Difference between revisions of "Continuously Stirred Tank Reactor (TACO)"
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| − | This page contains a model of the [[Continuously Stirred Tank Reactor problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. The original model can e.g. be found in < | + | This page contains a model of the [[Continuously Stirred Tank Reactor problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions. The original model can e.g. be found in <bib id="Diehl2001" />. |
Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod. | Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod. | ||
To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions. | To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions. | ||
| Line 5: | Line 5: | ||
=== AMPL === | === AMPL === | ||
| − | This is the source file | + | This is the source file cstr_taco.mod |
<source lang="AMPL"> | <source lang="AMPL"> | ||
# ---------------------------------------------------------------- | # ---------------------------------------------------------------- | ||
| − | # | + | # Continuously stirred tank reactor using AMPL and TACO |
# (c) Christian Kirches, Sven Leyffer | # (c) Christian Kirches, Sven Leyffer | ||
# | # | ||
# Source: M. Diehl, 2001 | # Source: M. Diehl, 2001 | ||
# ---------------------------------------------------------------- | # ---------------------------------------------------------------- | ||
| − | |||
| − | |||
include OptimalControl.mod; | include OptimalControl.mod; | ||
| Line 126: | Line 124: | ||
</source> | </source> | ||
| − | == | + | == References == |
| − | + | ||
| − | + | ||
| − | + | <biblist /> | |
[[Category:AMPL/TACO]] | [[Category:AMPL/TACO]] | ||
Latest revision as of 09:13, 24 July 2016
This page contains a model of the Continuously Stirred Tank Reactor problem in AMPL format, making use of the TACO toolkit for AMPL control optimization extensions. The original model can e.g. be found in [Diehl2001]Author: M. Diehl
School: Universit\"at Heidelberg
Title: Real-Time Optimization for Large Scale Nonlinear Processes
Url: http://www.ub.uni-heidelberg.de/archiv/1659/
Year: 2001
.
Note that you will need to include a generic AMPL/TACO support file, OptimalControl.mod.
To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.
AMPL
This is the source file cstr_taco.mod
# ---------------------------------------------------------------- # Continuously stirred tank reactor using AMPL and TACO # (c) Christian Kirches, Sven Leyffer # # Source: M. Diehl, 2001 # ---------------------------------------------------------------- include OptimalControl.mod; # time and fixed end time [in s] var t; var tf := 1500.0, >= 1500, <= 1500; # molar concentration of species A [mol/l] var cA := 2.14, >= -0.02, <= 6.0; # molar concentration of species B [mol/l] var cB := 1.09, >= -0.02, <= 4.0; # reactor temperature [degrees Celsius] var Tr := 114.2, >= 50.0, <= 160.0; # jacket temperature [degrees Celsius] var Tj := 112.9, >= 50.0, <= 160.0; # feed flow control [1/h] var ff := 14.19, >= 3.0, <= 35.0; let ff.type := "u0"; # cooling rate control [kJ/h] var cr := -1113.5, >= -9000.0, <= 0.0; let cr.type := "u0"; # pre-set deviation of initial state from steady state # set this to something different from 1.0 param alpha := 0.8; # various chemistry parameters param k10 := 1.287E+12; param k20 := 1.287E+12; param k30 := 9.043E+09; param cA0 := 5.1; param E1 := -9758.3; param E2 := -9758.3; param E3 := -8560.0; param theta0 := 104.9; param rho := 0.9342; param Cp := 3.01; param H1 := 4.2; param H2 := -11.0; param H3 := -41.85; param kw := 4032.0; param AR := 0.215; param VR := 10.0; param mK := 5.0; param CPK := 2.0; # steady state values param cAs := 2.14021053017; param cBs := 1.09030436131; param theta_s := 1.14191084421E+02; param theta_Ks := 1.12906592910E+02; param FFs := 14.19; param Qdot_Ks := -1113.5; # objective weights param Q11 := sqrt (0.2); param Q22 := sqrt (1.0); param Q33 := sqrt (0.5); param Q44 := sqrt (0.2); param R11 := sqrt (0.5); param R22 := sqrt (5.0E-7); # least-squares deviation from steady-state minimize Deviation: integral ( ((cA - cAs)*Q11)^2 + ((cB - cBs)*Q22)^2 + ((Tr - theta_s)*Q33)^2 + ((Tj - theta_Ks)*Q44)^2 + ((ff - FFs)*R11)^2 + ((cr - Qdot_Ks)*R22)^2, tf ); let Deviation.scale := 100.0; var k1 = (k10*exp(E1/(273.15+Tr))); var k2 = (k20*exp(E2/(273.15+Tr))); var k3 = (k30*exp(E3/(273.15+Tr))); # dynamics subject to ODE_cA: diff(cA,t) = (1.0/3600.0) * (ff*(cA0 - cA) - k1*cA - k3*cA^2); ODE_cB: diff(cB,t) = (1.0/3600.0) * (- ff*cB + k1*cA - k2*cB); ODE_Tr: diff(Tr,t) = (1.0/3600.0) * ( ff * (theta0 - Tr) - 1.0/(rho*Cp) * (k1*cA*H1 + k2*cB*H2 + k3*cA^2*H3) + kw*AR / (rho*Cp*VR) * (Tj - Tr) ); ODE_Tj: diff(Tj,t) = (1.0/3600.0) * ( 1.0/(mK*CPK) * (cr + kw*AR * (Tr - Tj)) ); # initial value constraint IVC_cA: eval(cA,0) = (1-alpha)*cAs; let IVC_cA.type := "dpc"; IVC_cB: eval(cB,0) = (1-alpha)*cBs; let IVC_cB.type := "dpc"; IVC_Tr: eval(Tr,0) = alpha*85.0 + (1-alpha)*theta_s; let IVC_Tr.type := "dpc"; IVC_Tj: eval(Tj,0) = alpha*85.0 + (1-alpha)*theta_Ks; let IVC_Tj.type := "dpc"; option solver ...; solve;
References
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