a56fcbedc2
First working nonlinear reach artifact for the PWR model. TMJets
Taylor-model scheme on the full 10-state closed-loop (unsaturated
ctrl_heatup, ramp reference via augmented time state x[11]).
Status:
T=10s : SUCCESS. 10583 reach-sets. T_c envelope [274.45, 295] C,
n envelope [-5.2e-4, 5.01e-3]. Over-approximation visible
(n can't be negative physically) but tube is sound and
bounded.
T=60s+ : FAILED. Exhausts 50k step budget then hits NaN in
precursor-decay term.
Root cause: prompt-neutron stiffness. Lambda=1e-4s forces TMJets'
adaptive stepper to ~1ms steps to resolve fast dynamics. 10583 steps
for 10s of sim time means we get ~10s/50000 = 2s horizon max before
step budget exhausts — inadequate for heatup's 5-hour obligation.
Remedy (next session): singular-perturbation reduction of the
neutronics. Treat n as quasi-static algebraic function of (T, C, rho)
rather than a dynamic state. Replaces stiff dn/dt with algebraic
relation, removes fast timescale from reach problem. Standard in
reactor-kinetics reach literature.
What this does prove:
- Julia/TMJets framework works for this system (previous
scaling-issue failure is gone with @taylorize'd RHS).
- Bilinear n*rho term handled correctly by Taylor models.
- Ramp reference via augmented time state x[11] is a workable
pattern for time-varying controller references in reach.
What this does NOT prove:
- Anything about heatup safety — 10s horizon is nowhere near the
mode's 5-hour obligation.
Includes sim_heatup.jl, a Rodas5 baseline using the same @taylorize-
able RHS form, for cross-validation of the reach tube against a
nominal trajectory once longer horizons are reachable.
WALKTHROUGH.md updated with the finding.
Hacker-Split: got partway up the Julia reach ladder, identified the
physical bottleneck (stiffness), named the fix (reduced-order PKE).
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
74 lines
2.8 KiB
Julia
74 lines
2.8 KiB
Julia
#!/usr/bin/env julia
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#
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# sim_heatup.jl — nominal heatup trajectory sim in Julia.
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#
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# Closed-loop nonlinear simulation using the SAME RHS form as
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# reach_heatup_nonlinear.jl (augmented time x[11], inlined constants)
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# but via OrdinaryDiffEq, not TMJets. Purpose: verify the @taylorize-able
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# RHS matches the MATLAB heatup baseline. Also generates a nominal
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# trajectory that reach tubes can be checked against.
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using Pkg
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Pkg.activate(joinpath(@__DIR__, ".."))
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using OrdinaryDiffEq
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# Constants (match reach_heatup_nonlinear.jl).
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const LAMBDA = 1e-4
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const BETA_1, BETA_2, BETA_3, BETA_4, BETA_5, BETA_6 =
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0.000215, 0.001424, 0.001274, 0.002568, 0.000748, 0.000273
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const BETA = BETA_1 + BETA_2 + BETA_3 + BETA_4 + BETA_5 + BETA_6
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const LAM_1, LAM_2, LAM_3, LAM_4, LAM_5, LAM_6 =
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0.0124, 0.0305, 0.111, 0.301, 1.14, 3.01
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const P0 = 1e9
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const M_F, C_F, M_C, C_C, HA, W_M, M_SG =
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50000.0, 300.0, 20000.0, 5450.0, 5e7, 5000.0, 30000.0
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const ALPHA_F, ALPHA_C = -2.5e-5, -1e-4
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const T_COLD0 = 290.0
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const DT_CORE = P0 / (W_M * C_C)
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const T_HOT0 = T_COLD0 + DT_CORE
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const T_C0 = (T_HOT0 + T_COLD0) / 2
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const T_F0 = T_C0 + P0 / HA
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const T_STANDBY = T_C0 - 33.333333
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const RAMP_RATE_CS = 28.0 / 3600
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const KP_HEATUP = 1e-4
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function rhs_heatup_sim!(dx, x, p, t)
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rho = KP_HEATUP * (T_STANDBY + RAMP_RATE_CS * x[11] - x[9])
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dx[1] = (rho - BETA) / LAMBDA * x[1] +
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LAM_1*x[2] + LAM_2*x[3] + LAM_3*x[4] +
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LAM_4*x[5] + LAM_5*x[6] + LAM_6*x[7]
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dx[2] = (BETA_1 / LAMBDA) * x[1] - LAM_1 * x[2]
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dx[3] = (BETA_2 / LAMBDA) * x[1] - LAM_2 * x[3]
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dx[4] = (BETA_3 / LAMBDA) * x[1] - LAM_3 * x[4]
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dx[5] = (BETA_4 / LAMBDA) * x[1] - LAM_4 * x[5]
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dx[6] = (BETA_5 / LAMBDA) * x[1] - LAM_5 * x[6]
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dx[7] = (BETA_6 / LAMBDA) * x[1] - LAM_6 * x[7]
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dx[8] = (P0 * x[1] - HA * (x[8] - x[9])) / (M_F * C_F)
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dx[9] = (HA * (x[8] - x[9]) - 2 * W_M * C_C * (x[9] - x[10])) / (M_C * C_C)
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dx[10] = (2 * W_M * C_C * (x[9] - x[10])) / (M_SG * C_C)
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dx[11] = 1.0
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return nothing
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end
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# IC = midpoint of X_entry polytope.
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n0 = 0.001
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C0 = [BETA_1/(LAM_1*LAMBDA), BETA_2/(LAM_2*LAMBDA), BETA_3/(LAM_3*LAMBDA),
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BETA_4/(LAM_4*LAMBDA), BETA_5/(LAM_5*LAMBDA), BETA_6/(LAM_6*LAMBDA)] .* n0
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x0 = [n0; C0; T_STANDBY + 5; T_STANDBY + 6; T_STANDBY + 4; 0.0]
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tspan = (0.0, 300.0)
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# Rodas5 is stiff-aware.
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prob = ODEProblem(rhs_heatup_sim!, x0, tspan)
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sol = solve(prob, Rodas5(); reltol=1e-8, abstol=1e-10)
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println("\n=== Heatup nominal trajectory (saturation disabled, Julia) ===")
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println(" t=0 : n=$(round(sol.u[1][1]; sigdigits=3)) T_c=$(round(sol.u[1][9]; digits=2)) C")
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for t_check in (10.0, 60.0, 120.0, 300.0)
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u = sol(t_check)
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println(" t=$(lpad(Int(t_check), 4))s : n=$(round(u[1]; sigdigits=3)) T_c=$(round(u[9]; digits=2)) C T_f=$(round(u[8]; digits=2)) C")
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end
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