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< title > Entropyk — Contrôle Inverse One-Shot< / title >
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< / style >
< / head >
< body >
< h1 > 🎯 Entropyk — Contrôle Inverse One-Shot< / h1 >
< p class = "sub" > Superheat control avec valve d'expansion — Story 5.3: Residual Embedding< / p >
< div class = "legend" >
< div class = "leg" > < div class = "leg-dot" style = "border-color:var(--purple)" > < / div > Constraint< / div >
< div class = "leg" > < div class = "leg-dot" style = "border-color:var(--orange)" > < / div > BoundedVariable< / div >
< div class = "leg" > < div class = "leg-dot" style = "border-color:var(--cyan)" > < / div > Lien One-Shot< / div >
< div class = "leg" > < div class = "leg-dot" style = "border-color:var(--green)" > < / div > Résultat< / div >
< / div >
< div class = "page" >
<!-- ═══ CONCEPT ═══ -->
< section >
< h2 > Concept — One-Shot Inverse Control< / h2 >
< div class = "flow-diagram" >
< span class = "blabel" > FR24: Inverse Control solved simultaneously with cycle equations< / span >
< div style = "display:flex;align-items:stretch;gap:24px;justify-content:center;flex-wrap:wrap;" >
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< div style = "font-size:.75rem;font-weight:600;color:var(--red);margin-bottom:12px;text-transform:uppercase;letter-spacing:.08em;" >
❌ Approche Traditionnelle
< / div >
< div style = "font-size:.72rem;color:var(--dim);line-height:1.8;" >
< div > 1. Fixer valve → Simuler< / div >
< div > 2. Mesurer superheat< / div >
< div > 3. Ajuster valve< / div >
< div > 4. < span style = "color:var(--red)" > Répéter (optimisation externe)< / span > < / div >
< div style = "border-top:1px solid var(--border);padding-top:8px;margin-top:8px;" >
< span style = "color:var(--red)" > → Lent, coûteux, non garanti< / span >
< / div >
< / div >
< / div >
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< div style = "font-size:.75rem;font-weight:600;color:var(--green);margin-bottom:12px;text-transform:uppercase;letter-spacing:.08em;" >
✅ Approche One-Shot (Entropyk)
< / div >
< div style = "font-size:.72rem;color:var(--dim);line-height:1.8;" >
< div > 1. Définir contrainte: superheat = 5K< / div >
< div > 2. Lier à variable: valve position< / div >
< div > 3. < span style = "color:var(--cyan)" > Valve devient inconnue du solveur< / span > < / div >
< div > 4. < span style = "color:var(--green)" > Résolution simultanée (1 appel)< / span > < / div >
< div style = "border-top:1px solid rgba(63,185,80,.3);padding-top:8px;margin-top:8px;" >
< span style = "color:var(--green)" > → Rapide, garanti, élégant< / span >
< / div >
< / div >
< / div >
< / div >
< div style = "margin-top:20px;padding:16px;background:var(--bg);border-radius:8px;text-align:center;" >
< div style = "font-size:.7rem;color:var(--dim);margin-bottom:8px;" > Vecteur de résidus étendu< / div >
< div style = "font-family:'JetBrains Mono',monospace;font-size:.85rem;color:var(--cyan);" >
r< sub > total< / sub > = [ r< sub > cycle< / sub > , r< sub > constraint< / sub > ]< sup > T< / sup > = 0
< / div >
< div style = "font-size:.65rem;color:var(--dim);margin-top:8px;" >
r< sub > constraint< / sub > = superheat< sub > mesuré< / sub > − < sub > cible< / sub >
< / div >
< / div >
< / div >
< / section >
<!-- ═══ MAPPING ═══ -->
< section >
< h2 > Mapping — Contrainte → Variable de Contrôle< / h2 >
< div class = "mapping-box" >
< div class = "node constraint" data-tip = "Constraint ID: superheat_control Output: Superheat(evaporator) Target: 5.0 K" >
< div class = "nm" > 📐 Constraint< / div >
< div class = "ty" > superheat_control< / div >
< div class = "vals" > target: 5.0 K< / div >
< / div >
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< / svg >
< div class = "lbl" > link_constraint_to_control()< / div >
< / div >
< div class = "node control" data-tip = "BoundedVariable ID: valve_position Value: 0.5 (50%) Bounds: [0.1, 1.0]" >
