645f2d8d27
Singular-perturbation reduction of the PKE+T/H system: set dn/dt=0,
solve algebraically n = Λ·Σλ_i·C_i / (β-ρ). State drops 10 -> 9 (no
n), removes Λ⁻¹ stiffness. Validated against full state on the heatup
scenario:
t [s] |Δn|/n_full T_c err [K]
60 3.7e-5 4e-6
300 3.8e-4 1.9e-4
1200 1.0e-3 2.2e-3
3000 5.0e-4 7.2e-3
Maximum relative error 0.1% on n, peak 7 mK on temperatures over
50 minutes. PJ approximation is excellent for slow heatup transients
(sub-prompt-critical regime).
Files:
- code/src/pke_th_rhs_pj.jl: reduced 9-state RHS
- code/scripts/validate_pj.jl: side-by-side sim
- code/scripts/reach_heatup_pj.jl: TMJets reach with PJ model
(probing T = 60, 300, 1800, 5400 s)
App v2 (Pluto):
- §9b: live ingestion of reach_operation_result.mat with per-
halfspace margins computed from JSON-defined inv2_holds.
- §9c: 2D projection chooser (n, T_f, T_c, T_cold) with reach
tube envelope overlay.
- §9d: PJ heatup reach summary (placeholder until first run lands).
Journal:
- Added 2026-04-20-overnight-prompt-jump.tex with PJ derivation,
validation table, soundness ledger update. apass markers for
the in-progress reach results.
This commit captures state mid-run; next commit will add the
populated reach results once TMJets returns.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
114 lines
4.3 KiB
Julia
114 lines
4.3 KiB
Julia
#!/usr/bin/env julia
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#
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# validate_pj.jl — quantify the prompt-jump approximation error.
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#
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# Two parallel sims of the same heatup scenario:
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# (i) full 10-state PKE+T/H (pke_th_rhs!)
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# (ii) reduced 9-state prompt-jump model (pke_th_rhs_pj!)
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#
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# After the prompt transient (~few hundred microseconds) the two
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# trajectories should agree closely on T_c, T_f, T_cold, and on the
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# reconstructed n vs the dynamic n. Quantify the error explicitly.
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using Pkg
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Pkg.activate(joinpath(@__DIR__, ".."))
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using Printf
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using LinearAlgebra
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using OrdinaryDiffEq
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using Plots
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include(joinpath(@__DIR__, "..", "src", "pke_params.jl"))
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include(joinpath(@__DIR__, "..", "src", "pke_th_rhs.jl"))
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include(joinpath(@__DIR__, "..", "src", "pke_th_rhs_pj.jl"))
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include(joinpath(@__DIR__, "..", "controllers", "controllers.jl"))
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plant = pke_params()
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T_standby = plant.T_c0 - 33.333333
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# Heatup scenario — same as sim_heatup.jl.
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ref_heat = (; T_start=T_standby, T_target=plant.T_c0, ramp_rate=28/3600)
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Q_sg = t -> 0.0
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# Initial conditions — both at n=1e-3, same temperatures.
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n0 = 1e-3
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C0 = (plant.beta_i ./ (plant.lambda_i .* plant.Lambda)) .* n0
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x0_full = [n0; C0; T_standby; T_standby; T_standby]
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x0_pj = [C0; T_standby; T_standby; T_standby]
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tspan = (0.0, 3000.0)
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# --- Full-state sim ---
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function rhs_full!(dx, x, p, t)
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u = ctrl_heatup(t, x, plant, ref_heat)
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pke_th_rhs!(dx, x, t, plant, Q_sg, u)
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end
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prob_full = ODEProblem(rhs_full!, x0_full, tspan)
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sol_full = solve(prob_full, Rodas5(); reltol=1e-8, abstol=1e-10)
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# --- Prompt-jump sim ---
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# ctrl_heatup expects 10-state x with T_f at index 8, T_c at 9.
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# We pass an adapter that maps 9-state to the controller's expected layout.
