## Direct Current (DC) Motor

This DC motor model includes the dynamics for the motor shaft and a load attached to the shaft. The rotor and shaft are related by a spring constant and mechanical damping associated with the drive.

### Model

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

! DC Electric Motor
Model motor

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 (friction: bm * dth)

jl = 1000*jm    ! load inertia (1000 times the rotor)
bl = 1.0e-3     ! load damping (friction)
k = 1.0e2       ! spring constant for motor shaft to load
b = 0.1         ! spring damping for motor shaft to load
End Parameters

Variables
i     = 0       ! motor electrical current (amps)
dth_m = 0       ! rotor angular velocity, omega (radians/sec)
th_m  = 0       ! rotor angle, theta (radians)
dth_l = 0       ! wheel angular velocity (rad/sec)
th_l  = 0       ! wheel angle (radians)
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

dth_m = $th_m dth_l =$th_l
End Equations

End Model