Objects
Objects are available in Python GEKKO and the APMonitor language to simplify the description of complex models.
Python GEKKO Object Library
Python GEKKO has equation functions and pre-built objects. GEKKO has objects in the Deep Learning (Brain) and Thermo & Flowsheet Chemical libraries. Some of the other pre-built objects and equation functions are:
- abs(x) absolute value |x|
- abs2(x) absolute value with MPCC
- abs3(x) absolute value with binary variable for switch
- acos(x) inverse cosine, cos^-1(x)
- acosh(x) inverse hyperbolic cosine, cosh^-1(x)
- Array(type,size) array of GEKKO objects
- arx auto-regressive exogenous input (time series) model
- asin(x) inverse sine, sin^-1(x)
- asinh(x) inverse hyperbolic sine, sinh^-1(x)
- atan(x) inverse tangent, tan^-1(x)
- atanh(x) inverse hyperbolic tangent, tanh^-1(x)
- bspline bspline for 2D data
- cos(x) cosine
- cspline cubic spline for 1D data
- erf(x) error function
- erfc(x) complementary error function
- exp(x) e^x
- if3(cond,x1,x2) switch between x1 (cond<0) and x2 (cond>=0)
- log(x) log_e (x), natural log
- log10(x) log_10 (x), log base 10
- max2(x1,x2) maximum value with MPCC
- max3(x1,x2) maximum value with binary variable for switch
- min2(x1,x2) minimum value with MPCC
- min3(x1,x2) minimum value with binary variable for switch
- periodic periodic (initial=final) for dynamic problems
- pwl piece-wise linear function
- sign2(x) signum operator with MPCC
- sign3(x) signum operator with binary variable for switch
- sin(x) sine
- sinh(x) hyperbolic sine
- sqrt(x) square root
- state_space continuous/discrete and dense/sparse state space
- sum summation of elements in a list or numpy array
- tan(x) tangent
- tanh(x) hyperbolic tangent
- vsum(x) vertical sum of a single variable in the data direction
In Python GEKKO, objects are defined as components of the model as m.object_name().
Python GEKKO Example Usage (abs3)
from gekko import GEKKO
# define new GEKKO model
m = GEKKO()
# variable
x = m.Var(-0.5)
# calculate y=abs(x) with abs3
y = m.abs3(x)
# solve with APOPT (MINLP solver)
m.solve()
# print solution
print('x: ' + str(x.value))
print('y: ' + str(y.value))
# define new GEKKO model
m = GEKKO()
# variable
x = m.Var(-0.5)
# calculate y=abs(x) with abs3
y = m.abs3(x)
# solve with APOPT (MINLP solver)
m.solve()
# print solution
print('x: ' + str(x.value))
print('y: ' + str(y.value))
Python GEKKO Example Usage (Array, abs3, sum)
from gekko import GEKKO
import numpy as np
m = GEKKO()
x1 = m.Param(-2)
x2 = m.Param(-1)
x3 = np.linspace(0,1,6)
x4 = m.Array(m.Param,3)
y4 = m.Array(m.Var,3)
for i in range(3):
x4[i].value=-0.2
y4[i] = m.abs3(x4[i])
# create variable
y = m.Var()
# y = 0.6 = -2 -1 + 3 + 0.6
m.Equation(y == sum([x1,x2]) + sum(x3) + sum(y4))
m.solve() # solve
print('x1: ' + str(x1.value))
print('x2: ' + str(x2.value))
print('y: ' + str(y.value))
import numpy as np
m = GEKKO()
x1 = m.Param(-2)
x2 = m.Param(-1)
x3 = np.linspace(0,1,6)
x4 = m.Array(m.Param,3)
y4 = m.Array(m.Var,3)
for i in range(3):
x4[i].value=-0.2
y4[i] = m.abs3(x4[i])
# create variable
y = m.Var()
# y = 0.6 = -2 -1 + 3 + 0.6
m.Equation(y == sum([x1,x2]) + sum(x3) + sum(y4))
m.solve() # solve
print('x1: ' + str(x1.value))
print('x2: ' + str(x2.value))
print('y: ' + str(y.value))
APMonitor Object Library
In APMonitor, objects are defined in the Objects ... End Objects section of the model file. New instances of an object are defined by declaring a new object name equal to the parent object type.
new_child = parent_object
! example use of ABS as MPEC
Objects
a = abs
End Objects
Connections
x = a.x
y = a.y
End Connections
Parameters
x = -5
End Parameters
Variables
y
End Variables
Objects
a = abs
End Objects
Connections
x = a.x
y = a.y
End Connections
Parameters
x = -5
End Parameters
Variables
y
End Variables
The object library consists of common mathematical functions and chemical processing equipment such as feed streams, reactors, pumps, mixers, flash columns, vessels, and distillation stages. It also includes other elements that support distributed control system emulation such as a LAG and a PID controller.
