## 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