dynamics.py

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"""Discrete-time dynamics model for robust DDP controller.
 
State vector: x = [P_copv, P_reg, P_u_F, P_u_O, P_d_F, P_d_O, V_u_F, V_u_O, m_gas_copv, m_gas_F, m_gas_O]
Control: u = [u_F, u_O] in [0, 1]
 
Gas masses are tracked for proper mass conservation and blowdown physics.
"""
 
from __future__ import annotations
 
from typing import Tuple, Optional, Dict, Any
import numpy as np
from dataclasses import dataclass
 
from .data_models import ControllerConfig
 
 
# State indices
IDX_P_COPV = 0
IDX_P_REG = 1
IDX_P_U_F = 2
IDX_P_U_O = 3
IDX_P_D_F = 4
IDX_P_D_O = 5
IDX_V_U_F = 6
IDX_V_U_O = 7
IDX_M_GAS_COPV = 8  # Gas mass in COPV [kg]
IDX_M_GAS_F = 9     # Gas mass in fuel tank ullage [kg]
IDX_M_GAS_O = 10    # Gas mass in oxidizer tank ullage [kg]
 
# Control indices
IDX_U_F = 0
IDX_U_O = 1
 
N_STATE = 11  # Expanded to include gas masses
N_CONTROL = 2
 
 
@dataclass
class DynamicsParams:
    """Parameters for dynamics model (extracted from ControllerConfig)."""
    # Required parameters (no defaults)
    copv_cF: float
    copv_cO: float
    copv_loss: float
    reg_ratio: float
    alpha_F: float  # Pressurization coefficient for fuel
    alpha_O: float  # Pressurization coefficient for oxidizer
    rho_F: float    # Propellant density for fuel
    rho_O: float    # Propellant density for oxidizer
    tau_line_F: float  # Feed line time constant for fuel
    tau_line_O: float  # Feed line time constant for oxidizer
    
    # Optional parameters with defaults (must come after required fields)
    reg_setpoint: Optional[float] = None  # Regulator setpoint [Pa] (None = derived from COPV)
    V_copv: float = 0.006  # COPV volume [m³] (default 6L)
    R_gas: float = 296.8  # Gas constant [J/(kg·K)] for N2
    T_gas: float = 293.0  # Initial gas temperature [K]
    Z_gas: float = 1.0    # Compressibility factor (1.0 for ideal gas, can be pressure-dependent)
    n_polytropic: float = 1.2  # Polytropic exponent (1.0=isothermal, 1.4=adiabatic, 1.2=typical for blowdown)
    use_polytropic: bool = True  # Use polytropic process (temperature changes) vs isothermal
    use_real_gas: bool = False  # Use real gas compressibility factor Z(P,T) vs ideal gas
    T_gas_copv_initial: float = 293.0  # Initial COPV gas temperature [K]
    T_gas_F_initial: float = 293.0  # Initial fuel tank gas temperature [K]
    T_gas_O_initial: float = 250.0  # Initial oxidizer tank gas temperature [K] (LOX tank is colder)
 
    # --- Pressurisation-path hardware ------------------------------------------------------
    # These were literals inside step(): a COPV -> regulator -> tank chain with the orifice
    # geometry baked into the function body, which is one of the four fragmented feed models
    # docs/adr/0001 calls out. They are real hardware numbers a user must be able to set once
    # this path is calibrated or replaced by lib/feedtwin. Defaults are exactly the values that
    # were hardcoded, so behaviour is unchanged unless someone overrides them.
    gamma_gas: float = 1.4        # Specific heat ratio of the pressurant (N2)
    Cd_regulator: float = 0.7     # Discharge coefficient, regulator orifice
    Cd_valve: float = 0.65        # Discharge coefficient, solenoid valve orifice
    A_regulator: float = 2e-5     # Regulator orifice area [m^2] (~20 mm^2)
    A_valve_F: float = 5e-5       # Fuel solenoid valve flow area [m^2] (~50 mm^2)
    A_valve_O: float = 5e-5       # Oxidiser solenoid valve flow area [m^2] (~50 mm^2)
    
    @classmethod
    def from_config(cls, config: ControllerConfig) -> DynamicsParams:
        """Create dynamics parameters from controller config."""
        return cls(
            copv_cF=config.copv_cF,
            copv_cO=config.copv_cO,
            copv_loss=config.copv_loss,
            V_copv=getattr(config, 'V_copv', 0.006),  # Default 6L
            R_gas=getattr(config, 'R_gas', 296.8),    # N2 gas constant
            T_gas=getattr(config, 'T_gas', 293.0),    # Initial gas temperature
            Z_gas=getattr(config, 'Z_gas', 1.0),      # Ideal gas (can be pressure-dependent)
            reg_setpoint=config.reg_setpoint,
            reg_ratio=config.reg_ratio,
            alpha_F=config.alpha_F,
            alpha_O=config.alpha_O,
            rho_F=config.rho_F,
            rho_O=config.rho_O,
            tau_line_F=config.tau_line_F,
            tau_line_O=config.tau_line_O,
            # Real-world physics parameters
            n_polytropic=getattr(config, 'n_polytropic', 1.2),  # Typical for blowdown
            use_polytropic=getattr(config, 'use_polytropic', True),  # Enable polytropic processes
            use_real_gas=getattr(config, 'use_real_gas', False),  # Real gas Z(P,T) lookup
            T_gas_copv_initial=getattr(config, 'T_gas_copv_initial', 293.0),  # COPV initial temp
            T_gas_F_initial=getattr(config, 'T_gas_F_initial', 293.0),  # Fuel tank initial temp
            T_gas_O_initial=getattr(config, 'T_gas_O_initial', 250.0),  # LOX tank initial temp (colder)
            # Pressurisation-path hardware; getattr so an older ControllerConfig still loads.
            gamma_gas=getattr(config, 'gamma_gas', 1.4),
            Cd_regulator=getattr(config, 'Cd_regulator', 0.7),
            Cd_valve=getattr(config, 'Cd_valve', 0.65),
            A_regulator=getattr(config, 'A_regulator', 2e-5),
            A_valve_F=getattr(config, 'A_valve_F', 5e-5),
            A_valve_O=getattr(config, 'A_valve_O', 5e-5),
        )
 
 
def step(
    x: np.ndarray,
    u: np.ndarray,
    dt: float,
    params: DynamicsParams,
    mdot_F: float,
    mdot_O: float,
) -> np.ndarray:
    """
    Discrete-time dynamics step.
    
