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.
! 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