<!DOCTYPE OMNotebook>
<Notebook>
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    <TextCell style="Text">
      <Text>&lt;!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0//EN" "http://www.w3.org/TR/REC-html40/strict.dtd">
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&lt;td style="border: none;">
&lt;p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">&lt;span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Examples to the Tutorial &amp;quot;Native Optimization features in OpenModelica&amp;quot; at Modelica Conference 2014&lt;/span>&lt;/p>
&lt;p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">&lt;span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Example Diesel model see:&lt;/span>&lt;/p>
&lt;p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">&lt;span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">M. Sivertsson and L. Eriksson:&lt;/span>&lt;/p>
&lt;p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">&lt;span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Optimal power response of a diesel-electric powertrain. ECOSM’12, Paris, France, 2012&lt;/span>&lt;/p>
&lt;p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">&lt;span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">B. Bachmann, L. Ochel, V. Ruge, M. Gebremedhin,  P. Fritzson,  V. Nezhadali,  L. Eriksson,  and M.  Sivertsson:&lt;/span>&lt;/p>
&lt;p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px;">&lt;span style=" font-family:'Times New Roman'; font-size:12pt; color:#000000;">Parallel  multiple-shooting  and collocation optimization with openmodelica.  International Modelica Conference, 2012&lt;/span>&lt;/p>&lt;/td>&lt;/tr>&lt;/table>&lt;/body>&lt;/html></Text>
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    <GraphCell style="Graph" closed="false">
      <Input>cd("D:/Temp/Tutorial")</Input>
      <Output>"D:/Temp/Tutorial"</Output>
    </GraphCell>
    <GraphCell style="Graph" closed="false">
      <Input>setCommandLineOptions("+g=Optimica")</Input>
      <Output>true</Output>
    </GraphCell>
    <GraphCell style="Graph" closed="false">
      <Input>optimization diesel_model (objective = cost1,
       objectiveIntegrand = cost2)
       

/*output */
output Real cost1 = (w_ice - 0.515309170685596)^2
                      + (p_im - 0.547055854225991)^2
                      + (p_em - 0.381048005791294)^2
                      + (w_tc - 0.271443000537680)^2;
output Real cost2 =dot_m_f;
/* States in the diesel engine model
-----------------------------------------------------------------------------*/
Real w_ice(start=2.4989941562646081e-01, min = 4/state_norm1, max =220/state_norm1, fixed=true);
Real p_im(start=5.0614999999999999e-01, min = 0.8*p_amb/state_norm2, max=2*p_amb/state_norm2, fixed=true);
Real p_em(start=3.3926666666666666e-01, min = p_amb/state_norm3, max=3*p_amb/state_norm3, fixed=true);
Real w_tc(start=6.8099999999999994e-02, min = 300/state_norm4, max=10000/state_norm4, fixed=true);

/* Control inputs
-----------------------------------------------------------------------------*/
input Real u_f(start=0.0, min=0.0, max = 250/control_norm1);
input Real u_wg(start=0.0, min=0.0, max = 1.0);