    Parameters:
    -----------
    x : np.ndarray, shape (N_STATE,)
        Current state: [P_copv, P_reg, P_u_F, P_u_O, P_d_F, P_d_O, V_u_F, V_u_O, m_gas_copv, m_gas_F, m_gas_O]
    u : np.ndarray, shape (N_CONTROL,)
        Control input: [u_F, u_O] in [0, 1]
    dt : float
        Time step [s]
    params : DynamicsParams
        Dynamics parameters
    mdot_F : float
        Fuel mass flow rate [kg/s] (from engine physics)
    mdot_O : float
        Oxidizer mass flow rate [kg/s] (from engine physics)
    
    Returns:
    --------
    x_next : np.ndarray, shape (N_STATE,)
        Next state
    """
    # Validate input state size
    if len(x) < 8:
        raise ValueError(f"State vector must have at least 8 elements, got {len(x)}")
    
    # Extract state
    P_copv = x[IDX_P_COPV]
    P_reg = x[IDX_P_REG]
    P_u_F = x[IDX_P_U_F]
    P_u_O = x[IDX_P_U_O]
    P_d_F = x[IDX_P_D_F]
    P_d_O = x[IDX_P_D_O]
    V_u_F = x[IDX_V_U_F]
    V_u_O = x[IDX_V_U_O]
    
    # Extract gas masses (if not in state, compute from pressures using ideal gas law)
    if len(x) > IDX_M_GAS_COPV:
        m_gas_copv = x[IDX_M_GAS_COPV]
        m_gas_F = x[IDX_M_GAS_F]
        m_gas_O = x[IDX_M_GAS_O]
    else:
        # Initialize gas masses from pressures (backward compatibility)
        # P = (m * R * T) / (V * Z), so m = (P * V * Z) / (R * T)
        T_copv_init = getattr(params, 'T_gas_copv_initial', params.T_gas)
        T_F_init = getattr(params, 'T_gas_F_initial', params.T_gas)
        T_O_init = getattr(params, 'T_gas_O_initial', 250.0)  # LOX tank is colder
        m_gas_copv = (P_copv * params.V_copv * params.Z_gas) / (params.R_gas * T_copv_init)
        m_gas_F = (P_u_F * V_u_F * params.Z_gas) / (params.R_gas * T_F_init) if V_u_F > 1e-10 else 0.0
        m_gas_O = (P_u_O * V_u_O * params.Z_gas) / (params.R_gas * T_O_init) if V_u_O > 1e-10 else 0.0
    
    # REAL-WORLD PHYSICS: Track gas temperatures for polytropic processes
    # In real systems, gas temperature changes during expansion/compression
    # Polytropic process: T = T0 * (rho/rho0)^(n-1) where rho = m/V
    # n = 1.0: isothermal (constant T)
    # n = 1.4: adiabatic (no heat transfer, γ for diatomic gas)
    # n = 1.2: typical for blowdown (some heat transfer with tank walls)
    
    # Reference state for the polytropic relation, captured on this params object's first
    # step. It used to live on the FUNCTION object as private attributes, which made it
    # process-global: the first trajectory ever stepped set the reference for every later
    # one, across configs. An optimizer evaluating thousands of candidates -- exactly the
    # Layer X access pattern docs/adr/0001 describes -- would hand candidates 2..N the
    # reference state of candidate 1. Scoping it to `params` makes it per-config.
    if not getattr(params, '_temp_initialized', False):
        params._T_copv_0 = getattr(params, 'T_gas_copv_initial', params.T_gas)
        params._T_F_0 = getattr(params, 'T_gas_F_initial', params.T_gas)
        params._T_O_0 = getattr(params, 'T_gas_O_initial', 250.0)  # LOX tank colder
        params._m_copv_0 = m_gas_copv
        params._m_F_0 = m_gas_F
        params._m_O_0 = m_gas_O
        params._V_F_0 = V_u_F
        params._V_O_0 = V_u_O
        params._temp_initialized = True
    
    # Compute current gas temperatures using polytropic relation
    # T = T0 * (rho/rho0)^(n-1) = T0 * (m/V) / (m0/V0))^(n-1)
    # This accounts for both volume expansion and mass changes
    use_polytropic = getattr(params, 'use_polytropic', True)
    n_poly = getattr(params, 'n_polytropic', 1.2)
    
    if use_polytropic:
        # COPV temperature: polytropic expansion/compression
        if params._m_copv_0 > 1e-10 and params.V_copv > 1e-10:
            rho_copv_0 = params._m_copv_0 / params.V_copv
            rho_copv = m_gas_copv / params.V_copv if params.V_copv > 1e-10 else rho_copv_0
            if rho_copv_0 > 1e-10:
                T_copv = params._T_copv_0 * (rho_copv / rho_copv_0) ** (n_poly - 1.0)
                T_copv = max(200.0, min(400.0, T_copv))  # Clamp to reasonable range [200-400 K]
            else:
                T_copv = params._T_copv_0
        else:
            T_copv = params._T_copv_0
        
        # Fuel tank temperature: polytropic expansion/compression
        if params._m_F_0 > 1e-10 and params._V_F_0 > 1e-10:
            rho_F_0 = params._m_F_0 / params._V_F_0
            rho_F = m_gas_F / V_u_F if V_u_F > 1e-10 else rho_F_0
            if rho_F_0 > 1e-10:
                T_gas_F = params._T_F_0 * (rho_F / rho_F_0) ** (n_poly - 1.0)
                T_gas_F = max(200.0, min(400.0, T_gas_F))  # Clamp to reasonable range
            else:
                T_gas_F = params._T_F_0
        else:
            T_gas_F = params._T_F_0
        
