Difference between revisions of "Batch distillation problem (TACO)"

# ----------------------------------------------------------------
# Batch distillation problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
#
# Source: M.Diehl/H.G.Bock/E.Kostina'06
# ----------------------------------------------------------------
include OptimalControl.mod;
 
# time and free end-time
 
var t;
var tf := 2.5, >= 0.5, <= 10.0;
 
# constant parameters
 
param Pur := 0.99;		# percent
param V := 100.0;		# mol/h
param m := 0.1;			# mol
param mC := 0.1;		# mol
 
# control
 
var R := 8.0, >= 0.0, <= 15.0;
let R.type := "u1";
let R.scale := 0.1;
 
# differential states
 
param NDIS := 5;		# PDE discretization points
 
var M0;
var x{0..NDIS+1};
var MD;
var xD;
var alpha;
 
 
# algebraic expressions eliminated by AMPL's presolve
 
var L = R/(1+R)*V;
var y{i in 0..NDIS} = (1+alpha)*x[i]/(alpha+x[i]);
 
var dot0 = ( L*x[1] - V*y[0] + (V-L)*x[0] ) / M0;
var dot{i in 1..NDIS} = ( L*x[i+1] - V*y[i] + V*y[i-1] - L*x[i] )/m;
var dotNDISp1 = V/mC * (-x[NDIS+1] + y[NDIS]);
 
 
# objective function
 
minimize Compromise:
	eval (t - MD, tf);
 
 
# terminal constraint
 
subject to Purity_Constraint:
	eval(xD, tf) >= Pur;
 
 
# ODE system
 
subject to ODE_M0:
	diff(M0, t) = -V+L;
 
subject to ODE_x_0:
	diff(x[0], t) = dot0;
 
subject to ODE_x{i in 1..NDIS}:
	diff(x[i], t) = dot[i];
 
subject to ODE_x_NDISp1:
	diff(x[NDIS+1], t) = dotNDISp1;
 
subject to ODE_MD:
	diff(MD, t) = V-L;
 
subject to ODE_xD:
	diff(xD, t) = (V-L) * (x[NDIS] - xD)/MD;
 
subject to ODE_alpha:
	diff(alpha, t) = 0.0;
 
 
# Initial value constraints
 
subject to IVC_M0:
	eval(M0, 0) = 100.0;
 
subject to IVC_x_0:
	eval(x[0], 0) = 0.5;
 
subject to IVC_x{i in 1..NDIS+1}:
	eval(x[i], 0) = 1;
 
subject to IVC_MD:
	eval(MD, 0) = 0.1;
 
subject to IVC_xD:
	eval(xD, 0) = 1;
 
subject to IVC_alpha:
	eval(alpha, 0) = 0.2;
 
option solver ...;
 
solve;