/* Constants
-----------------------------------------------------------------------------*/
protected
  constant Real pi = 3.141592653589793;
  constant Real p_amb = 1.0111134146341463e+005;
  constant Real T_amb = 2.9846362195121958e+002;
  constant Real gamma_a = 1.3964088397790055e+000;
  constant Real R_a = 2.8700000000000000e+002;
  constant Real cp_a = 1.0110000000000000e+003;
  constant Real cv_a = 7.2400000000000000e+002;
  constant Real p_es = 1.0111134146341463e+005;
  constant Real gamma_e = 1.2734225621414914e+000;
  constant Real R_e = 2.8600000000000000e+002;
  constant Real cp_e = 1.3320000000000000e+003;
  constant Real Hlhv = 4.2900000000000000e+007;
  constant Real AFs = 1.4570000000000000e+001;
  constant Real gamma_cyl = 1.3500000000000001e+000;
  constant Real T_im = 3.0061857317073162e+002;
  constant Real x_r0 = 0.0000000000000000e+000;
  constant Real T_10 = 3.0064178823529403e+002;
  constant Real n_cyl = 6.0000000000000000e+000;
  constant Real V_D = 1.2699999999999999e-002;
  constant Real r_c = 1.7300000000000001e+001;
  constant Real A_wg_eff = 8.8357293382212933e-004;
  constant Real J_genset = 3.5000000000000000e+000;
  constant Real d_pipe = 1.0000000000000001e-001;
  constant Real n_pipe = 2.0000000000000000e+000;
  constant Real l_pipe = 1.0000000000000000e+000;
  constant Real R_c = 4.0000000000000001e-002;
  constant Real V_is = 2.1302555405064521e-002;
  constant Real V_em = 2.0024706650635410e-002;
  constant Real R_t = 4.0000000000000001e-002;
  constant Real J_tc = 1.9777955929704147e-004;
  constant Real state_norm1 = 2.2000000000000000e+002;
  constant Real state_norm2 = 2.0000000000000000e+005;
  constant Real state_norm3 = 3.0000000000000000e+005;
  constant Real state_norm4 = 1.0000000000000000e+004;
  constant Real control_norm1 = 2.5000000000000000e+002;
  constant Real control_norm2 = 1.0000000000000000e+000;
  constant Real control_norm3 = 2.5400000000000000e+005;
  constant Real Psi_max = 1.4374756793329366e+000;
  constant Real dot_m_c_corr_max = 5.2690636559024850e-001;
  constant Real eta_igch = 6.8768988621327665e-001;
  constant Real c_fr1 = 7.1957840228405290e-001;
  constant Real c_fr2 = -1.4144357053459333e-001;
  constant Real c_fr3 = 3.5904197283929118e-001;
  constant Real eta_sc = 1.0515746242284574e+000;
  constant Real x_cv = 5.7966369236798054e-001;
  constant Real A_t_eff = 9.9877716035454514e-004;
  constant Real eta_c = 5.2227332577901808e-001;
  constant Real eta_t = 6.8522930965034778e-001;
  constant Real eta_vol = 8.9059680994120261e-001;
  constant Real w_fric = 2.4723010996875069e-005;

/* States and controls
-----------------------------------------------------------------------------*/
protected
  Real W_ICE;
  Real P_IM;
  Real P_EM;
  Real W_TC;
  Real U_F;

/* Compressor Massflow
-----------------------------------------------------------------------------*/
  Real Pi_c;
  Real w_tc_corr;
  Real Pi_c_max;
  Real Cm_temp; //must be greater than 0
  Real dot_m_c;
  Real P_c;

/* Cylinder Airflow
-----------------------------------------------------------------------------*/
  Real dot_m_ci;

/* Cylinder Fuelflow
-----------------------------------------------------------------------------*/
  Real dot_m_f;

/* Cylinder Torque
-----------------------------------------------------------------------------*/
  Real eta_ig;
  Real T_pump;
  Real T_ig;
  Real T_fric;
  Real T_ice;

/* Cylinder Temperature Out
-----------------------------------------------------------------------------*/
  Real Pi_e;
  Real q_in;
  Real x_p;
  Real T_eo;

/* Turbine Massflow
-----------------------------------------------------------------------------*/
  Real Pi_t;
  Real Pi_ts_low;
  Real Pi_ts;
  Real Psi_t;
  Real dot_m_t;

/* Turbine Power
-----------------------------------------------------------------------------*/
  Real P_t;

  /* Wastegate Massflow
-----------------------------------------------------------------------------*/
  Real Pi_wg;
  Real Pi_wgs;
  Real Psi_wg;
  Real dot_m_wg;
  Real P_ICE;

equation
  W_ICE = state_norm1*w_ice;
  P_IM = state_norm2*p_im;
  P_EM = state_norm3*p_em;
  W_TC = state_norm4*w_tc;
  U_F = control_norm1*u_f;

