Models

src.pcgym.model_classes

cstr dataclass

Bases: BaseModel

first_order_system dataclass

First-order system model.

Attributes:

Name	Type	Description
K	float	Gain
tau	float	Time constant
int_method	str	Integration method ('jax' or other)

__call__(x, u)

Calculate the state derivative for the first-order system.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state [x]	required
u	ndarray	Input [u]	required

Returns:

Type	Description
ndarray	np.ndarray: State derivative [dx/dt]

info()

Get model information.

Returns:

Name	Type	Description
dict	dict	Dictionary containing model parameters, states, inputs, and disturbances.

multistage_extraction dataclass

Multistage extraction model.

Attributes:

Name	Type	Description
Vl	float	Liquid volume in each stage
Vg	float	Gas volume in each stage
m	float	Equilibrium constant
Kla	float	Mass transfer capacity constant (1/hr)
eq_exponent	float	Nonlinearity of the equilibrium relationship
X0	float	Feed concentration of liquid
Y6	float	Feed concentration of gas
int_method	str	Integration method ('jax' or other)

__call__(x, u)

Calculate the state derivatives for the multistage extraction model.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state [X1, Y1, X2, Y2, X3, Y3, X4, Y4, X5, Y5]	required
u	ndarray	Input [L, G] or [L, G, X0, Y6]	required

Returns:

Type	Description
ndarray	np.ndarray: State derivatives

info()

Get model information.

Returns:

Name	Type	Description
dict	dict	Dictionary containing model parameters, states, inputs, and disturbances.

nonsmooth_control dataclass

Nonsmooth control model (Bang-Bang Control).

Attributes:

Name	Type	Description
int_method	str	Integration method ('jax' or other)
a_11,	a_12, a_21, a_22 (float	System matrix coefficients
b_1,	b_2 (float	Input vector coefficients

__call__(x, u)

Calculate the state derivatives for the nonsmooth control model.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state [x1, x2]	required
u	ndarray	Input [u]	required

Returns:

Type	Description
ndarray	np.ndarray: State derivatives [dx1/dt, dx2/dt]

info()

Get model information.

Returns:

Name	Type	Description
dict	dict	Dictionary containing model parameters, states, inputs, and disturbances.

distillation_column dataclass

Distillation column model.

Attributes:

Name	Type	Description
D	float	Distillate flow rate (kmol/hr)
q	float	Feed quality (q=1 is saturated liquid)
alpha	float	Relative volatility of more volatile component
X_feed	float	Feed composition
M0,	Mb, M (float	Holdup in different sections of the column

__call__(x, u)

Calculate the state derivatives for the distillation column.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state [X0, X1, X2, X3, Xf, X4, X5, X6, Xb]	required
u	ndarray	Input [R, F]	required

Returns:

Type	Description
	np.ndarray: State derivatives

info()

Get model information.

Returns:

Name	Type	Description
dict		Dictionary containing model parameters, states, inputs, and disturbances.

cstr_series_recycle dataclass

CSTR series with recycle model.

Attributes:

Name	Type	Description
C_O	float	Initial concentration (mol/m3)
T_O	float	Initial temperature (K)
V1,	V2 (float	Reactor volumes (m3)
U1A1,	U2A2 (float	Heat transfer coefficients times areas (kJ/s*K)
rho	float	Density (kg/m3)
cp	float	Heat capacity (kJ/kg*K)
k	float	Reaction rate constant (s-1)
E	float	Activation energy (kJ/mol)
deltaH	float	Heat of reaction (kJ/mol)
R	float	Gas constant (kJ/mol K)

__call__(x, u)

Calculate the state derivatives for the CSTR series with recycle.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state [C1, T1, C2, T2]	required
u	ndarray	Input [F, L, Tc1, Tc2]	required

Returns:

Type	Description
	np.ndarray: State derivatives

info()

Get model information.

Returns:

Name	Type	Description
dict		Dictionary containing model parameters, states, inputs, and disturbances.

multistage_extraction_reactive dataclass

Multistage extraction with reactive components model.

Attributes:

Name	Type	Description
Vl	float	Liquid volume in each stage
Vg	float	Gas volume in each stage
m	float	Equilibrium constant
Kla	float	Mass transfer capacity constant (1/hr)
k	float	Reaction equilibrium constant
eq_exponent	float	Nonlinearity of the equilibrium relationship
XA0	float	Feed concentration of component A in liquid phase
YA6,	YB6, YC6 (float	Feed concentrations in gas phase

__call__(x, u)

Calculate the state derivatives for the multistage extraction with reactive components.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state [XA1, YA1, YB1, YC1, XA2, YA2, YB2, YC2, XA3, YA3, YB3, YC3, XA4, YA4, YB4, YC4, XA5, YA5, YB5, YC5]	required
u	ndarray	Input [L, G]	required

Returns:

Type	Description
	np.ndarray: State derivatives

info()

Get model information.

Returns:

Name	Type	Description
dict		Dictionary containing model parameters, states, inputs, and disturbances.

four_tank dataclass

Four-tank system model.

Attributes:

Name	Type	Description
g	float	Acceleration due to gravity (m/s2)
gamma_1,	gamma_2 (float	Fraction bypassed by valves
k1,	k2 (float	Pump gains (m3/Volts S)
a1,	a2, a3, a4 (float	Cross-sectional areas of outlets (m2)
A1,	A2, A3, A4 (float	Cross-sectional areas of tanks (m2)
int_method	str	Integration method ('jax' or other)

__call__(x, u)

Calculate the state derivatives for the four-tank system.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state [h1, h2, h3, h4]	required
u	ndarray	Input [v1, v2]	required

Returns:

Type	Description
	np.ndarray: State derivatives

info()

Get model information.