        # Oxidizer tank temperature: polytropic expansion/compression
        if params._m_O_0 > 1e-10 and params._V_O_0 > 1e-10:
            rho_O_0 = params._m_O_0 / params._V_O_0
            rho_O = m_gas_O / V_u_O if V_u_O > 1e-10 else rho_O_0
            if rho_O_0 > 1e-10:
                T_gas_O = params._T_O_0 * (rho_O / rho_O_0) ** (n_poly - 1.0)
                T_gas_O = max(200.0, min(400.0, T_gas_O))  # Clamp to reasonable range
            else:
                T_gas_O = params._T_O_0
        else:
            T_gas_O = params._T_O_0
    else:
        # Isothermal process: temperature constant
        T_copv = params._T_copv_0
        T_gas_F = params._T_F_0
        T_gas_O = params._T_O_0
    
    # Extract control
    u_F = np.clip(u[IDX_U_F], 0.0, 1.0)
    u_O = np.clip(u[IDX_U_O], 0.0, 1.0)
    
    # 1. Compute gas mass flow rates using PHYSICALLY ACCURATE choked flow equations
    # Flow path: COPV -> Regulator -> Tanks (when valves open)
    # Model: Compressible gas flow through orifices with proper choked/subsonic flow
    
    # Pressurant properties and orifice geometry now come from DynamicsParams rather than
    # being literals here -- same defaults, but settable per vehicle. See docs/adr/0001: this
    # COPV -> regulator -> tank chain is one of the feed models lib/feedtwin absorbs.
    gamma_gas = params.gamma_gas
    Cd_regulator = params.Cd_regulator
    Cd_valve = params.Cd_valve
 
    A_regulator = params.A_regulator
    A_valve_F = params.A_valve_F
    A_valve_O = params.A_valve_O
    
    # Gas flow from COPV to regulator [kg/s]
    # CRITICAL: Flow ONLY happens when at least one valve is open (u > 0)
    # When both valves are closed (u_F = 0, u_O = 0), NO flow from COPV to regulator
    # This is the key: control gates the flow - no control = no flow = pure blowdown
    u_total = max(u_F, u_O)  # Flow happens if either valve is open
    
    # Regulator can only supply flow if COPV pressure is above regulator setpoint
    # Use current COPV pressure (P_copv) for flow calculation, not next (P_copv_next)
    # P_copv_next will be calculated later after we determine the flow
    if params.reg_setpoint is not None:
        # Regulator maintains setpoint as long as COPV > setpoint
        reg_output_pressure = params.reg_setpoint
        can_supply = P_copv >= params.reg_setpoint
    else:
        # No setpoint: use ratio-based model
        reg_output_pressure = min(P_copv, P_reg)
        can_supply = P_copv > P_reg
    
    # CRITICAL: Only flow if at least one valve is open AND regulator can supply
    # If u_total = 0 (both valves closed), mdot_gas_to_reg = 0 (no flow)
    if u_total > 1e-6 and can_supply:
        # PHYSICALLY ACCURATE: Use choked flow equation for compressible gas
        # Flow from COPV to regulator through regulator orifice
        # Regulator maintains fixed output at setpoint, so downstream pressure is setpoint
        if params.reg_setpoint is not None:
            P_downstream = params.reg_setpoint  # Regulator output pressure
        else:
            P_downstream = P_reg  # Fallback to current regulator pressure
        
        # Calculate compressible gas flow using proper choked flow equation
        # Critical pressure ratio for choked flow
        pr_crit = (2.0 / (gamma_gas + 1.0)) ** (gamma_gas / (gamma_gas - 1.0))
        pr_ratio = P_downstream / P_copv if P_copv > 0 else 0.0
        
        if pr_ratio < pr_crit:
            # CHOKED FLOW: Flow is sonic at orifice
            # mdot = Cd * A * P_up * sqrt(gamma/(R*T)) * (2/(gamma+1))^((gamma+1)/(2(gamma-1)))
            C_star = np.sqrt(gamma_gas * (2.0 / (gamma_gas + 1.0)) ** ((gamma_gas + 1.0) / (gamma_gas - 1.0)))
            mdot_gas_to_reg_max = Cd_regulator * A_regulator * P_copv / np.sqrt(params.R_gas * params.T_gas) * C_star
        else:
            # SUBSONIC FLOW: Flow is subsonic
            # mdot = Cd * A * P_up * sqrt(2*gamma/((gamma-1)RT)) * sqrt(pr^(2/gamma) - pr^((gamma+1)/gamma))
            # Use actual COPV temperature (not constant T_gas)
            term1 = (2.0 * gamma_gas) / ((gamma_gas - 1.0) * params.R_gas * T_copv)
            term2 = pr_ratio ** (2.0 / gamma_gas) - pr_ratio ** ((gamma_gas + 1.0) / gamma_gas)
            mdot_gas_to_reg_max = Cd_regulator * A_regulator * P_copv * np.sqrt(term1 * term2)
        
        # Scale by control input (u_total) - flow is gated by valve opening
        # When u_total = 0, no flow; when u_total = 1, full flow
        mdot_gas_to_reg = mdot_gas_to_reg_max * u_total
        
        # Clamp to reasonable maximum and ensure non-negative
        mdot_gas_to_reg = max(0.0, min(mdot_gas_to_reg, 0.2))  # [kg/s] - reasonable max for COPV
    else:
        mdot_gas_to_reg = 0.0
    
    # Gas flow from regulator to tanks [kg/s]
    # Split flow based on control inputs and pressure differences
    # When u_F > 0 and P_reg > P_u_F: gas flows to fuel tank
    # Flow rate: proportional to control input and pressure difference
    # CRITICAL: Flow depends on pressure difference, not ullage volume
    # Ullage volume affects pressure (P = m*R*T/V), but flow is driven by delta_P
    # Use alpha_F and alpha_O as pressurization rate coefficients [1/s per unit pressure]
    # Convert to mass flow: mdot = alpha * u * (P_reg - P_u) * effective_volume / (R*T)
    # For choked flow: mdot ~ sqrt(delta_P), but linear approximation works for small delta_P
    # Gas flow from regulator to tanks [kg/s]
    # CRITICAL: This is where control actually affects the system!
    # When u > 0, gas flows from regulator to tanks, increasing tank pressure
    # Flow is proportional to control input and pressure difference
    # alpha_F and alpha_O are pressurization rate coefficients [1/s per unit pressure]
    # For choked flow through orifice: mdot = Cd * A * P_up * sqrt(gamma/(R*T)) * constant
    # Linear approximation: mdot ~ alpha * u * (P_reg - P_u) * effective_area / (R*T)
    # Use a reasonable effective flow area based on typical solenoid valve characteristics
    # Typical solenoid: A ~ 1e-5 m² (10 mm²), Cd ~ 0.6-0.8
    # For choked flow: mdot_max ~ 0.01-0.1 kg/s for typical pressures
    # Scale alpha to give reasonable flow rates
    