  // Compressor Massflow----
  Pi_c = P_IM/p_amb;
  w_tc_corr = state_norm4*w_tc/sqrt(T_amb/T_amb);
  Pi_c_max = (((((w_tc_corr^2)*(R_c^2)*Psi_max)/((2*cp_a*T_amb)))+1)^(gamma_a/(gamma_a-1)));
  Cm_temp = 1-((Pi_c/Pi_c_max)^2); ////Måste vara större en 0
  dot_m_c = (dot_m_c_corr_max*sqrt(Cm_temp))*(p_amb/p_amb)/sqrt(T_amb/T_amb);
  P_c = dot_m_c*cp_a*T_amb*((Pi_c^((gamma_a-1)/gamma_a))-1)/eta_c;

  // Cylinder Airflow------------------------
  dot_m_ci = eta_vol*P_IM*W_ICE*V_D/(4*pi*R_a*T_im);

  // Cylinder Fuelflow---------------------------
  dot_m_f = U_F*W_ICE*n_cyl*(1e-6)/(4*pi);

  // Cylinder Torque---------------------------
  eta_ig = eta_igch*(1-(1/(r_c^(gamma_cyl-1))));
  T_pump = V_D*(P_EM-P_IM);
  T_ig = n_cyl*Hlhv*eta_ig*u_f*control_norm1*(1e-6);
  T_fric = V_D*(10^5)*(c_fr1*((W_ICE*60/(2*pi*1000))^2)+c_fr2*(W_ICE*60/(2*pi*1000))+c_fr3);
  T_ice = (T_ig-T_fric-T_pump)/(4*pi);

  // Cylinder Temperature Out---------------------------
  Pi_e = P_EM/P_IM;
  q_in = dot_m_f*Hlhv/(dot_m_f+dot_m_ci);
  x_p = 1+q_in*x_cv/(cv_a*T_im*(r_c^(gamma_a-1)));
  T_eo = eta_sc*(Pi_e^(1-1/gamma_a))*(r_c^(1-gamma_a))*(x_p^(1/gamma_a-1))*(q_in*((1-x_cv)/cp_a+x_cv/cv_a)+T_im*(r_c^(gamma_a-1)));

  // Turbine Massflow-------
  Pi_t = p_es/P_EM;
  Pi_ts_low = ((2/(gamma_e+1))^(gamma_e/(gamma_e-1)));
  Pi_ts = sqrt(Pi_t);
  Psi_t = sqrt((2*gamma_e/(gamma_e-1))*((Pi_ts^(2/gamma_e))-(Pi_ts^((gamma_e+1)/gamma_e))));
  dot_m_t = P_EM*Psi_t*A_t_eff/(sqrt(T_eo*R_e));

  // Turbine Power--------
  P_t = dot_m_t*cp_e*T_eo*eta_t*(1-(Pi_t^((gamma_e-1)/gamma_e)));

  // Wastegate Massflow-------------------------------------
  Pi_wg = p_amb/P_EM;
  Pi_wgs = Pi_wg;
  Psi_wg = sqrt(2*gamma_e/(gamma_e-1)*((Pi_wgs^(2/gamma_e))-(Pi_wgs^((gamma_e+1)/gamma_e))));
  dot_m_wg = P_EM*Psi_wg*A_wg_eff*u_wg/(sqrt(T_eo*R_e));

  // Limit equations---------------------------
  P_ICE = T_ice*W_ICE/control_norm3;

  // DIFFERENTIAL EQUATION---------------------
  der(w_ice) = 0.0012987012987013*(T_ice);
  der(p_im) = 20.2505119361145*((0.526906365590249*sqrt(Cm_temp))-dot_m_ci);
  der(p_em) = 0.0476078551344513*(T_eo*(dot_m_ci+dot_m_f-dot_m_t-dot_m_wg));
  der(w_tc) = 0.0001*((P_t-P_c)/(0.000197779559297041*W_TC)-2.47230109968751E-005*W_TC*W_TC);
 
