Continuously Stirred Tank Reactor (TACO)

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 <bibref>Diehl2001</bibref>. 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 goddart_taco.mod

# ----------------------------------------------------------------
# Goddart's rocket problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
#
# Source: M. Diehl, 2001
# ----------------------------------------------------------------
include OptimalControl.mod;
 
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;

Other Descriptions

Other descriptions of this problem are available in

• Mathematical notation at Continuously Stirred Tank Reactor problem