    # Gas flow from regulator to tanks [kg/s]
    # CRITICAL: Model discrete PWM valve behavior to create spikes/ripple
    # PWM means valve is either FULLY OPEN (u=1) or FULLY CLOSED (u=0), switching rapidly
    # Duty cycle determines fraction of time valve is open
    # To see spikes, model valve as binary: ON or OFF based on duty cycle
    # Simple model: valve is ON if duty cycle > 0.5 (50%), OFF otherwise
    # This creates discrete switching behavior and pressure spikes
    
    # Gas flow from regulator to tanks [kg/s]
    # CRITICAL: Model discrete PWM valve behavior to create spikes/ripple
    # PWM means valve switches between fully open and fully closed
    # Duty cycle = fraction of time valve is open
    # To create visible spikes, model valve as binary (ON/OFF) with aggressive response
    # When valve opens, pressure spikes up immediately
    # When valve closes, pressure decays
    
    # Model valve as binary based on duty cycle
    # For realistic PWM: valve is ON for duty_cycle fraction of time, OFF otherwise
    # To see spikes: use duty cycle directly but make flow response very aggressive
    # Higher duty cycle = more time valve is open = more flow = higher pressure
    
    # Use regulator output pressure for flow calculation
    # CRITICAL: When COPV >= setpoint, regulator outputs at setpoint
    # When COPV < setpoint, regulator output drops with COPV
    # Use the actual regulator output pressure (which we'll compute, but for now use current logic)
    if params.reg_setpoint is not None:
        if P_copv >= params.reg_setpoint:
            P_reg_effective = params.reg_setpoint  # Regulator maintains setpoint
        else:
            P_reg_effective = P_copv  # Regulator output limited by COPV (drops below setpoint)
    else:
        P_reg_effective = P_reg  # Fallback to current regulator pressure
    
    # PHYSICALLY ACCURATE: Gas flow from regulator to fuel tank through solenoid valve
    if u_F > 1e-6 and P_reg_effective > P_u_F:
        # Use proper choked flow equation for compressible gas through valve orifice
        pr_ratio_F = P_u_F / P_reg_effective if P_reg_effective > 0 else 0.0
        pr_crit = (2.0 / (gamma_gas + 1.0)) ** (gamma_gas / (gamma_gas - 1.0))
        
        if pr_ratio_F < pr_crit:
            # CHOKED FLOW: Flow is sonic at valve
            # Use regulator temperature (assume same as COPV for now, or could use T_reg)
            T_reg_flow = T_copv  # Regulator output temperature (close to COPV temp)
            C_star = np.sqrt(gamma_gas * (2.0 / (gamma_gas + 1.0)) ** ((gamma_gas + 1.0) / (gamma_gas - 1.0)))
            mdot_gas_F_max = Cd_valve * A_valve_F * P_reg_effective / np.sqrt(params.R_gas * T_reg_flow) * C_star
        else:
            # SUBSONIC FLOW: Flow is subsonic
            T_reg_flow = T_copv  # Regulator output temperature
            term1 = (2.0 * gamma_gas) / ((gamma_gas - 1.0) * params.R_gas * T_reg_flow)
            term2 = pr_ratio_F ** (2.0 / gamma_gas) - pr_ratio_F ** ((gamma_gas + 1.0) / gamma_gas)
            mdot_gas_F_max = Cd_valve * A_valve_F * P_reg_effective * np.sqrt(term1 * term2)
        
        # Scale by duty cycle (u_F) - valve is open for u_F fraction of time (PWM)
        # Average flow = max_flow * duty_cycle
        mdot_gas_F = mdot_gas_F_max * u_F
        
        # Clamp to available flow from regulator (mass conservation)
        if u_total > 1e-6 and mdot_gas_to_reg > 0:
            # Split available flow proportionally to control inputs
            mdot_gas_F = min(mdot_gas_F, mdot_gas_to_reg * u_F / u_total)
        
        mdot_gas_F = max(mdot_gas_F, 0.0)  # Ensure non-negative
    else:
        mdot_gas_F = 0.0  # Valve closed or no pressure difference - no flow
    
    # PHYSICALLY ACCURATE: Gas flow from regulator to oxidizer tank through solenoid valve
    if u_O > 1e-6 and P_reg_effective > P_u_O:
        # Use proper choked flow equation for compressible gas through valve orifice
        pr_ratio_O = P_u_O / P_reg_effective if P_reg_effective > 0 else 0.0
        pr_crit = (2.0 / (gamma_gas + 1.0)) ** (gamma_gas / (gamma_gas - 1.0))
        
        if pr_ratio_O < pr_crit:
            # CHOKED FLOW: Flow is sonic at valve
            T_reg_flow = T_copv  # Regulator output temperature
            C_star = np.sqrt(gamma_gas * (2.0 / (gamma_gas + 1.0)) ** ((gamma_gas + 1.0) / (gamma_gas - 1.0)))
            mdot_gas_O_max = Cd_valve * A_valve_O * P_reg_effective / np.sqrt(params.R_gas * T_reg_flow) * C_star
        else:
            # SUBSONIC FLOW: Flow is subsonic
            T_reg_flow = T_copv  # Regulator output temperature
            term1 = (2.0 * gamma_gas) / ((gamma_gas - 1.0) * params.R_gas * T_reg_flow)
            term2 = pr_ratio_O ** (2.0 / gamma_gas) - pr_ratio_O ** ((gamma_gas + 1.0) / gamma_gas)
            mdot_gas_O_max = Cd_valve * A_valve_O * P_reg_effective * np.sqrt(term1 * term2)
        
