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APMonitor Modeling Language

https://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

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• 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).

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 sometimes called omega (radians/sec)
• rotor angle, theta (radians)
• wheel angular velocity (rad/sec)
• wheel angle (radians)
• vehicle velocity (m/sec)
• distance travelled (m)
• electric.apm