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>
plant-model
PWR plant model (point kinetics + lumped thermal-hydraulics) and mode-specific continuous controllers for the HAHACS preliminary example.
Overview
A 10-state coupled neutronics + thermal-hydraulics model in MATLAB:
- 6 delayed neutron precursor groups (U-235 thermal fission, Keepin)
- Lumped fuel, core coolant, and SG/cold-leg thermal nodes
- Steam generator heat removal
Q_sg(t)as the bounded disturbance input - Doppler and moderator temperature reactivity feedback
- External rod reactivity
uas the controllable input
State vector: x = [n; C1..C6; T_f; T_c; T_cold] (10 states). See
CLAUDE.md for the naming convention.
Quick Start
Open MATLAB in this directory and run:
main
The default scenario runs two simulations of a 100% → 80% SG demand step:
once with ctrl_null (plant feedback only) and once with ctrl_operation
(proportional rod reactivity on T_avg error), and plots the comparison.
Files
| File | Role |
|---|---|
main.m |
Entry point — scenario config and run |
pke_params.m |
Plant parameters and steady-state derivation |
pke_th_rhs.m |
Dynamics ẋ = f(t, x, plant, Q_sg, u) |
pke_initial_conditions.m |
Analytic steady-state x0 |
pke_solver.m |
Closed-loop driver — takes a controller function handle |
plot_pke_results.m |
4-panel results plot |
load_profile.m |
SG heat demand shapes |
controllers/ctrl_null.m |
u = 0 baseline |
controllers/ctrl_operation.m |
Stabilizing mode: P on T_avg |
Controllers
Controllers share a single signature:
u = ctrl_<mode>(t, x, plant, ref)
Returns scalar u (external rod reactivity in dk/k). The solver swaps
controllers via function handle:
[t, X, U] = pke_solver(plant, Q_sg, @ctrl_operation, ref, tspan);
Additional modes (ctrl_heatup, ctrl_scram, ctrl_shutdown) will land in
controllers/ following the same signature.
Running Different Scenarios
Swap Q_sg in main.m:
% Step down to 90% at t = 10s
Q_sg = @(t) plant.P0 * (1.0 - 0.1 * (t >= 10));
% Interpolated time series
t_data = [0, 100, 200, 300];
q_data = [1.0, 0.85, 0.9, 1.0] * plant.P0;
Q_sg = @(t) interp1(t_data, q_data, t, 'linear', 'extrap');
Swap the controller:
[t, X, U] = pke_solver(plant, Q_sg, @ctrl_null, [], tspan);
Change the reference (for modes that use one):
ref.T_avg = plant.T_c0 + 5; % track 5 C above nominal
Requirements
MATLAB (R2020b or newer, tested on R2025b). Uses ode15s from base MATLAB
— no toolboxes required.