Question

D.C. motor is shown below, where the inductance L and the resistance R model the armature circuit. The voltage V_brepresents the back-emf which is proportional to dθ/dt via K_f. The torque T generated by the motor is proportional to the i via a constant K_t. In this application, let the constants K_t = K_f. The inertia Jrepresents the combined inertia of the motor and load. The viscous friction acting on the output shaft is b. Attached to the shaft is a N1:N2 gear train that decreases the output velocity. There is no load on the motor. (Note: DO NOT neglect the electrical characteristics of the motor with relationship to the mechanical characteristics.)

A. Given the diagram shown, find the transfer function Gp(s) between the input voltage V, and the angular position θ out after the gear train of the output shaft in terms of the Laplace variable S.

B. For the values L=0.25H, R=5Ohm, J=0.15 Kg m², b= 0.4 N m s and K_t = K_f = 0.1, N1=30, N2= 600 . Find the time domain response c(t) if the input is a unit step function.

NI:N2 out Vb input final be Rotor where K K

Answer 1

pcs) s乜し~a@e-bL) s+ bere")