        # Scale by duty cycle (u_O) - valve is open for u_O fraction of time (PWM)
        # Average flow = max_flow * duty_cycle
        mdot_gas_O = mdot_gas_O_max * u_O
        
        # Clamp to available flow from regulator (mass conservation)
        if u_total > 1e-6 and mdot_gas_to_reg > 0:
            # Split available flow proportionally to control inputs
            mdot_gas_O = min(mdot_gas_O, mdot_gas_to_reg * u_O / u_total)
        
        mdot_gas_O = max(mdot_gas_O, 0.0)  # Ensure non-negative
    else:
        mdot_gas_O = 0.0  # Valve closed or no pressure difference - no flow
    
    # Add leakage loss from COPV (always present, even when valves closed)
    # Model as small constant flow rate [kg/s]
    # Typical leakage: ~0.001-0.01 kg/s depending on system
    mdot_gas_loss = (params.copv_loss * params.V_copv) / (params.R_gas * params.T_gas)
    mdot_gas_loss = max(0.0, min(mdot_gas_loss, 0.01))  # Clamp to reasonable range
    
    # CRITICAL: Mass conservation - total gas mass flow out of COPV
    # mdot_gas_total = mdot_gas_to_reg + mdot_gas_loss
    # Note: mdot_gas_to_reg already accounts for valve states (u_total)
    mdot_gas_total = mdot_gas_to_reg + mdot_gas_loss
    
    # Verify mass conservation: gas flowing to tanks should not exceed gas from COPV
    mdot_gas_to_tanks = mdot_gas_F + mdot_gas_O
    if mdot_gas_to_tanks > mdot_gas_to_reg + 1e-6:  # Allow small numerical tolerance
        # Clamp to available flow (mass conservation)
        if mdot_gas_to_reg > 1e-6:
            scale_factor = mdot_gas_to_reg / mdot_gas_to_tanks
            mdot_gas_F = mdot_gas_F * scale_factor
            mdot_gas_O = mdot_gas_O * scale_factor
    
    # Update COPV gas mass
    # CRITICAL: Gas mass decreases as gas flows out (to regulator and loss)
    # As gas mass decreases, pressure decreases (P = m*R*T/V)
    # This models the finite gas supply in the COPV
    m_gas_copv_next = m_gas_copv - dt * mdot_gas_total
    m_gas_copv_next = max(m_gas_copv_next, 0.0)  # Clamp to non-negative
    
    # REAL-WORLD PHYSICS: Compute COPV pressure from gas mass using ideal gas law with temperature
    # P = (m * R * T) / (V * Z)
    # As m decreases (gas flows out), P decreases
    # As T decreases (polytropic expansion), P decreases further
    # This is the key: limited gas supply + temperature drop means pressure drops faster
    if params.V_copv > 1e-10:
        # Update COPV temperature for next step (polytropic expansion)
        if use_polytropic and params._m_copv_0 > 1e-10:
            rho_copv_next = m_gas_copv_next / params.V_copv
            rho_copv_0 = params._m_copv_0 / params.V_copv
            if rho_copv_0 > 1e-10:
                T_copv_next = params._T_copv_0 * (rho_copv_next / rho_copv_0) ** (n_poly - 1.0)
                T_copv_next = max(200.0, min(400.0, T_copv_next))
            else:
                T_copv_next = T_copv
        else:
            T_copv_next = T_copv
        
        P_copv_next = (m_gas_copv_next * params.R_gas * T_copv_next) / (params.V_copv * params.Z_gas)
    else:
        P_copv_next = 0.0
    P_copv_next = max(P_copv_next, 0.0)  # Clamp to non-negative
    
    # 2. Regulator pressure - MATCH HARDWARE BEHAVIOR
    # HARDWARE OBSERVATION: Upstream pressure (regulator) oscillates with control activity
    # - Oscillations: ~128-140 psi when control is active (regular, ~5-10 Hz)
    # - Tank pressures (P_fuel) are much smoother (damped by tank volume)
    # 
    # Real regulator behavior:
    # - Maintains setpoint when COPV can supply it
    # - Shows oscillations due to valve opening/closing (PWM control)
    # - Output pressure responds to downstream demand
    # - When COPV drops below setpoint, output drops with COPV
    if params.reg_setpoint is not None:
        # Fixed setpoint regulator: output is clamped to setpoint when COPV can supply it
        if P_copv >= params.reg_setpoint:
            # COPV can supply setpoint - regulator maintains setpoint
            base_pressure = params.reg_setpoint
            
            # HARDWARE: Regulator output shows oscillations due to PWM valve switching
            # Oscillations are more pronounced when control is active
            # Hardware shows: oscillations between ~128-140 psi (setpoint ~1000 psi = 6.9 MPa)
            # This is ~±5-7% oscillation around setpoint
            if u_total > 1e-6:
                # Add oscillation based on control activity (PWM switching)
                # Amplitude: ~5-7% of setpoint (matches hardware ~128-140 psi range)
                # Frequency: PWM frequency (would need time for proper modeling)
                # For now, use control magnitude to estimate oscillation amplitude
                oscillation_amplitude = 0.06 * params.reg_setpoint * u_total  # ~6% of setpoint
                # Simple oscillation: varies with control magnitude
                # Hardware shows regular oscillations, so use a pattern
                # Use sum of control inputs to create oscillation pattern
                control_sum = u_F + u_O
                oscillation = oscillation_amplitude * np.sin(control_sum * np.pi * 2.0)  # Oscillates with control
                P_reg_next = base_pressure + oscillation
                # Clamp to reasonable range (±10% of setpoint)
                P_reg_next = max(base_pressure * 0.9, min(base_pressure * 1.1, P_reg_next))
            else:
                P_reg_next = base_pressure  # No control = no oscillation (stable at setpoint)
        else:
            # COPV pressure below setpoint - regulator CANNOT maintain setpoint
            # Output drops with COPV (regulator output limited by input)
            P_reg_next = P_copv  # Output limited by COPV (drops below setpoint when COPV < setpoint)
    else:
        # No setpoint: use ratio-based model (less realistic)
        P_reg_next = params.reg_ratio * P_copv
        # Clamp to not exceed current COPV
        P_reg_next = min(P_reg_next, P_copv)
    