Returns:

Name	Type	Description
dict		Dictionary containing model parameters, states, inputs, and disturbances.

heat_exchanger dataclass

Heat exchanger model.

Attributes:

Name	Type	Description
Utm	float	Tube-metal overall heat transfer coefficient (kW/m2 K)
Usm	float	Shell-metal overall heat transfer coefficient (kW/m2 K)
L	float	Length segment of each stage
Dt	float	Internal diameter of tube wall (m)
Dm	float	Outside diameter of metal wall (m)
Ds	float	Shell wall diameter (m)
cpt,	cpm, cps (float	Heat capacities (kJ/kg K)
rhot,	rhom, rhos (float	Densities (kg/m3)

__call__(x, u)

Calculate the state derivatives for the heat exchanger.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state [Tt1, Tm1, Ts1, ..., Tt8, Tm8, Ts8]	required
u	ndarray	Input [Ft, Fs, Tt0, Ts9]	required

Returns:

Type	Description
	np.ndarray: State derivatives

info()

Get model information.

Returns:

Name	Type	Description
dict		Dictionary containing model parameters, states, inputs, and disturbances.

biofilm_reactor dataclass

Biofilm reactor model.

Attributes:

Name	Type	Description
V	float	Volume of one reactor stage (L)
Va	float	Volume of absorber tank (L)
Kla	float	Transfer coefficient (hr)
m	float	Equilibrium constant
eq_exponent	float	Nonlinearity of equilibrium relationship
O_air	float	Concentration of oxygen in air (mg/L)
vm_1,	vm_2 (float	Maximum velocities through fluidized bed (mg/L hr)
K1,	K2 (float	Equilibrium constants for reactions
KO_1,	KO_2 (float	Equilibrium constants for oxygen
int_method	str	Integration method ('jax' or other)

__call__(x, u)

Calculate the state derivatives for the biofilm reactor.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state [S1_1, S2_1, S3_1, O_1, ..., S1_A, S2_A, S3_A, O_A]	required
u	ndarray	Input [F, Fr, S1_F, S2_F, S3_F]	required

Returns:

Type	Description
	np.ndarray: State derivatives

info()

Get model information.

Returns:

Name	Type	Description
dict		Dictionary containing model parameters, states, inputs, and disturbances.

polymerisation_reactor dataclass

Polymerisation reactor model.

Attributes:

Name	Type	Description
Ap,	Ad, At (float	Pre-exponential factors (1/sec)
Ep_over_R,	Ed_over_R, Et_over_R (float	Activation energies over R (K)
f	float	Reactivity fraction for free radicals
V	float	Reactor volume (m3)
deltaHp	float	Heat of reaction per monomer unit (kJ/kmol)
rho	float	Density of input fluid mixture (kg/m3)
cp	float	Heat capacity of fluid mixture (kj/kg K)

__call__(x, u)

Calculate the state derivatives for the polymerisation reactor.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state [T, M, I]	required
u	ndarray	Input [F, Tf, Mf, If]	required

Returns:

Type	Description
	np.ndarray: State derivatives

info()

Get model information.

Returns:

Name	Type	Description
dict		Dictionary containing model parameters, states, inputs, and disturbances.

crystallization dataclass

Crystallization of K2SO4 Control (PBE Model).

This model represents a highly nonlinear crystallization process based on population balance equations (PBE). It simulates the evolution of crystal size distribution and concentration during the crystallization process.

Attributes:

Name	Type	Description
ka	float	Nucleation rate constant
kb	float	Nucleation activation energy parameter
kc	float	Nucleation supersaturation exponent
kd	float	Nucleation crystal density exponent
kg	float	Growth rate constant
k1	float	Growth activation energy parameter
k2	float	Growth supersaturation exponent
a	float	Moment model parameter for nucleation
b	float	Moment model parameter for growth
alfa	float	Shape factor for volume calculation
ro	float	Crystal density (g/cm^3)
int_method	str	Integration method ('jax' or other)

Reference

https://pubs.acs.org/doi/10.1021/acs.iecr.3c00739

__call__(x, u)

Calculate the state derivatives for the crystallization model.

This method computes the rates of change for the moments of the crystal size distribution and the solute concentration based on the current state and input temperature.

Parameters:

Name	Type	Description	Default
x	ndarray	Current state vector containing: - mu0 (float): 0th moment of crystal size distribution - mu1 (float): 1st moment of crystal size distribution - mu2 (float): 2nd moment of crystal size distribution - mu3 (float): 3rd moment of crystal size distribution - conc (float): Solute concentration	required
u	ndarray	Input vector containing: - T (float): Temperature (°C)	required

Returns:

Type	Description
	np.ndarray: State derivatives vector containing: - dmu0/dt: Rate of change of 0th moment - dmu1/dt: Rate of change of 1st moment - dmu2/dt: Rate of change of 2nd moment - dmu3/dt: Rate of change of 3rd moment - dconc/dt: Rate of change of solute concentration

info()

Get model information.

This method returns a dictionary containing information about the model's parameters, states, inputs, and disturbances.

Returns:

Name	Type	Description
dict		Dictionary containing: - parameters: Model parameters - states: Names of state variables - inputs: Names of input variables - disturbances: Names of disturbance variables (if any)