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function ctrl_heatup_pj(t, x_pj, plant_arg, ref_arg)
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# Construct a fake 10-state with n placeholder; controller doesn't read n.
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x10 = [0.0; x_pj[1:6]; x_pj[7]; x_pj[8]; x_pj[9]]
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return ctrl_heatup(t, x10, plant_arg, ref_arg)
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end
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function rhs_pj!(dx, x, p, t)
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u = ctrl_heatup_pj(t, x, plant, ref_heat)
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pke_th_rhs_pj!(dx, x, t, plant, Q_sg, u)
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end
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prob_pj = ODEProblem(rhs_pj!, x0_pj, tspan)
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sol_pj = solve(prob_pj, Rodas5(); reltol=1e-8, abstol=1e-10)
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# --- Compare at sampled times ---
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function get_n_full(sol, t) sol(t)[1] end
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function get_T_c_full(sol, t) sol(t)[9] end
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function get_T_f_full(sol, t) sol(t)[8] end
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function get_T_cold_full(sol, t) sol(t)[10] end
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function get_T_c_pj(sol, t) sol(t)[8] end
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function get_T_f_pj(sol, t) sol(t)[7] end
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function get_T_cold_pj(sol, t) sol(t)[9] end
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function get_n_pj(sol, t)
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x = sol(t)
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u = ctrl_heatup_pj(t, x, plant, ref_heat)
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pj_reconstruct_n(x, plant, u)
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end
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println("\n=== PJ vs full-state, heatup scenario ===")
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println(" t [s] n_full n_pj |Δn|/n_full T_c err T_f err T_cold err")
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for t_check in (1.0, 5.0, 10.0, 60.0, 300.0, 1200.0, 3000.0)
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n_f = get_n_full(sol_full, t_check)
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n_p = get_n_pj(sol_pj, t_check)
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Tc_err = abs(get_T_c_full(sol_full, t_check) - get_T_c_pj(sol_pj, t_check))
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Tf_err = abs(get_T_f_full(sol_full, t_check) - get_T_f_pj(sol_pj, t_check))
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Tcold_err = abs(get_T_cold_full(sol_full, t_check) - get_T_cold_pj(sol_pj, t_check))
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@printf " %6.1f %.3e %.3e %8.2e %.3e %.3e %.3e\n" t_check n_f n_p abs(n_f-n_p)/abs(n_f) Tc_err Tf_err Tcold_err
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end
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# --- Plot trajectory overlay ---
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figdir = joinpath(@__DIR__, "..", "..", "docs", "figures")
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isdir(figdir) || mkpath(figdir)
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CtoF(T) = T*9/5 + 32
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t_grid = range(0, 3000, length=600)
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n_full_arr = [get_n_full(sol_full, t) for t in t_grid]
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n_pj_arr = [get_n_pj(sol_pj, t) for t in t_grid]
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Tc_full_arr = [get_T_c_full(sol_full, t) for t in t_grid]
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Tc_pj_arr = [get_T_c_pj(sol_pj, t) for t in t_grid]
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p_n = plot(t_grid ./ 60, n_full_arr, lw=2, color=:blue, label="full-state",
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xlabel="t [min]", ylabel="n", title="Power: full vs PJ")
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plot!(p_n, t_grid ./ 60, n_pj_arr, lw=1.5, ls=:dash, color=:red, label="prompt-jump")
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p_Tc = plot(t_grid ./ 60, CtoF.(Tc_full_arr), lw=2, color=:blue, label="full-state",
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xlabel="t [min]", ylabel="T_avg [F]", title="T_avg: full vs PJ")
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plot!(p_Tc, t_grid ./ 60, CtoF.(Tc_pj_arr), lw=1.5, ls=:dash, color=:red, label="prompt-jump")
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fig = plot(p_n, p_Tc, layout=(1,2), size=(1200, 450),
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plot_title="PJ vs full-state, heatup scenario (3000 s)")
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savefig(fig, joinpath(figdir, "validate_pj_heatup.png"))
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println("\nFigure: $figdir/validate_pj_heatup.png")
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