< div class = "nm" > 🎚 BoundedVar< / div >
< div class = "ty" > valve_position< / div >
< div class = "vals" > [0.1, 1.0]< / div >
< / div >
< div class = "mapping-arrow" >
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< / svg >
< div class = "lbl" > state[idx]< / div >
< / div >
< div class = "node result" data-tip = "Résultat One-Shot 7 itérations Convergence: 1e-8" >
< div class = "nm" > ✓ Résolu< / div >
< div class = "ty" > valve = 38%< / div >
< div class = "vals" > SH = 5.02 K< / div >
< / div >
< / div >
< / section >
<!-- ═══ DOF ═══ -->
< section >
< h2 > Validation des Degrés de Liberté (DoF)< / h2 >
< div class = "dof-box" >
< div class = "dof-side" >
< div class = "title" > Équations< / div >
< div class = "count" style = "color:var(--blue)" > 9< / div >
< div class = "detail" > composants: 8< br > contraintes: +1< / div >
< / div >
< div class = "dof-equals" > =< / div >
< div class = "dof-side" >
< div class = "title" > Inconnues< / div >
< div class = "count" style = "color:var(--orange)" > 9< / div >
< div class = "detail" > états bords: 8< br > contrôles: +1< / div >
< / div >
< / div >
< div style = "text-align:center;margin-top:12px;" >
< span class = "status-badge ok" > ✓ Système bien posé — validate_inverse_control_dof() = Ok< / span >
< / div >
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< div style = "font-size:.7rem;color:var(--green);font-weight:600;" > Équilibré< / div >
< div style = "font-size:.6rem;color:var(--dim);font-family:'JetBrains Mono',monospace;margin-top:4px;" > n_eqs == n_unknowns< / div >
< div class = "status-badge ok" style = "margin-top:8px;" > Résolvable< / div >
< / div >
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< div style = "font-size:.7rem;color:var(--red);font-weight:600;" > Sur-contraint< / div >
< div style = "font-size:.6rem;color:var(--dim);font-family:'JetBrains Mono',monospace;margin-top:4px;" > n_eqs > n_unknowns< / div >
< div class = "status-badge error" style = "margin-top:8px;" > Erreur< / div >
< / div >
< div style = "background:rgba(227,179,65,.1);border:1px solid rgba(227,179,65,.3);border-radius:8px;padding:12px;text-align:center;" >
< div style = "font-size:.7rem;color:var(--yellow);font-weight:600;" > Sous-contraint< / div >
< div style = "font-size:.6rem;color:var(--dim);font-family:'JetBrains Mono',monospace;margin-top:4px;" > n_eqs < n_unknowns< / div >
< div class = "status-badge warn" style = "margin-top:8px;" > Warning< / div >
< / div >
< / div >
< / section >
<!-- ═══ ÉQUATIONS ═══ -->
< section >
< h2 > Équations du système étendu< / h2 >
< div style = "display:grid;grid-template-columns:1fr 1fr;gap:16px;" >
< div class = "eq-box" >
< div style = "font-size:.8rem;font-weight:600;color:var(--blue);margin-bottom:12px" > 📦 Équations du cycle (8 éq.)< / div >
< table class = "eq-table" >
< thead > < tr > < th > Composant< / th > < th > Équation< / th > < th > État< / th > < / tr > < / thead >
< tbody >
< tr > < td class = "cat" > Compresseur< / td > < td class = "formula" > r₁(P,h) = 0< / td > < td class = "result" > 2 éq.< / td > < / tr >
< tr > < td class = "cat" > Condenseur< / td > < td class = "formula" > r₂(P,h) = 0< / td > < td class = "result" > 2 éq.< / td > < / tr >
< tr > < td class = "cat" > EXV< / td > < td class = "formula" > r₃(P,h) = 0< / td > < td class = "result" > 2 éq.< / td > < / tr >
< tr > < td class = "cat" > Évaporateur< / td > < td class = "formula" > r₄(P,h) = 0< / td > < td class = "result" > 2 éq.< / td > < / tr >
< / tbody >
< / table >
< / div >
< div class = "eq-box" >
< div style = "font-size:.8rem;font-weight:600;color:var(--purple);margin-bottom:12px" > 📐 Équations de contrainte (+1 éq.)< / div >
< table class = "eq-table" >
< thead > < tr > < th > Type< / th > < th > Équation< / th > < th > Valeur< / th > < / tr > < / thead >
< tbody >
< tr > < td class = "cat" > Superheat< / td > < td class = "formula" > r_c = SH − < / td > < td class = "result" > 5.02 − < / td > < / tr >
