#########################################################################################
##
## Blocks for residence time modeling
## (blocks/fusion/residencetime.py)
##
#########################################################################################
# IMPORTS ===============================================================================
import numpy as np
from ..dynsys import DynamicalSystem
# BLOCKS ================================================================================
[docs]
class ResidenceTime(DynamicalSystem):
"""Chemical process block with residence time model.
This block implements an internal 1st order linear ode with
multiple inputs, outputs, an internal constant source term
and no direct passthrough.
The internal ODE with inputs :math:`u_i` :
.. math::
\\dot{x} = - x / \\tau + \\mathrm{src} + \\sum_i \\beta_i u_i
And the output equation for every output `i` :
.. math::
y_i = \\gamma_i x
Parameters
----------
tau : float
residence time, inverse natural frequency (eigenvalue)
betas: None | list[float] | np.ndarray[float]
weights of inputs that are accumulated in state, optional
gammas : None | list[float] | np.ndarray[float]
weights of states (fractions) for output, optional
initial_value : float
initial value of state / initial quantity of process
source_term : float
constant source term / generation term of the process
"""
def __init__(self, tau=1, betas=None, gammas=None, initial_value=0, source_term=0):
#input validation
if np.isclose(tau, 0):
raise ValueError(f"'tau' must be nonzero but is {tau}")
#time constant and input/output weights
self.tau = tau
self.betas = 1 if betas is None else np.array(betas)
self.gammas = 1 if gammas is None else np.array(gammas)
self.source_term = source_term
#rhs of residence time ode
def _fn_d(x, u, t):
return -x/self.tau + self.source_term + sum(self.betas*u)
#jacobian of rhs wrt x
def _jc_d(x, u, t):
return -1/self.tau
#output function of residence time ode
def _fn_a(x, u, t):
return self.gammas * x
#initialization just like `DynamicalSystem` block
super().__init__(func_dyn=_fn_d, jac_dyn=_jc_d, func_alg=_fn_a, initial_value=initial_value)
[docs]
class Process(ResidenceTime):
"""Simplified version of the `ResidenceTime` model block
with all inputs being summed equally and only the state
and the flux being returned to the output
This block implements an internal 1st order linear ode with
multiple inputs, outputs and no direct passthrough.
The internal ODE with inputs :math:`u_i` :
.. math::
\\dot{x} = - x / \\tau + \\mathrm{src} + \\sum_i u_i
And the output equations for output `i=0` and `i=1`:
.. math::
y_0 = x
.. math::
y_1 = x / \\tau
Parameters
----------
tau : float
residence time, inverse natural frequency (eigenvalue)
initial_value : float
initial value of state / initial quantity of process
source_term : float
constant source term / generation term of the process
"""
#max number of ports
_n_out_max = 2
#maps for input and output port labels
_port_map_out = {"x": 0, "x/tau": 1}
def __init__(self, tau=1, initial_value=0, source_term=0):
super().__init__(tau, 1, [1, 1/tau], initial_value, source_term)