    # 3. Ullage volume dynamics (blowdown)
    # V_u increases as propellant is consumed
    # V_u,i[k+1] = V_u,i[k] + dt * mdot_i / rho_i
    # CRITICAL: Mass flow to chamber ALWAYS happens (pressure-dependent, not gated by control)
    # Control input (u) only affects gas flow INTO tank, not propellant flow OUT
    # Propellant flows out based on feed pressure and injector characteristics
    # mdot_F and mdot_O come from engine physics (pressure-dependent)
    # 
    # BLOWDOWN: When u = 0 (valves closed):
    #   - No gas flows into tanks (mdot_gas_F = 0, mdot_gas_O = 0)
    #   - Gas mass in tanks stays constant (m_gas_F = const, m_gas_O = const)
    #   - Propellant still flows to chamber (mdot_F > 0, mdot_O > 0)
    #   - Ullage volumes increase (V_u_F increases, V_u_O increases)
    #   - Pressure decreases: P = (m * R * T) / (V * Z)
    #     Since m constant and V increases, P decreases (BLOWDOWN)
    #   - CRITICAL: As pressure decreases, mdot decreases (pressure-dependent)
    #     This makes blowdown EXPONENTIAL: dP/dt ~ -k*P, so P(t) = P0*exp(-k*t)
    
    # Ensure mdot values are valid (non-negative, finite)
    mdot_F_valid = max(0.0, mdot_F) if np.isfinite(mdot_F) else 0.0
    mdot_O_valid = max(0.0, mdot_O) if np.isfinite(mdot_O) else 0.0
    
    # CRITICAL: Make mdot pressure-dependent for exponential blowdown
    # When pressure drops, mdot should decrease proportionally
    # Model: mdot ~ sqrt(P) for choked flow, or mdot ~ P for linear approximation
    # Use ullage pressure (P_u) as it's the driving pressure for flow
    # For exponential blowdown: as P decreases, mdot decreases, making decay exponential
    
    # Pressure-dependent scaling for mdot (makes blowdown exponential)
    # When pressure is high, mdot is high; when pressure drops, mdot drops
    # Use a reference pressure (e.g., regulator setpoint or typical operating pressure)
    # For choked injector flow: mdot ~ sqrt(P), but linear approximation also works
    P_ref_F = 5e6  # Reference pressure for fuel [Pa] (~725 psi, typical operating pressure)
    P_ref_O = 5e6  # Reference pressure for oxidizer [Pa]
    
    # Pressure-dependent mdot scaling
    # For choked flow: mdot ~ sqrt(P), but linear is simpler and still gives exponential decay
    # When P drops, mdot drops proportionally, making ullage growth slow down
    # This creates exponential pressure decay: dP/dt = -k*P -> P(t) = P0*exp(-k*t)
    # Use sqrt for choked flow behavior (more realistic)
    mdot_scale_F = np.sqrt(max(P_u_F, 1e5) / P_ref_F)  # sqrt(P/P_ref) for choked flow
    mdot_scale_O = np.sqrt(max(P_u_O, 1e5) / P_ref_O)
    
    # Clamp scaling to reasonable range (0.1 to 2.0)
    # Prevents mdot from becoming too small or too large
    mdot_scale_F = max(0.1, min(2.0, mdot_scale_F))
    mdot_scale_O = max(0.1, min(2.0, mdot_scale_O))
    
    # Apply pressure-dependent scaling to mdot
    # CRITICAL: This makes blowdown exponential - as pressure drops, mdot drops, decay accelerates
    # Higher pressure -> higher mdot -> faster ullage growth -> faster pressure drop initially
    # Lower pressure -> lower mdot -> slower ullage growth -> but pressure still drops (exponential)
    mdot_F_pressure_dependent = mdot_F_valid * mdot_scale_F
    mdot_O_pressure_dependent = mdot_O_valid * mdot_scale_O
    
    # CRITICAL: When u=0 (valves closed), we have PURE BLOWDOWN
    # In pure blowdown: no gas enters (mdot_gas = 0), so gas mass is constant
    # Pressure drops because ullage volume increases (propellant consumed)
    # With pressure-dependent mdot, this creates EXPONENTIAL decay: P(t) = P0*exp(-k*t)
    # Make blowdown more aggressive when valves are closed
    # Note: u_total is already defined earlier in the function (line 152)
    if u_total < 1e-6:  # Both valves closed - pure blowdown
        # In blowdown, mdot should be MORE pressure-dependent (stronger exponential decay)
        # Scale mdot more aggressively with pressure to make blowdown visible
        # This ensures exponential decay is clearly visible when solenoids are closed
        blowdown_factor = 1.5  # Make blowdown 1.5x more aggressive
        mdot_F_pressure_dependent = mdot_F_pressure_dependent * blowdown_factor
        mdot_O_pressure_dependent = mdot_O_pressure_dependent * blowdown_factor
    
    # Ullage volume growth: V_u increases as propellant is consumed
    # CRITICAL: As pressure increases, mdot increases (from engine physics), 
    # which makes ullage grow FASTER (non-linear growth)
    # Higher pressure -> higher mdot -> faster ullage growth -> exponential-like behavior
    # When pressure is high, mdot is high, so ullage grows fast
    # When pressure drops, mdot drops, so ullage grows slower
    # This creates non-linear (exponential-like) ullage growth
    #
    # CRITICAL STARTUP BEHAVIOR: When flow starts, ullage volume increases IMMEDIATELY
    # This causes pressure to drop INSTANTLY because P = (m*R*T)/(V*Z)
    # As V increases (propellant consumed), P decreases even if m stays constant
    # This is the key: at startup, when flow begins, pressure should drop significantly
    V_u_F_next = V_u_F + dt * mdot_F_pressure_dependent / params.rho_F
    V_u_O_next = V_u_O + dt * mdot_O_pressure_dependent / params.rho_O
    
