Batch distillation problem (TACO)
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This page contains a model of the Batch distillation problem in AMPL format, making use of the TACO toolkit for AMPL control optimization extensions. The original model can be found in <bibref>Diehl2006c</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 batchdist_taco.mod
# ---------------------------------------------------------------- # 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;
Other Descriptions
Other descriptions of this problem are available in
- Mathematical notation at Batch distillation problem
References
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