- Abs - Absolute value
- ARX, Linear Time Invariant Model
- Basis spline (b-spline)
- Cubic spline (c-spline)
- Feed - Feed stream
- Feedback - Internal feedback
- Flash - Flash
- Flash_column - Flash column
- Info - Info file for variable classification
- Info_FV - Fixed Variable
- Info_MV - Manipulated Variable
- Info_SV - State Variable
- Info_CV - Controlled Variable
- Lag - First order lag
- Lookup - Lookup table
- LTI - Linear time-invariant, discrete or continuous
- Mass - Mass of a reserve
- Massflow - Massflow of a stream
- Massflows - Massflows of a stream
- Max - Maximum value (MPEC)
- Min - Minimum value (MPEC)
- Mixer - Mixer of 2 or more streams
- Periodic - Periodic boundary condition
- PID - Proportional Integral Derivative Controller
- Poly_reactor - Polymerization reactor
- Pump - Pump for changes in pressure
- PWL - Piece-wise Linear
- Reactor - Vessel with reaction of individual species
- Recovery - Separation by recovery
- Sign - Number Sign (-1 or 1)
- Splitter - Split of one stream into 2 or more streams
- Stage_1 - Distillation stage (type 1)
- Stage_2 - Distillation stage (type 2)
- Stream_lag - First order lag of streams
- Sum - Summation of multiple parameters and/or variables
- Table - Data table that creates parameters or initializes variables
- Thermo_* - Thermodynamic properties (* see Thermo information for specific properties)
- Vessel - Molar reserve with multiple inlet streams
- Vesselm - Mass reserve with multiple inlet streams
- VSum - Summation of a single variable in data dimension
Example - MIN Function
Example - Mixer Application
Example - Distillation Column
Model distill
Compounds
ethylene
propylene
propane
hydrogen
nitrogen
End Compounds
Objects
! feed stream
feed = Feed
feed_lag = Stream_Lag
feed_cooler = Vessel
feed_flash = Flash
liq_mixer = Mixer
vap_mixer = Mixer
! condenser and reflux
condenser = Vessel
drum = Flash
reflux = Splitter
! column stages
stage[1:8] = Stage_1
! reboiler
sump = Vessel
reboiler = Vessel
reboiler_flash = Flash
! mass and massflows
sump_mass = Mass
feed_massflow = Massflow
cleu_massflow = Massflow
btms_massflow = Massflow
End Objects
Connections
! feed streams
feed.* = feed_lag.inlet.*
feed_lag.outlet.* = feed_cooler.inlet.*
feed_cooler.outlet.* = feed_flash.inlet.*
feed_flash.outlet_vap.* = vap_mixer.inlet[1].*
feed_flash.outlet_liq.* = liq_mixer.inlet[1].*
! liquid down the column
liq_mixer.inlet[2].* = stage[1].l_out.*
liq_mixer.outlet.* = stage[2].l_in.*
stage[2:7].l_out.* = stage[3:8].l_in.*
stage[8].l_out.* = sump.inlet.*
! reboiler
sump.outlet.* = reboiler.inlet.*
reboiler.outlet.* = reboiler_flash.inlet.*
! vapor up the column
reboiler_flash.outlet_vap.* = stage[8].v_in.*
stage[3:8].v_out.* = stage[2:7].v_in.*
vap_mixer.inlet[2].* = stage[2].v_out.*
vap_mixer.outlet.* = stage[1].v_in.*
! condenser
stage[1].v_out.* = condenser.inlet.*
condenser.outlet.* = drum.inlet.*
drum.outlet_liq.* = reflux.inlet.*
reflux.outlet[2].* = stage[1].l_in.*
! mass and massflow meters