< tr > < td class = "cat" > Jacobian< / td > < td class = "formula" > ∂r_c/∂valve< / td > < td class = "result" > ≈ 1.0< / td > < / tr >
< tr style = "background:var(--green-bg)" >
< td class = "cat" > State idx< / td > < td class = "formula" > 2·edges + i< / td > < td class = "result" style = "color:var(--green)" > idx = 8< / td >
< / tr >
< / tbody >
< / table >
< / div >
< / div >
< / section >
<!-- ═══ CONVERGENCE ═══ -->
< section >
< h2 > Convergence — Newton-Raphson< / h2 >
< div class = "info-grid" >
< div class = "icard" >
< h3 > Superheat (K)< / h3 >
< div class = "conv-grid" >
< div class = "conv-cell" > < div class = "iter" > i=0< / div > < div class = "val" > 2.30< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=1< / div > < div class = "val" > 3.12< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=2< / div > < div class = "val" > 3.89< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=3< / div > < div class = "val" > 4.41< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=4< / div > < div class = "val" > 4.73< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=5< / div > < div class = "val" > 4.91< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=6< / div > < div class = "val" > 5.01< / div > < / div >
< div class = "conv-cell active" > < div class = "iter" > i=7< / div > < div class = "val" > 5.02< / div > < / div >
< / div >
< / div >
< div class = "icard" >
< h3 > Valve Position (%)< / h3 >
< div class = "conv-grid" >
< div class = "conv-cell" > < div class = "iter" > i=0< / div > < div class = "val" > 50.0< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=1< / div > < div class = "val" > 46.2< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=2< / div > < div class = "val" > 43.5< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=3< / div > < div class = "val" > 41.3< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=4< / div > < div class = "val" > 39.8< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=5< / div > < div class = "val" > 38.9< / div > < / div >
< div class = "conv-cell" > < div class = "iter" > i=6< / div > < div class = "val" > 38.3< / div > < / div >
< div class = "conv-cell active" > < div class = "iter" > i=7< / div > < div class = "val" > 38.0< / div > < / div >
< / div >
< / div >
< / div >
< / section >
<!-- ═══ VALEURS FINALES ═══ -->
< section >
< h2 > Valeurs au point de fonctionnement< / h2 >
< div class = "info-grid" >
< div class = "icard" >
< h3 > Contrainte Superheat< / h3 >
< div class = "irow" > < span class = "k" > ID< / span > < span class = "v p" > superheat_control< / span > < / div >
< div class = "irow" > < span class = "k" > Output< / span > < span class = "v" > Superheat(evaporator)< / span > < / div >
< div class = "irow" > < span class = "k" > Target< / span > < span class = "v c" > 5.0 K< / span > < / div >
< div class = "irow" > < span class = "k" > Mesuré< / span > < span class = "v g" > 5.02 K< / span > < / div >
< div class = "irow" > < span class = "k" > Résidu< / span > < span class = "v g" > 0.02 K< / span > < / div >
< div class = "irow" > < span class = "k" > Satisfait< / span > < span class = "v g" > ✓< / span > < / div >
< / div >
< div class = "icard" >
< h3 > Variable de Contrôle< / h3 >
< div class = "irow" > < span class = "k" > ID< / span > < span class = "v o" > valve_position< / span > < / div >
< div class = "irow" > < span class = "k" > Initial< / span > < span class = "v" > 50.0%< / span > < / div >
< div class = "irow" > < span class = "k" > Final< / span > < span class = "v g" > 38.0%< / span > < / div >
< div class = "irow" > < span class = "k" > Bounds< / span > < span class = "v" > [10%, 100%]< / span > < / div >
< div class = "irow" > < span class = "k" > Saturé< / span > < span class = "v c" > Non< / span > < / div >
< div class = "irow" > < span class = "k" > State idx< / span > < span class = "v b" > 8< / span > < / div >