end diesel_model;</Input>
      <Output>{diesel_model}</Output>
    </GraphCell>
    <GraphCell style="Graph" closed="false">
      <Input>optimize(diesel_model, stopTime=0.5, numberOfIntervals=100,tolerance=1e-10, simflags="-lv LOG_IPOPT")</Input>
      <Output>record SimulationResult
    resultFile = "diesel_model_res.mat",
    messages = "Optimizer Variables
========================================================
State[0]:w_tc(start = 0.0681, nominal = 1, min = 0.03, max = 1, init = 0.0681)
State[1]:p_em(start = 0.339267, nominal = 1.01111, min = 0.337038, max = 1.01111, init = 0.339267)
State[2]:p_im(start = 0.50615, nominal = 1.01111, min = 0.404445, max = 1.01111, init = 0.50615)
State[3]:w_ice(start = 0.249899, nominal = 1, min = 0.0181818, max = 1, init = 0.249899)
Input[4]:u_f(start = 0, nominal = 1, min = 0, max = 1)
Input[5]:u_wg(start = 0, nominal = 1, min = 0, max = 1)
--------------------------------------------------------
========================================================

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit http://projects.coin-or.org/Ipopt
******************************************************************************

NOTE: You are using Ipopt by default with the MUMPS linear solver.
      Other linear solvers might be more efficient (see Ipopt documentation).


This is Ipopt version 3.11.3, running with linear solver mumps.

Number of nonzeros in equality constraint Jacobian...:     8700
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:     6003

Total number of variables............................:     1802
                     variables with only lower bounds:        0
                variables with lower and upper bounds:     1802
                     variables with only upper bounds:        0
Total number of equality constraints.................:     1200
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0 1.2555574e-001 2.79e-002 4.82e-003   0.0 0.00e+000    -  0.00e+000 0.00e+000   0
   1 7.9508285e-002 4.22e-004 4.63e-003  -4.9 7.43e-002    -  2.01e-001 1.00e+000h  1
   2 3.5896458e-002 1.70e-003 5.27e-003  -4.3 1.10e+000    -  4.90e-001 2.64e-001h  1
   3 6.3727027e-003 6.01e-003 9.95e-003  -4.4 5.65e-001    -  5.62e-001 1.00e+000h  1
   4 3.0206144e-003 1.36e-003 1.71e-003  -4.7 3.44e-001    -  6.58e-001 8.84e-001h  1
   5 2.1687231e-003 6.39e-004 1.57e-003  -5.5 4.48e-001    -  7.15e-001 1.00e+000h  1
   6 1.8062569e-003 2.39e-004 4.68e-004  -5.8 3.43e-001    -  7.57e-001 1.00e+000h  1
   7 1.5323621e-003 7.32e-005 2.76e-005  -6.2 1.02e-001  -4.0 9.94e-001 1.00e+000h  1
   8 1.3726647e-003 1.97e-005 1.09e-005  -7.5 3.97e-002  -3.6 9.97e-001 1.00e+000h  1
   9 1.2674300e-003 5.47e-005 1.10e-005  -8.1 9.21e-002  -4.1 1.00e+000 9.99e-001h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  10 1.2204377e-003 2.19e-004 1.64e-005  -8.9 2.86e-001  -4.5 7.56e-001 6.11e-001h  1
  11 1.2122403e-003 7.23e-005 1.12e-005  -7.2 1.44e-001  -4.1 1.00e+000 9.49e-001h  1
  12 1.2201141e-003 2.05e-004 7.59e-006  -6.6 1.99e-001  -4.6 1.00e+000 8.58e-001h  1
  13 1.1991327e-003 1.47e-004 1.65e-005  -6.7 3.87e-001  -5.1 1.00e+000 4.78e-001h  1
  14 1.1652186e-003 8.36e-005 5.38e-006  -7.2 1.14e-001  -4.6 1.00e+000 1.00e+000h  1
  15 1.1453923e-003 1.81e-004 5.07e-006  -7.5 1.94e-001  -5.1 7.16e-001 7.84e-001h  1