sump.reserve.* = sump_mass.acc.*
feed.* = feed_massflow.stream.*
drum.outlet_vap.* = cleu_massflow.stream.*
reboiler_flash.outlet_liq.* = btms_massflow.stream.*
! stream pressures
strm_p = stage[1].v_out.p
strm_p = stage[2:8].l_out.p
strm_p = stage[3:8].v_out.p
! feed and stage pressures
fd_p = stage[1:8].l_res.p
End Connections
Model custom
Parameters
fd_t = 370.0 ! K
fd_p = 3.11e6 ! Pa
fd_c2h4 = 0.28 ! mol%
fd_c3h6 = 0.6184 ! mol%
fd_c3h8 = 0.0916 ! mol%
fd_h2 = 0.01 ! mol%
strm_p = fd_p ! Pa
fd_ndot = 1.0
End Parameters
Variables
fd_mdot = 0.395 ! kg/sec
End Variables
Connections
fd_t = feed.t
fd_p = feed.p
fd_c2h4 = feed.x[1]
fd_c3h6 = feed.x[2]
fd_c3h8 = feed.x[3]
fd_h2 = feed.x[4]
fd_mdot = feed_massflow.mdot
fd_ndot = feed.ndot
End Connections
Intermediates
End Intermediates
Equations
End Equations
End Model
Compounds
ethylene
propylene
propane
hydrogen
nitrogen
End Compounds
Objects
! feed stream
feed = Feed
feed_lag = Stream_Lag
feed_cooler = Vessel
feed_flash = Flash
liq_mixer = Mixer
vap_mixer = Mixer
! condenser and reflux
condenser = Vessel
drum = Flash
reflux = Splitter
! column stages
stage[1:8] = Stage_1
! reboiler
sump = Vessel
reboiler = Vessel
reboiler_flash = Flash
! mass and massflows
sump_mass = Mass
feed_massflow = Massflow
cleu_massflow = Massflow
btms_massflow = Massflow
End Objects
Connections
! feed streams
feed.* = feed_lag.inlet.*
feed_lag.outlet.* = feed_cooler.inlet.*
feed_cooler.outlet.* = feed_flash.inlet.*
feed_flash.outlet_vap.* = vap_mixer.inlet[1].*
feed_flash.outlet_liq.* = liq_mixer.inlet[1].*
! liquid down the column
liq_mixer.inlet[2].* = stage[1].l_out.*
liq_mixer.outlet.* = stage[2].l_in.*
stage[2:7].l_out.* = stage[3:8].l_in.*
stage[8].l_out.* = sump.inlet.*
! reboiler
sump.outlet.* = reboiler.inlet.*
reboiler.outlet.* = reboiler_flash.inlet.*
! vapor up the column
reboiler_flash.outlet_vap.* = stage[8].v_in.*
stage[3:8].v_out.* = stage[2:7].v_in.*
vap_mixer.inlet[2].* = stage[2].v_out.*
vap_mixer.outlet.* = stage[1].v_in.*
! condenser
stage[1].v_out.* = condenser.inlet.*
condenser.outlet.* = drum.inlet.*
drum.outlet_liq.* = reflux.inlet.*
reflux.outlet[2].* = stage[1].l_in.*
! mass and massflow meters
sump.reserve.* = sump_mass.acc.*
feed.* = feed_massflow.stream.*
drum.outlet_vap.* = cleu_massflow.stream.*
reboiler_flash.outlet_liq.* = btms_massflow.stream.*
! stream pressures
strm_p = stage[1].v_out.p
strm_p = stage[2:8].l_out.p
strm_p = stage[3:8].v_out.p
! feed and stage pressures
fd_p = stage[1:8].l_res.p
End Connections
Model custom
Parameters
fd_t = 370.0 ! K
fd_p = 3.11e6 ! Pa
fd_c2h4 = 0.28 ! mol%
fd_c3h6 = 0.6184 ! mol%
fd_c3h8 = 0.0916 ! mol%
fd_h2 = 0.01 ! mol%
strm_p = fd_p ! Pa
fd_ndot = 1.0
End Parameters
Variables
fd_mdot = 0.395 ! kg/sec
End Variables
Connections
fd_t = feed.t
fd_p = feed.p
fd_c2h4 = feed.x[1]
fd_c3h6 = feed.x[2]
fd_c3h8 = feed.x[3]
fd_h2 = feed.x[4]
fd_mdot = feed_massflow.mdot
fd_ndot = feed.ndot
End Connections
Intermediates
End Intermediates
Equations
End Equations
End Model