## 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
! 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