View source for Electric car problem (AMPL)

This page contains a discretized version of the MIOCP [[Electric Car]] in [http://www.ampl.org AMPL] format. You should be aware of the comments regarding discretization made on the [[:Category:AMPL|AMPL overview]] page. Note that you will need to include two generic [[support AMPL files]], ampl_general.mod and ampl_general.dat.

=== AMPL ===

The model in AMPL code for a fixed control discretization grid with a collocation method. We need a model file ampl_car.mod,
<source lang="AMPL">
# ----------------------------------------------------
# Electric car problem with collocation (implicit Euler)
# (c) Sebastian Sager, Frederic Messine 2013
# ----------------------------------------------------

# Parameters
param mysum;
param mycounter;
param myeta;

param R_bot;
param V_alim;
param R_m;
param K_m;
param L_m;
param r;
param K_r;
param M;
param g;
param K_f;
param rho;
param S;
param C_x;
param T    > 0;
param nt   > 0;
param ntperu > 0;
param dt := T / (nt-1);

set I:= 0..nt;
set U:= 0..nt/ntperu-1;
set UI := 1..ntperu-1;

# Variables
var x {I, 0..3};
var w {I} >= -1, <= 1;

minimize Mayer: x[nt,3];

subject to ODE_current {i in I diff {0}}:
   x[i,0] = x[i-1,0] + dt * ( (w[i-1]*V_alim - R_m*x[i,0] - K_m*x[i,1]) / L_m ) ;

subject to ODE_angularvelocity {i in I diff {0}}:
   x[i,1] = x[i-1,1] + dt * ( K_r*K_r/(M*r*r) * ( K_m * x[i,0] - r/K_r * ( M*g*K_f + 0.5*rho*S*C_x * x[i,1]*x[i,1]*r*r / (K_r*K_r) ) ) ) ;

subject to ODE_position {i in I diff {0}}:
   x[i,2] = x[i-1,2] + dt * ( x[i,1]*r / K_r ) ;

subject to ODE_energyobjective {i in I diff {0}}:
#   x[i,3] = x[i-1,3] + dt * ( w[i-1] * x[i,0] * V_alim + R_bot * w[i-1]*w[i-1]*x[i,0]*x[i,0] ) ;
   x[i,3] = x[i-1,3] + dt * ( w[i-1] * x[i,0] * V_alim + R_bot * x[i,0]*x[i,0] ) ;

subject to initialvalues {j in {0..3}}:
   x[0,j] = 0;

subject to boundedcurrentU {i in I}:
   x[i,0] <= 150;

subject to boundedcurrentL {i in I}:
   x[i,0] >= -150;

subject to endvalues:
   x[nt,2] = 100;

subject to couple_controls {j in U, i in UI}:
   w[j*ntperu+i] = w[j*ntperu];

subject to couple_last_control:
   w[nt] = w[nt-1];
</source>
a data file ampl_car.dat,
<source lang="AMPL">
# ----------------------------------------------------
# Electric car problem with collocation
# (c) Sebastian Sager, Frederic Messine 2013
# ----------------------------------------------------

# Algorithmic parameters
param nt := 1000;
param ntperu := 1;

# Problem parameters
param R_bot := 0.05;
param V_alim := 150;
param R_m := 0.03;
param K_m := 0.27;
param L_m := 0.05;
param r := 0.33;
param K_r := 10;
param M := 250;
param g := 9.81;
param K_f := 0.03;
param rho := 1.293;
param S := 2;
param C_x := 0.4;
param T := 10.0;
</source>
and a running script ampl_car.run,
<source lang="AMPL">
# ----------------------------------------------------
# Electric car problem with collocation
# (c) Sebastian Sager, Frederic Messine 2013
# ----------------------------------------------------

model ampl_car.mod;
data ampl_car.dat;

options solver ipopt;
solve;

</source>


[[Category:AMPL]]