Simplified Electric Vehicle

The principal input to the model is the voltage to the motor. Motor parameters include resistance (ohm), motor inductance (henrys), back emf constant (volt-sec/rad), torque constant (N-m/a), rotor inertia (kg m^2), and mechanical damping. The automotive parameters include vehicle inertia, vehicle damping (friction), transmission dynamics, gearing ratios, and a simplified model of tire friction on the paved surface. The electric vehicle models tracks system including motor electrical current (amps), rotor angular velocity (radians/sec), rotor angle (radians), wheel angular velocity (rad/sec), wheel angle (radians), vehicle velocity (m/sec), and distance travelled (m).



! APMonitor Modeling Language
! http://www.apmonitor.com

! Electric Vehicle Model
Model car

  Parameters
    ! motor parameters (dc motor)
    v   = 36        ! input voltage to the motor (volts)
    rm  = 0.1       ! motor resistance (ohm)
    lm  = 0.01      ! motor inductance (henrys)
    kb  = 6.5e-4    ! back emf constant (volt-sec/rad)
    kt  = 0.1       ! torque constant (N-m/a)
    jm  = 1.0e-4    ! rotor inertia (kg m^2)
    bm  = 1.0e-5    ! mechanical damping (linear model of friction: bm * dth)

    ! automobile parameters
    jl = 1000*jm    ! vehicle inertia (1000 times the rotor)
    bl = 1.0e-3     ! vehicle damping (friction)
    k = 1.0e2       ! spring constant for connection rotor/drive shaft
    b = 0.1         ! spring damping for connection rotor/drive shaft
    rl = 0.005      ! gearing ratio between motor and tire (meters travelled
                    !  per radian of motor rotation)
    tau = 2         ! time constant of a lag between motor torque and car
                    !   velocity.  this lag is a simplified model of the power
                    !   train. (sec)
  End Parameters

  Variables
    i     = 0       ! motor electrical current (amps)
    dth_m = 0       ! rotor angular velocity sometimes called omega (radians/sec)
    th_m  = 0       ! rotor angle, theta (radians)
    dth_l = 0       ! wheel angular velocity (rad/sec)
    th_l  = 0       ! wheel angle (radians)
    dth_v = 0       ! vehicle velocity (m/sec)
    th_v  = 0       ! distance travelled (m)
  End Variables

  Equations
    lm*$i - v = -rm*i -    kb *$th_m
    jm*$dth_m =  kt*i - (bm+b)*$th_m - k*th_m +     b *$th_l + k*th_l
    jl*$dth_l =             b *$th_m + k*th_m - (b+bl)*$th_l - k*th_l

    tau * $dth_v = rl * dth_l - dth_v

    dth_m = $th_m
    dth_l = $th_l 
    dth_v = $th_v
  End Equations

End Model