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
! http://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 (linear model of friction: bm * dth)

    ! load parameters
    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 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)
  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