  16 1.1480162e-003 3.18e-004 1.33e-005  -6.9 4.20e-001  -5.6 1.00e+000 4.88e-001h  1
  17 1.1403294e-003 1.61e-004 2.93e-006  -7.1 3.42e-001    -  1.00e+000 9.81e-001h  1
  18 1.1353000e-003 1.02e-004 1.62e-006  -7.2 2.73e-001    -  1.00e+000 1.00e+000h  1
  19 1.1311580e-003 1.15e-004 2.18e-006  -7.3 2.78e-001    -  1.00e+000 1.00e+000h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  20 1.1285649e-003 6.68e-005 1.79e-006  -7.4 3.30e-001    -  1.00e+000 1.00e+000h  1
  21 1.1258105e-003 9.23e-005 4.46e-006  -7.5 4.59e-001    -  1.00e+000 1.00e+000h  1
  22 1.1224668e-003 7.87e-005 1.30e-006  -7.6 3.31e-001    -  1.00e+000 1.00e+000h  1
  23 1.1213293e-003 5.21e-005 1.93e-006  -7.7 3.99e-001    -  1.00e+000 1.00e+000h  1
  24 1.1185586e-003 5.94e-005 1.23e-006  -7.9 2.09e-001    -  1.00e+000 1.00e+000h  1
  25 1.1168160e-003 7.31e-005 2.50e-006  -8.0 4.81e-001    -  1.00e+000 1.00e+000h  1
  26 1.1153408e-003 2.33e-005 3.50e-007  -8.2 1.94e-001    -  1.00e+000 1.00e+000h  1
  27 1.1145168e-003 4.06e-005 1.34e-006  -8.3 3.19e-001    -  1.00e+000 1.00e+000h  1
  28 1.1137720e-003 8.16e-006 5.43e-008  -8.4 1.87e-001    -  1.00e+000 1.00e+000h  1
  29 1.1129362e-003 1.45e-005 6.90e-007  -8.6 2.62e-001    -  9.71e-001 1.00e+000h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
  30 1.1125932e-003 1.17e-005 2.36e-007  -8.7 1.97e-001    -  1.00e+000 1.00e+000h  1
  31 1.1120786e-003 1.02e-005 7.14e-007  -9.0 1.14e-001    -  1.00e+000 1.00e+000h  1
  32 1.1118009e-003 7.57e-006 1.39e-007  -9.4 1.23e-001    -  1.00e+000 1.00e+000h  1
  33 1.1116575e-003 5.20e-006 2.79e-008  -9.8 1.54e-001    -  1.00e+000 1.00e+000h  1
  34 1.1115664e-003 1.16e-006 2.05e-008 -10.9 4.10e-002    -  9.96e-001 1.00e+000h  1
  35 1.1115646e-003 8.36e-008 1.50e-009 -11.0 1.01e-002    -  1.00e+000 1.00e+000h  1
  36 1.1115646e-003 5.66e-009 3.51e-011 -11.0 1.73e-003    -  1.00e+000 1.00e+000h  1
  37 1.1115646e-003 3.27e-011 8.70e-013 -11.0 1.60e-004    -  1.00e+000 1.00e+000h  1

Number of Iterations....: 37

                                   (scaled)                 (unscaled)
Objective...............:  1.1115645525613652e-003   1.1115645525613652e-003
Dual infeasibility......:  8.6998661373553892e-013   8.6998661373553892e-013
Constraint violation....:  3.2684965844964609e-011   3.2684965844964609e-011
Complementarity.........:  1.0006390781170692e-011   1.0006390781170692e-011
Overall NLP error.......:  3.2684965844964609e-011   3.2684965844964609e-011


Number of objective function evaluations             = 38
Number of objective gradient evaluations             = 38
Number of equality constraint evaluations            = 38
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 38
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 37
Total CPU secs in IPOPT (w/o function evaluations)   =      0.794
Total CPU secs in NLP function evaluations           =      4.175

EXIT: Optimal Solution Found.
"
end SimulationResult;</Output>
    </GraphCell>
    <GraphCell style="Graph" closed="false">
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      <Input>plot({w_ice,p_im,p_em,w_tc})</Input>
      <Output>[done]</Output>
    </GraphCell>
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Color="4278190335"/>
      </OMCPlot>
      <Input>plot({u_f,u_wg})</Input>
      <Output>[done]</Output>
    </GraphCell>
  </GroupCell>
</Notebook>
