Supermarket refrigeration system (optimica)

// Supermarket benchmark problem from the HYCON NoE.
// (c) Sebastian Sager, 2005-2009
// More info on http://mintoc.de/index.php/Supermarket_refrigeration_system
 
package supermarket_pack
 
  optimization supermarket_opt (objective = cost(finalTime),
                         startTime = 0,
                         finalTime=1)
 
    // Parameters
    parameter Real Q_airload = 3000.00;             
    parameter Real m_ref = 0.20;             
    parameter Real M_goods=200.00;
    parameter Real Cp_goods=1000.00;
    parameter Real UA_goods=300.00;
    parameter Real M_wall=260.00;
    parameter Real Cp_wall=385.00;
    parameter Real UA_air=500.00;
    parameter Real M_air=50.00;
    parameter Real Cp_air=1000.00;
    parameter Real UA_wall=4000.00;
    parameter Real t_fill=40.00;
    parameter Real T_sh=10.00;
    parameter Real M_ref=1.00;
    parameter Real V_suc=5.00;
    parameter Real V_sl=0.08;             
    parameter Real eta_vol=0.81;
    parameter Real tf(free=true,min=650,max=750)=650;
 
   // Differential states
    Real x0;
    Real x1;
    Real x2;
    Real x3;
    Real x4;
    Real x5;
    Real x6;
    Real x7;
    Real x8;
    Real cost(start=0);
 
    // The control signal
    input Real u0(free=true,min=0,max=1,initialGuess=0.5);
    input Real u1(free=true,min=0,max=1,initialGuess=0.5);
    input Real u2(free=true,min=0,max=1,initialGuess=1);
 
  equation
    der(x0) = ((1.0/(V_suc*(-0.0329*x0*x0*x0+0.2161*x0*x0-0.4742*x0+5.4817)))*((UA_wall/(M_ref*((0.0217*x0*x0-0.1704*x0+2.2988)*10^5)))*(x4*(x2-(-4.3544*x0*x0+29.224*x0-51.2005))+x8*(x6-(-4.3544*x0*x0+29.224*x0-51.2005)))+M_ref-eta_vol*V_sl*0.5*(u2)*(4.6073*x0+0.3798)))*tf;
    der(x1) =(-UA_goods*(x1-x3)/(M_goods*Cp_goods))*tf;
    der(x2)=((UA_air*(x3-x2)-(UA_wall/M_ref)*x4*(x2-(-4.3544*x0*x0+29.224*x0-51.2005)))/(M_wall*Cp_wall))*tf;
    der(x3)=((UA_goods*(x1-x3)+Q_airload-UA_air*(x3-x2))/(M_air*Cp_air))*tf;
    der(x4)=(((M_ref-x4)/t_fill)*u0-((UA_wall/(M_ref*((0.0217*x0*x0-0.1704*x0+2.2988)*10^5)))*x4*(x2-(-4.3544*x0*x0+29.224*x0-51.2005)))*(1-u0))*tf;
    der(x5)=(-UA_goods*(x5-x7)/(M_goods*Cp_goods))*tf;
    der(x6)=((UA_air*(x7-x6)-(UA_wall/M_ref)*x8*(x6-(-4.3544*x0*x0+29.224*x0-51.2005)))/(M_wall*Cp_wall))*tf;
    der(x7)=((UA_goods*(x5-x7)+Q_airload-UA_air*(x7-x6))/(M_air*Cp_air))*tf;
    der(x8)=(((M_ref-x8)/t_fill)*u1-((UA_wall/(M_ref*((0.0217*x0*x0-0.1704*x0+2.2988)*10^5)))*x8*(x6-(-4.3544*x0*x0+29.224*x0-51.2005)))*(1-u1))*tf;
    der(cost) = ((-1.0/(((1/*time*/)*tf)))*cost+(1.0/(((1/*time*/))*tf))*((u2)*0.5*eta_vol*V_sl*((0.0265*x0*x0*x0-0.4346*x0*x0+2.4923*x0+1.2189)*10^5)))*tf;
//    der(cost) = 1.0 / 650 * (((u2)*0.5*eta_vol*V_sl*((0.0265*x0*x0*x0-0.4346*x0*x0+2.4923*x0+1.2189)*10^5)))*tf;
 
  constraint
    x3>=2.0;
    x3<=5.0;
    x7>=2.0;
    x7<=5.0;
    x0<=1.7;
    cost(startTime)=0.0;
    x0(finalTime)=x0(startTime);
    x1(finalTime)=x1(startTime);
    x2(finalTime)=x2(startTime);
    x3(finalTime)=x3(startTime);
    x4(finalTime)=x4(startTime);
    x5(finalTime)=x5(startTime);
    x6(finalTime)=x6(startTime);
    x7(finalTime)=x7(startTime);
    x8(finalTime)=x8(startTime);
 
  end supermarket_opt;
 
end supermarket_pack;