a_cold = 2*W*c_c / (M_c*c_c) = +0.5000 /s
Sum = 0 exact (equilibrium when all T's equal).
Limit chosen: +/- 50 C/hr (tech-spec 28 C/hr + transient overshoot
budget). Verified on actual heatup sim: max dT_c/dt = 48.5 C/hr, min
= 0 C/hr. Passes our placeholder but tight — a strict 28 C/hr tech-
spec invariant would be violated by current ctrl_heatup tuning
(overshoot factor ~1.7x during mid-ramp).
Generalized load_predicates.m to accept multi-coefficient halfspace
rows via "row": [[state_idx, coeff], ...] format, in addition to the
existing single-coefficient {state_index, coeff} form. Backward
compatible.
inv1_holds now conjoins fuel_centerline, cold_leg_subcooled, and the
two rate halfspaces. DNBR still not modeled (would need an
augmented predicate with a correlation-based safety margin).
Hacker-Split: Dane asked about heatup rate invariant; realizing
my earlier 'needs state augmentation' claim was wrong and the rate
constraint is already linear. Fix it, verify against actual sim.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
21 lines
1.0 KiB
Matlab
21 lines
1.0 KiB
Matlab
%% test_heatup_rate.m — measure the actual heatup-rate trajectory from ctrl_heatup
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clear; addpath('controllers'); addpath('../reachability');
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plant = pke_params();
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pred = load_predicates(plant);
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x0 = [1e-3; (plant.beta_i ./ (plant.lambda_i * plant.Lambda)) * 1e-3; ...
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pred.constants.T_standby; pred.constants.T_standby; pred.constants.T_standby];
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ref = struct('T_start', pred.constants.T_standby, ...
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'T_target', plant.T_c0, ...
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'ramp_rate', 28/3600);
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[t, X, U] = pke_solver(plant, @(t) 0, @ctrl_heatup, ref, [0 5400], x0);
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a_f = 0.4587; a_c = -0.9587; a_cold = 0.5000;
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dTcdt = a_f*X(:,8) + a_c*X(:,9) + a_cold*X(:,10); % C/s
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fprintf('\n=== Heatup rate statistics ===\n');
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fprintf(' max dT_c/dt: %.4f C/s = %6.1f C/hr\n', max(dTcdt), max(dTcdt)*3600);
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fprintf(' min dT_c/dt: %.4f C/s = %6.1f C/hr\n', min(dTcdt), min(dTcdt)*3600);
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fprintf(' rate limit: +/- 0.01389 C/s = +/- 50.0 C/hr\n');
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fprintf(' violates upper? %s\n', string(any(dTcdt > 0.01389)));
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fprintf(' violates lower? %s\n', string(any(dTcdt < -0.01389)));
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