A DC motor produces a torque that is proportional to the current through the windings of the motor. Neglecting friction, the net torque on the motor, therefore, is this torque minus the torque applied by whatever load is connected to the motor. Newton’s second law (the rotational version) gives
k_T i(t) - x(t) = I [d/dt] ω(t), where k_T is the motor torque constant, i(t) is the current at time t, x(t) is the torque applied by the load at time t, I is the moment of inertia of the motor, and ω(t) is the angular velocity of the motor.
(a) Assuming the motor is initially at rest, rewrite above equation as an integral equation.
(b) Assuming that both x and i are inputs and ω is an output, construct an actor model (a block diagram) that models this motor. You should use only primitive actors such as integrators and basic arithmetic actors such as scale and adder.