    # Ensure volumes are non-negative
    V_u_F_next = max(V_u_F_next, 0.0)
    V_u_O_next = max(V_u_O_next, 0.0)
    
    # CRITICAL: Ensure ullage volume grows immediately when flow starts
    # If mdot > 0, ullage MUST grow, causing immediate pressure drop
    # This models the realistic behavior: flow starts -> propellant consumed -> ullage grows -> pressure drops
    if mdot_F_pressure_dependent > 1e-6 and V_u_F_next <= V_u_F:
        # Force ullage growth if flow is happening
        V_u_F_next = V_u_F + dt * mdot_F_pressure_dependent / params.rho_F
    if mdot_O_pressure_dependent > 1e-6 and V_u_O_next <= V_u_O:
        # Force ullage growth if flow is happening
        V_u_O_next = V_u_O + dt * mdot_O_pressure_dependent / params.rho_O
    
    # 4. Ullage pressure dynamics - track gas mass
    # Key principle: Gas mass in ullage changes due to:
    #   - Gas flow IN from regulator (when valve open, u > 0)
    #   - Gas mass stays constant when valve closed (no gas enters)
    # Pressure changes due to:
    #   - Gas mass changes (from regulator flow)
    #   - Ullage volume changes (from propellant consumption - BLOWDOWN)
    #
    # CRITICAL PHYSICS: P = (m * R * T) / (V * Z)
    # - As ullage volume V increases (propellant consumed), same gas mass m gives lower pressure
    # - As gas mass m increases (valve open), pressure increases, but volume also increases
    # - Net effect depends on relative rates: if V increases faster than m, pressure decreases (blowdown)
    # - When valve closed: m constant, V increases -> pressure always decreases (pure blowdown)
    # - CRITICAL: With pressure-dependent mdot, blowdown is EXPONENTIAL
    #   As P decreases, mdot decreases, V grows slower, but P still decreases exponentially
    #   dP/dt = -k*P -> P(t) = P0*exp(-k*t) (exponential decay)
    
    # Fuel ullage pressure
    # Update gas mass: increases when valve open (gas flows in)
    m_gas_F_next = m_gas_F + dt * mdot_gas_F
    m_gas_F_next = max(m_gas_F_next, 0.0)  # Clamp to non-negative
    
    # LIQUID ENGINE PHYSICS: Pressure from ideal gas law P = (m * R * T) / (V * Z)
    # 
    # CRITICAL STARTUP: Sudden pressure drop when flow starts (controller catch-up)
    # - Flow begins -> ullage volume increases IMMEDIATELY -> pressure drops INSTANTLY
    # - Controller hasn't responded yet, so pressure drops before control can compensate
    # - This is the realistic startup: dynamics have instantly changed
    #
    # CRITICAL END STATE: Final pressure MUCH LOWER than start pressure
    # - COPV volume is SMALL (4.5-6L) at high pressure (2750 psi)
    # - Tank volumes are HUGE (11-17L, grow as propellant consumed)
    # - When COPV gas flows to tanks, it expands into much larger volumes
    # - P_final ≈ P_initial * (V_copv / V_tank_final) - MUCH LOWER
    # - With both tanks and growing ullage, final pressure can be 10-20% of initial
    # - This is liquid engine physics: gas expands into huge tank volumes
    #
    # Both m, V, and T affect pressure:
    # - Larger V (more ullage) requires more m to maintain same pressure
    # - Lower T (polytropic expansion) reduces pressure further
    # - When V increases faster than m, pressure decreases (blowdown)
    # - When m increases faster than V, pressure increases (pressurization)
    if V_u_F_next > 1e-10:
        # Update fuel tank temperature for next step (polytropic expansion)
        if use_polytropic and params._m_F_0 > 1e-10 and params._V_F_0 > 1e-10:
            rho_F_next = m_gas_F_next / V_u_F_next
            rho_F_0 = params._m_F_0 / params._V_F_0
            if rho_F_0 > 1e-10:
                T_gas_F_next = params._T_F_0 * (rho_F_next / rho_F_0) ** (n_poly - 1.0)
                T_gas_F_next = max(200.0, min(400.0, T_gas_F_next))
            else:
                T_gas_F_next = T_gas_F
        else:
            T_gas_F_next = T_gas_F
        
        # LIQUID ENGINE PHYSICS: Pressure calculation with polytropic temperature
        # P = (m * R * T) / (V * Z)
        # When gas flows from small COPV to large tanks, pressure DROPS SIGNIFICANTLY
        # because tanks are much larger (11-17L vs 4.5-6L COPV)
        P_u_F_next = (m_gas_F_next * params.R_gas * T_gas_F_next) / (V_u_F_next * params.Z_gas)
    else:
        P_u_F_next = 0.0
    
    # CRITICAL: Ensure pressure drops immediately when flow starts
    # If ullage volume increased (flow happened), pressure MUST decrease
    # This models the realistic startup behavior: flow starts -> pressure drops instantly
    if V_u_F_next > V_u_F and mdot_F_pressure_dependent > 1e-6:
        # Flow started: ullage grew, so pressure should drop
        # The ideal gas law already handles this, but ensure it's pronounced
        # If pressure didn't drop enough, it means gas mass might be increasing too fast
        # In pure blowdown (u=0), gas mass is constant, so pressure MUST drop
        if u_F < 1e-6:  # Valve closed - pure blowdown
            # In blowdown, gas mass is constant, so pressure drop is purely from volume increase
            # This should be IMMEDIATE and SIGNIFICANT at startup
            pass  # Ideal gas law already handles this correctly
    P_u_F_next = max(P_u_F_next, 0.0)  # Clamp to non-negative
    
    # Oxidizer ullage pressure
    # Update gas mass: increases when valve open (gas flows in), constant when valve closed
    # CRITICAL: When u_O = 0, mdot_gas_O = 0, so m_gas_O stays constant
    m_gas_O_next = m_gas_O + dt * mdot_gas_O
    m_gas_O_next = max(m_gas_O_next, 0.0)  # Clamp to non-negative
    
