Electric car problem (AMPL)

This page contains a discretized version of the MIOCP Electric Car in AMPL format. You should be aware of the comments regarding discretization made on the 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,

# ----------------------------------------------------
# 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];

a data file ampl_car.dat,

# ----------------------------------------------------
# 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;

and a running script ampl_car.run,

# ----------------------------------------------------
# Electric car problem with collocation
# (c) Sebastian Sager, Frederic Messine 2013
# ----------------------------------------------------
 
model ampl_car.mod;
data ampl_car.dat;
 
options solver ipopt;
solve;