< / div >
< div class = "icard" >
< h3 > Solveur Newton-Raphson< / h3 >
< div class = "irow" > < span class = "k" > Itérations< / span > < span class = "v c" > 7< / span > < / div >
< div class = "irow" > < span class = "k" > Tolérance< / span > < span class = "v" > 1e-8< / span > < / div >
< div class = "irow" > < span class = "k" > ‖r‖ final< / span > < span class = "v g" > 3.2e-9< / span > < / div >
< div class = "irow" > < span class = "k" > Méthode< / span > < span class = "v" > One-Shot< / span > < / div >
< div class = "irow" > < span class = "k" > Temps< / span > < span class = "v g" > 12 ms< / span > < / div >
< / div >
< div class = "icard" >
< h3 > DoF Validation< / h3 >
< div class = "irow" > < span class = "k" > Edges< / span > < span class = "v" > 4 (× < / span > < / div >
< div class = "irow" > < span class = "k" > Controls< / span > < span class = "v o" > +1< / span > < / div >
< div class = "irow" > < span class = "k" > Total unknowns< / span > < span class = "v b" > 9< / span > < / div >
< div class = "irow" > < span class = "k" > Components< / span > < span class = "v" > 4 (× < / span > < / div >
< div class = "irow" > < span class = "k" > Constraints< / span > < span class = "v p" > +1< / span > < / div >
< div class = "irow" > < span class = "k" > Total equations< / span > < span class = "v b" > 9< / span > < / div >
< div class = "irow" > < span class = "k" > Balance< / span > < span class = "v g" > 9 = 9 ✓< / span > < / div >
< / div >
< / div >
< / section >
<!-- ═══ API RUST ═══ -->
< section >
< h2 > API Rust — Utilisation< / h2 >
< pre style = "color:#d4d4d4" > < span style = "color:#6a9955" > // ══════════════════════════════════════════════════════════════════════< / span >
< span style = "color:#6a9955" > // Story 5.3: Residual Embedding for Inverse Control< / span >
< span style = "color:#6a9955" > // ══════════════════════════════════════════════════════════════════════< / span >
< span style = "color:#569cd6" > use< / span > entropyk_solver::inverse::{
< span style = "color:#4ec9b0" > Constraint< / span > , < span style = "color:#4ec9b0" > ConstraintId< / span > , < span style = "color:#4ec9b0" > ComponentOutput< / span > ,
< span style = "color:#4ec9b0" > BoundedVariable< / span > , < span style = "color:#4ec9b0" > BoundedVariableId< / span > ,
};
< span style = "color:#6a9955" > // 1. Définir la contrainte: superheat = 5K< / span >
< span style = "color:#569cd6" > let< / span > constraint = < span style = "color:#4ec9b0" > Constraint< / span > ::< span style = "color:#dcdcaa" > new< / span > (
< span style = "color:#4ec9b0" > ConstraintId< / span > ::< span style = "color:#dcdcaa" > new< / span > (< span style = "color:#ce9178" > "superheat_control"< / span > ),
< span style = "color:#4ec9b0" > ComponentOutput< / span > ::< span style = "color:#4ec9b0" > Superheat< / span > { component_id: < span style = "color:#ce9178" > "evaporator"< / span > .< span style = "color:#dcdcaa" > into< / span > () },
< span style = "color:#b5cea8" > 5.0< / span > , < span style = "color:#6a9955" > // target: 5 Kelvin< / span >
);
system.< span style = "color:#dcdcaa" > add_constraint< / span > (constraint)?;
< span style = "color:#6a9955" > // 2. Définir la variable de contrôle bornée< / span >
< span style = "color:#569cd6" > let< / span > control = < span style = "color:#4ec9b0" > BoundedVariable< / span > ::< span style = "color:#dcdcaa" > new< / span > (
< span style = "color:#4ec9b0" > BoundedVariableId< / span > ::< span style = "color:#dcdcaa" > new< / span > (< span style = "color:#ce9178" > "valve_position"< / span > ),
< span style = "color:#b5cea8" > 0.5< / span > , < span style = "color:#b5cea8" > 0.1< / span > , < span style = "color:#b5cea8" > 1.0< / span > , < span style = "color:#6a9955" > // init, min, max< / span >
)?;
system.< span style = "color:#dcdcaa" > add_bounded_variable< / span > (control)?;