    # REAL-WORLD PHYSICS: Same logic as fuel with polytropic temperature
    # BLOWDOWN CASE (u_O = 0):
    #   - m_gas_O = constant (no gas flow in)
    #   - V_u_O increases (propellant consumed)
    #   - T_gas_O decreases (polytropic expansion)
    #   - P_u_O = (m_gas_O * R * T) / (V_u_O * Z)
    #   - As V_u_O increases and T decreases, P_u_O decreases (BLOWDOWN)
    #
    # CRITICAL STARTUP BEHAVIOR: When flow starts, pressure drops IMMEDIATELY
    # This is the realistic behavior: flow begins -> ullage grows -> T drops -> pressure drops instantly
    if V_u_O_next > 1e-10:
        # Update oxidizer tank temperature for next step (polytropic expansion)
        if use_polytropic and params._m_O_0 > 1e-10 and params._V_O_0 > 1e-10:
            rho_O_next = m_gas_O_next / V_u_O_next
            rho_O_0 = params._m_O_0 / params._V_O_0
            if rho_O_0 > 1e-10:
                T_gas_O_next = params._T_O_0 * (rho_O_next / rho_O_0) ** (n_poly - 1.0)
                T_gas_O_next = max(200.0, min(400.0, T_gas_O_next))
            else:
                T_gas_O_next = T_gas_O
        else:
            T_gas_O_next = T_gas_O
        
        # CRITICAL: Pressure calculation MUST account for volume expansion
        # Same as fuel: when gas flows from small COPV to large tank, pressure DROPS SIGNIFICANTLY
        P_u_O_next = (m_gas_O_next * params.R_gas * T_gas_O_next) / (V_u_O_next * params.Z_gas)
    else:
        P_u_O_next = 0.0
    
    # CRITICAL STARTUP BEHAVIOR: Immediate pressure drop when flow starts
    # Same as fuel: sudden drop because dynamics have instantly changed
    # Flow begins -> ullage grows -> pressure drops instantly (controller catch-up)
    if V_u_O_next > V_u_O and mdot_O_pressure_dependent > 1e-6:
        # Flow started: ullage grew, so pressure MUST drop
        # Ideal gas law P = m*R*T/V handles this correctly
        pass  # Ideal gas law already handles this correctly
    
    # CRITICAL END STATE: Final pressure should be MUCH LOWER
    # Same as fuel: when all gas flows from COPV to tanks, final pressure is much lower
    # because tanks are much larger than COPV
    P_u_O_next = max(P_u_O_next, 0.0)  # Clamp to non-negative
    
    # 5. Feed pressure dynamics (first-order lag with increased damping)
    # HARDWARE OBSERVATION: Downstream pressures are much smoother than upstream
    # This is due to:
    # 1. Tank volume damping (large volume smooths out pressure changes)
    # 2. Feed line damping (first-order lag)
    # 3. Inertia of liquid propellant
    #
    # P_d_i[k+1] = P_d_i[k] + dt*( (P_u,i - P_d_i)/tau_line_i )
    # Increase tau_line to match hardware smoothness (hardware shows very smooth downstream)
    # Hardware: downstream pressure is smooth even when upstream oscillates
    tau_line_F_effective = params.tau_line_F * 2.0  # Increase damping to match hardware
    tau_line_O_effective = params.tau_line_O * 2.0
    
    P_d_F_next = P_d_F + dt * (P_u_F - P_d_F) / tau_line_F_effective
    P_d_O_next = P_d_O + dt * (P_u_O - P_d_O) / tau_line_O_effective
    
    # Assemble next state (including gas masses)
    x_next = np.array([
        P_copv_next,
        P_reg_next,
        P_u_F_next,
        P_u_O_next,
        P_d_F_next,
        P_d_O_next,
        V_u_F_next,
        V_u_O_next,
        m_gas_copv_next,
        m_gas_F_next,
        m_gas_O_next,
    ], dtype=np.float64)
    
    # Validate output state size
    if len(x_next) != N_STATE:
        raise ValueError(f"Output state vector must have {N_STATE} elements, got {len(x_next)}")
    
    return x_next
 
 
def linearize(
    x: np.ndarray,
    u: np.ndarray,
    dt: float,
    params: DynamicsParams,
    mdot_F: float,
    mdot_O: float,
    eps: float = 1e-6,
) -> Tuple[np.ndarray, np.ndarray]:
    """
    Linearize dynamics via finite differences.
    
    Computes A and B matrices such that:
    x[k+1] ≈ A @ x[k] + B @ u[k] + c
    
    Parameters:
    -----------
    x : np.ndarray, shape (N_STATE,)
        State vector
    u : np.ndarray, shape (N_CONTROL,)
        Control vector
    dt : float
        Time step [s]
    params : DynamicsParams
        Dynamics parameters
    mdot_F : float
        Fuel mass flow rate [kg/s]
    mdot_O : float
        Oxidizer mass flow rate [kg/s]
    eps : float
        Finite difference step size
    
    Returns:
    --------
    A : np.ndarray, shape (N_STATE, N_STATE)
        State Jacobian matrix
    B : np.ndarray, shape (N_STATE, N_CONTROL)
        Control Jacobian matrix
    """
    # Nominal next state
    x_nom = step(x, u, dt, params, mdot_F, mdot_O)
    
    # Compute A matrix (∂f/∂x) via finite differences
    A = np.zeros((N_STATE, N_STATE), dtype=np.float64)
    for i in range(N_STATE):
        x_pert = x.copy()
        x_pert[i] += eps
        x_pert_next = step(x_pert, u, dt, params, mdot_F, mdot_O)
        A[:, i] = (x_pert_next - x_nom) / eps
    
    # Compute B matrix (∂f/∂u) via finite differences
    B = np.zeros((N_STATE, N_CONTROL), dtype=np.float64)
    for i in range(N_CONTROL):
        u_pert = u.copy()
        u_pert[i] += eps
        u_pert[i] = np.clip(u_pert[i], 0.0, 1.0)  # Ensure in [0, 1]
        u_pert_next = step(x, u_pert, dt, params, mdot_F, mdot_O)
        B[:, i] = (u_pert_next - x_nom) / eps
    
    return A, B