< span style = "color:#6a9955" > // 3. Lier contrainte → contrôle (One-Shot!)< / span >
system.< span style = "color:#dcdcaa" > link_constraint_to_control< / span > (
< span style = "color:#569cd6" > & < / span > < span style = "color:#4ec9b0" > ConstraintId< / span > ::< span style = "color:#dcdcaa" > new< / span > (< span style = "color:#ce9178" > "superheat_control"< / span > ),
< span style = "color:#569cd6" > & < / span > < span style = "color:#4ec9b0" > BoundedVariableId< / span > ::< span style = "color:#dcdcaa" > new< / span > (< span style = "color:#ce9178" > "valve_position"< / span > ),
)?;
< span style = "color:#6a9955" > // 4. Valider DoF + Finalize< / span >
system.< span style = "color:#dcdcaa" > validate_inverse_control_dof< / span > ()?;
system.< span style = "color:#dcdcaa" > finalize< / span > ()?;
< span style = "color:#6a9955" > // 5. Résoudre (One-Shot)< / span >
< span style = "color:#569cd6" > let< / span > result = < span style = "color:#4ec9b0" > NewtonRaphson< / span > ::< span style = "color:#dcdcaa" > new< / span > ().< span style = "color:#dcdcaa" > solve< / span > (< span style = "color:#569cd6" > & < / span > system)?;
< span style = "color:#6a9955" > // 6. Résultat< / span >
< span style = "color:#569cd6" > let< / span > valve = system.< span style = "color:#dcdcaa" > get_bounded_variable< / span > (< span style = "color:#569cd6" > & < / span > < span style = "color:#4ec9b0" > BoundedVariableId< / span > ::< span style = "color:#dcdcaa" > new< / span > (< span style = "color:#ce9178" > "valve_position"< / span > )).< span style = "color:#dcdcaa" > unwrap< / span > ();
< span style = "color:#dcdcaa" > println!< / span > (< span style = "color:#ce9178" > "Valve: {:.1}% SH: {:.2} K"< / span > , valve.< span style = "color:#dcdcaa" > value< / span > ()< span style = "color:#569cd6" > *< / span > < span style = "color:#b5cea8" > 100.0< / span > , sh);< / pre >
< / section >
<!-- ═══ API MÉTHODES ═══ -->
< section >
< h2 > API — Méthodes System< / h2 >
< div class = "eq-box" >
< table class = "eq-table" >
< thead > < tr > < th > Méthode< / th > < th > Description< / th > < th > Retour< / th > < / tr > < / thead >
< tbody >
< tr > < td class = "formula" > add_constraint(c)< / td > < td class = "cat" > Ajoute une contrainte< / td > < td class = "result" > Result< (), ConstraintError> < / td > < / tr >
< tr > < td class = "formula" > add_bounded_variable(v)< / td > < td class = "cat" > Ajoute variable bornée< / td > < td class = "result" > Result< (), BoundedVariableError> < / td > < / tr >
< tr > < td class = "formula" > link_constraint_to_control(cid, vid)< / td > < td class = "cat" > Lie contrainte → contrôle< / td > < td class = "result" > Result< (), DoFError> < / td > < / tr >
< tr > < td class = "formula" > unlink_constraint(cid)< / td > < td class = "cat" > Supprime le lien< / td > < td class = "result" > Option< BoundedVariableId> < / td > < / tr >
< tr > < td class = "formula" > validate_inverse_control_dof()< / td > < td class = "cat" > Valide éq == inconnues< / td > < td class = "result" > Result< (), DoFError> < / td > < / tr >
< tr > < td class = "formula" > control_variable_state_index(id)< / td > < td class = "cat" > Index vecteur d'état< / td > < td class = "result" > Option< usize> < / td > < / tr >
< tr > < td class = "formula" > full_state_vector_len()< / td > < td class = "cat" > Longueur totale< / td > < td class = "result" > usize< / td > < / tr >
< tr > < td class = "formula" > compute_constraint_residuals(...)< / td > < td class = "cat" > Calcule résidus contraintes< / td > < td class = "result" > usize< / td > < / tr >
< tr > < td class = "formula" > compute_inverse_control_jacobian(...)< / td > < td class = "cat" > Jacobian ∂r/∂control< / td > < td class = "result" > Vec< (row,col,val)> < / td > < / tr >
< / tbody >
< / table >
< / div >
< / section >
< / div >
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